Critical BCVA Threshold and Refractive Error Modulation for Fixation Instability in Strabismic Amblyopia: Revealed by Eye-Tracking and GAM Modeling

Critical BCVA Threshold and Refractive Error Modulation for Fixation Instability in Strabismic Amblyopia: Revealed by Eye-Tracking and GAM Modeling | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article Critical BCVA Threshold and Refractive Error Modulation for Fixation Instability in Strabismic Amblyopia: Revealed by Eye-Tracking and GAM Modeling Xin Xiao, Lu Pan, Meng Ru, Yuxing Huang, Wuqiang Luo, Lili Li, and 7 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9490101/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 4 You are reading this latest preprint version Abstract Purpose To determine the critical best-corrected visual acuity (BCVA) threshold associated with binocular fixation instability in children with strabismic amblyopia, and to evaluate the modulatory effect of refractive error on this sensory–motor coupling using high-resolution eye tracking and nonlinear modeling. Methods In this multicenter case-control study, 536 children with amblyopia and 159 sex-matched controls were enrolled from the China Amblyopia Behavior Cohort (CABC, 2024–2025). Binocular fixation stability (primary outcome: targeting displacement [TD]) was measured with a 133 Hz Tobii Eye Tracker 4. LOESS smoothing and generalized additive models (GAMs) were applied to characterize nonlinear BCVA–TD relationships. Tensor product interactions tested the moderating effect of spherical equivalent (SE). Results All amblyopia subtypes exhibited significantly greater fixation instability compared with controls (all P < 0.001). A nonlinear BCVA–TD relationship was observed exclusively in strabismic amblyopia, with fixation instability increasing sharply beyond a BCVA threshold of 0.321 logMAR (effective degrees of freedom, 4.46; P = 0.002). Higher SE amplified BCVA-related TD increases in ametropic (P = 0.013) and strabismic (P = 0.004) subtypes, demonstrating refractive error modulation of sensory-motor coupling. The interaction model explained 27.9% of TD variance (adjusted R² = 0.251). Conclusions Strabismic amblyopia shows abrupt fixation instability beyond 0.321 logMAR; refractive error exacerbates this in ametropic/strabismic subtypes. Fixation stability should be a routine biomarker, with optimized refractive correction before strabismic BCVA falls below this threshold. Health sciences/Diseases/Eye diseases/Refractive errors Health sciences/Medical research/Epidemiology Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Introduction Amblyopia, a neurodevelopmental disorder affecting 2%–4% of children worldwide, is characterized by reduced best-corrected visual acuity (BCVA) in the absence of structural ocular abnormalities and despite optimal optical correction 1 – 3 . Beyond impairing spatial vision and stereopsis, amblyopia is increasingly recognized as a disorder of oculomotor control. Binocular fixation instability—quantified as targeting displacement (TD) during sustained gaze—has emerged as a key biomarker of sensory–motor dysfunction 4 – 6 . Importantly, fixation instability manifests in a subtype-specific manner: strabismic amblyopia is associated with excessive fixation drift due to ocular misalignment, while anisometropic amblyopia shows a progressive increase in TD with declining acuity 7 , 8 . Such instability exacerbates visual blur, impedes information acquisition, and correlates strongly with poor stereopsis and reading performance 5 , 9 , underscoring its clinical relevance for prognosis and rehabilitation 10 . Despite these insights, several knowledge gaps remain. First, most prior studies have relied on monocular recordings 6 , 9 , 11 , thereby neglecting natural binocular viewing conditions in which interocular interactions strongly influence fixation control 12 . Second, the relationship between BCVA and fixation instability has often been modeled as linear 13 , 14 , overlooking potential threshold effects suggested in strabismic amblyopia 4 . Third, the role of refractive error, particularly spherical equivalent (SE), as a moderator of sensory–motor coupling remains poorly understood. Evidence indicates that uncorrected refractive error alters microsaccade dynamics and spatial processing 15 , 16 , but whether SE interacts with BCVA to drive fixation collapse in different amblyopia subtypes is unknown. To address these gaps, we leveraged data from the China Amblyopia Behavior Cohort (CABC) to investigate binocular fixation stability using high-resolution eye-tracking. We applied generalized additive models (GAMs) to: (1) identify a critical BCVA threshold associated with fixation instability in strabismic amblyopia; and (2) test whether refractive error modulates sensory-motor coupling (BCVA–TD association) in a subtype-specific manner. We hypothesized that: BCVA degradation beyond a functional threshold would disproportionately disrupt fixation stability in strabismic amblyopia due to compromised cortical integration of misaligned inputs 7 , 17 ; Higher SE would amplify BCVA-driven TD increases in ametropic and strabismic subtypes by exacerbating optical defocus and neural noise 1 , 16 . Therefore, this study aims to delineate the precise, potentially non-linear, relationship between BCVA and fixation instability under binocular viewing conditions, and to elucidate how refractive error modulates this sensory-motor coupling across different amblyopia subtypes. These findings aim to inform subtype-stratified rehabilitation targeting both sensory and motor deficits. Methods 1. Study Design and Participants This multicenter case-control study analyzed baseline data from the China Amblyopia Behavior Cohort (CABC, 2024–2025). A total of 536 children with clinically confirmed amblyopia (303 ametropic, 201 anisometropic, 32 strabismic) and 159 sex-matched controls were recruited from three tertiary eye hospitals in Guangxi, Guangdong, and Sichuan, China. Amblyopia subtypes were defined according to the Chinese Ophthalmological Society guidelines 18 : (1) Ametropic amblyopia: Bilateral BCVA reduction with interocular SE difference < 0.75 D; (2) Anisometropic amblyopia: Interocular SE difference ≥ 1.50 D or cylindrical difference ≥ 1.00 D; (3) Strabismic amblyopia: amblyopia associated with manifest strabismus, confirmed by prism cover test (> 8Δ) 19 . Control participants had normal BCVA (logMAR ≤ 0.10 in both eyes), no history of amblyopia, ocular surgery, or neurological disease. Sample size was determined using a priori power analysis (target power 0.90, α = 0.05, effect size f² = 0.05), Specifically, the effect size f² = 0.05 was determined based on relevant literature, indicating a minimum of 335 participants to detect nonlinear effects in GAMs 20 . The study adhered to the Declaration of Helsinki and was approved by the Ethics Committee of the People's Hospital of Guangxi Zhuang Autonomous Region (KY-KJT-2023-285). Written informed consent was obtained from all legal guardians. 2. Ophthalmic Examination Protocol All participants underwent standardized ophthalmic examinations and stereoacuity assessment (Fig. 1 ). BCVA was measured using a standard logarithmic visual acuity chart at 5 m, the result was recorded via the LogMAR scale. Anterior segment and fundus evaluation were examined using slit-lamp biomicroscopy and ophthalmoscopy. Ocular alignment was assessed using prism cover test (strabismus: median 19.69Δ, range from 8.75 ~ 43.75Δ) and fixation behavior assessment. Cycloplegic refraction was performed 30–40 min after instillation of 1% atropine sulfate (three drops at 10-min intervals). SE was calculated as sphere + 0.5 × cylinder. Fine stereoacuity was measured with the Brain Imaging Bio-Stimulation Training System (National Engineering Research Center for Medical Devices, China). Participants, seated 80 cm from the display and wearing polarized glasses, identified the orientation of E-shaped targets (3° × 3°). Fine stereoacuity thresholds were graded logarithmically: grade 0 (2.90), grade 1 (2.60), grade 2 (2.48), grade 3 (2.30), grade 4 (2.00), with higher grades indicating better fine stereoacuity. 3. Binocular Fixation Stability Assessment 3.1 Eye-Tracking System Binocular fixation stability was measured using the Tobii Eye Tracker 4 (Tobii 4C, Sweden), sampling at 133 Hz with average spatial accuracy of 0.5–1.0° and precision of 0.03° RMS. Participants were seated 80 cm from a 23-inch monitor (1920×1080 pixels) in a dimly lit, sound-attenuated room. A nine-point binocular calibration was performed prior to each task, with calibration error required to be < 0.5°. 3.2 Sustained Fixation Task A high-contrast yellow circular target (10° diameter) was presented sequentially at eight peripheral locations (± 5° horizontally and vertically) and centrally. Each stimulus lasted 2 s, with 0.5 s transition intervals. Participants were instructed to maintain fixation while minimizing head movement. Gaze coordinates were recorded in pixels. 3.3 Targeting Displacement (TD) Binocular fixation stability was quantified as TD. TD is calculated as the average offset from the fixation point to the target center per frame, yielding horizontal (Fix_X), vertical (Fix_Y), and average TD values for each trial (Fig. 1 ). Targeting Displacement (TD) Calculated using the formula: TD= \(\:\frac{1}{\text{N}}{\sum\:}_{i=1}^{N}\sqrt{{{\left({x}_{i}-{x}_{c}\right)}^{2}+({y}_{i}-{y}_{c})}^{2}}\) Where (x i , y i ) represents the binocular gaze coordinates for sample i, and (x c , y c ) denotes the coordinates of the target center. This metric is a standard measure of fixation dispersion 21 , 22 . Data segments with an eye tracking loss rate > 20% are excluded from analysis to ensure data quality 23 .TD represents spatial dispersion of binocular gaze points, conceptually similar to the dispersion component of the bivariate contour ellipse area (BCEA). Unlike BCEA, which models a 68–95% probability ellipse based on variance and covariance, TD reflects frame-wise Euclidean deviation and has been widely used in pediatric and low-vision eye-tracking studies. As BCEA requires longer stable fixation intervals, TD was selected for the current design involving brief multi-position fixations. 4. Statistical Modeling of Sensory-Motor Coupling LOESS smoothing (span = 0.75) was used for exploratory visualization of BCVA–TD relationships by subtype. Nonlinear effects were tested using GAMs with thin-plate regression splines: TD ~ s (BCVA, by = subtype) + age + sex + SE + stereoacuity To assess moderation by refractive error, tensor product interactions were modeled: TD ~ ti (BCVA, SE, by = subtype) + covariates Significance of smooth and interaction terms was determined using false discovery rate (FDR)–corrected P values. Threshold identification was using first-derivative analysis of marginal effects. Robustness was validated through bootstrap resampling (n = 1,000) in the strabismic subgroup, 95% CI for effective degrees of freedom (edf), proportion of P < 0.01 resamples were reported. Analyses were conducted in R (version 4.5.1; mgcv package), β coefficients and 95% CIs reported for all models. Results 1. Clinical Characteristics A total of 695 participants were included: 536 children with amblyopia (303 ametropic, 201 anisometropic, 32 strabismic) and 159 controls. Demographic and clinical data are summarized in Table 1 . Significant group differences were observed for age, SE, BCVA, stereoacuity, and fixation stability (all P < 0.001). Children with strabismic amblyopia exhibited the poorest BCVA (median logMAR 0.60) and highest SE (median + 4.8 D). Table 1 Demographic and Clinical Characteristics of Amblyopia Subtypes and Controls Variable Total (N = 695). Ametropic (n = 303) Anisometropic (n = 201) Strabismic (n = 32) Control (159) P value Gender, n (%) 0.760 Boys 339 (48.8) 154 (50.8) 97 (48.3) 14 (43.8) 74 (46.5) Girls 356 (51.2) 149 (49.2) 104 (51.7) 18 (56.2) 85 (53.5) Age, Median (IQR) 6.0 (5.0, 7.0) 6.0 (5.0, 6.0) 6.0 (5.0, 6.0) 6.0 (5.0, 6.0) 7.0 (6.0, 9.0) < 0.001 SE, Median (IQR) 0.6 (0.0, 3.5) 0.9 (-0.2, 3.5) 2.5 (0.4, 4.5) 4.8 (0.9, 6.7) 0.0 (0.0, 0.0) < 0.001 BCVA, Median (IQR) 0.3 (0.2, 0.4) 0.3 (0.2, 0.4) 0.4 (0.2, 0.5) 0.4 (0.3, 0.5) 0.0 (0.0, 0.1) < 0.001 Fine stereopsis Median (IQR) 2.3 (2.0, 2.9) 2.3 (2.0, 2.9) 2.9 (2.3, 2.9) 2.9 (2.6, 2.9) 2.0 (2.0, 2.0) < 0.001 Fix_X Median (IQR) 116.7 (61.8, 216.7) 133.4 (70.7, 233.8) 115.2 (69.9, 197.7) 301.7 (142.0, 643.6) 76.3 (45.4, 154.3) < 0.001 Fix_Y, Median (IQR) 116.4 (75.7, 176.8) 130.0 (81.7, 189.3) 123.0 (82.4, 175.6) 160.0 (111.4, 208.8) 83.3 (59.3, 131.6) < 0.001 Fixation_TD, Median (IQR) 121.4 (72.2, 198.4) 141.1 (81.8, 212.0) 124.9 (81.8, 189.3) 257.9 (143.8, 487.7) 84.9 (58.0, 144.2) < 0.001 Values are presented as median (interquartile range, IQR) or number (percentage). SE = spherical equivalent; BCVA = best-corrected visual acuity; Fix_X = horizontal targeting displacement; Fix_Y = vertical targeting displacement; TD = targeting displacement. P values are from Kruskal–Wallis or χ² tests as appropriate. 2. Subtype-Specific Fixation Instability Binocular fixation instability, quantified as TD, was significantly greater in all amblyopia subtypes compared with controls (all P < 0.001). The magnitude of instability differed by subtype, median TD difference was + 40.3px [95% CI: 25.7–55.7] in ametropic amblyopia, + 32.1px [19.6–45.6] in anisometropic amblyopia, and + 149.3px [92.7–213.5] in strabismic amblyopia respectively (all P < 0.001; Fig. 2 ). The largest effect was observed in strabismic amblyopia, which showed marked deficits in horizontal (Fix_X), vertical (Fix_Y), and mean TD (all P < 0.001 vs. other subtypes). 3. Nonlinear BCVA–TD Association in Strabismic Amblyopia LOESS plots revealed a distinct threshold-dependent relationship exclusively in strabismic amblyopia (Fig. 3 ). While ametropic, anisometropic, and control groups showed flat BCVA–TD curves, strabismic cases exhibited accelerated TD escalation when BCVA exceeded 0.3 logMAR. 4. GAMs Ananlysis and Threshold Identification GAM analysis confirmed a significant nonlinear association between BCVA and TD in strabismic amblyopia (edf = 4.46, P = 0.002). Marginal effect analysis identified a critical inflection point at 0.321 logMAR (Fig. 4 A), beyond which TD increase sharply. Specifically, each 0.1 logMAR decrease in acuity was associated with an additional 38.2 px increase in TD (95% CI: 25.7–50.7; Fig. 4 ). 5. Refractive Error Modulation Tensor product interactions indicated that higher SE amplification BCVA-related increases in fixation instability (TD) in ametropic amblyopia ( β = +17.3 px/D per logMAR unit, P = 0.013) and strabismic ( β = +42.6 px/D per logMAR unit, P = 0.004). The interaction model explained 27.9% of TD variance (adjusted R² = 0.251), outperforming the main-effect model (Δdeviance explained = 4.6%, P < 0.001; Table 2 ). Table 2 Comparison of Parametric and Smooth Effects Between the Main Effect and Interaction Models Variable Model1 Model2 Parametric Terms Estimate p-value Estimate p-value (Intercept) 103.490 0.003 110.071 0.001 Age -11.250 < 0.001 -10.551 < 0.001 Gender Boys 0(ref) 0(ref) Girls -23.728 0.004 -21.803 0.008 SE 2.341 0.155 — — Fine stereopsis 57.987 < 0.001 52.618 < 0.001 Type_group Ametropic 0(ref) 0(ref) Anisometropic -28.015 0.057 -23.129 0.111 Strabismic 199.350 < 0.001 215.116 < 0.001 Control -22.227 0.268 -19.070 0.334 Smooth Terms edf p-value edf p-value s(BCVA): Ametropic 3.764 0.404 3.732 0.228 s(BCVA): Anisometropic 1.001 0.472 1.001 0.610 s(BCVA): Strabismic 4.460 0.002 4.473 0.002 s(BCVA): Control 1.002 0.472 1.001 0.622 s(SE) — — 1.585 0.524 Interaction Terms edf p-value edf p-value ti(BCVA, SE): Ametropic — — 2.708 0.013 ti(BCVA, SE): Anisometropic — — 1.001 0.977 ti(BCVA, SE): Strabismic — — 4.703 0.004 ti(BCVA, SE): Control — — 0.001 0.977 R-sq.(adj) 0.213 0.251 Deviance explained 23.3% 27.9% Parametric terms represent fixed effects. Smooth terms are modeled using thin-plate regression splines. Interaction terms represent tensor product interactions between BCVA (best-corrected visual acuity) and SE (spherical equivalent). Model 1 = main-effect model; Model 2 = interaction model. Adjusted R² and deviance explained reflect overall model performance. Significant effects are bolded. 6. Bootstrap Validation of Nonlinear Effects In the strabismic subgroup (n = 32), bootstrap resampling (n = 1,000 iterations) confirmed robustness of nonlinear effect: the 95% CI for edf of the BCVA smooth term ranged from 3.1–7.2, and 38.7% of resamples showed P < 0.01 for nonlinearity. 7. Sensory-Motor Decoupling Beyond the Threshold Marginal effect curves illustrated an abrupt shift in fixation stability in strabismic amblyopia at the identified BCVA threshold (Fig. 5 ). Below 0.321 logMAR, TD remained stable (slope = -5.2 px/logMAR). Above the threshold, TD increased steeply (slope = + 49.1 px/logMAR, 95% CI: +32.7–+65.5), consistent with a collapse of binocular fixation control. Discussions 1. Principal Findings This study identified a critical BCVA threshold of 0.321 logMAR (≈ 20/42 Snellen), beyond which binocular fixation stability deteriorated sharply in children with strabismic amblyopia. Refractive error further amplified this sensory–motor decoupling in both ametropic and strabismic subtypes. These findings extend previous work by demonstrating that fixation instability is not merely proportional to acuity loss, but instead follows a threshold-dependent trajectory in strabismus. 2. Integration with Previous Research Our results confirm and refine prior observations that fixation instability is a hallmark of amblyopia 6 , 7 . Subramanian et al. 6 reported reduced fixation stability in amblyopic children using monocular recordings, while Kelly et al. 7 demonstrated greater instability in binocular conditions. By applying nonlinear modeling, we show that strabismic amblyopia is uniquely characterized by an abrupt inflection point, consistent with Birch's hypothesis of cortical integration failure when acuity loss surpasses a functional limit 4 . This may explain why some smaller studies failed to detect clear associations between acuity and fixation 14 —linear models likely masked threshold effects. We also found that higher SE exacerbates fixation instability in ametropic and strabismic amblyopia, consistent with Wahl et al.'s proposal that optical defocus increases neural noise and disrupts microsaccade control 16 . In contrast, anisometropic amblyopia showed little BCVA–TD coupling, unlike strabismic amblyopia caused by ocular misalignment and abnormal dorsal oculomotor circuits, anisometropic amblyopia is mainly characterized by interocular aniseikonia and asymmetric retinal image quality, rather than strabismus 24 . Long-term binocular perceptual imbalance during visual development leads to specific cortical remodeling and compensatory fixation control in anisometropic amblyopia 12 . instead of increased neural noise in oculomotor pathways. Combined with preserved ocular alignment 8 , this subtype-specific mechanism may explain the weak BCVA–TD coupling in anisometropic amblyopia. Taken together, these findings indicate that fixation instability in amblyopia is not uniform, but varies by subtype, acuity threshold, and refractive factors; this threshold-dependent pattern likely reflects underlying cortical and oculomotor mechanisms. 3. Neurobiological Interpretation Building on the threshold-dependent pattern observed in strabismic amblyopia, the identified threshold at 0.321 logMAR likely reflects a transition in cortical control of fixation. Below this level, residual binocular input may stabilize gaze through dorsal stream regulation of the superior colliculus 25 . Beyond the threshold, imbalanced input to V1/V2 disrupts efferent copy signals to frontal eye fields, precipitating fixation collapse 26 , 27 . Functional MRI studies in amblyopia have documented abnormal parvocellular pathway activation and impaired integration across extrastriate areas 28 , 29 , supporting this interpretation. 4. Clinical Translation and Rehabilitation Implications These findings have several clinical applications. (1) Threshold-Guided Intervention: For strabismic amblyopia with BCVA worse than 0.321 logMAR, early refractive correction is critical to mitigate SE-related amplification of instability ( β = +42.6 px/D), followed by binocular integration training (e.g., dichoptic motion tasks) to restore sensory–motor integration 27 . (2) Subtype-Specific strategies: Strabismic amblyopia may benefit from gaze stabilization therapy (Counteracts threshold-triggered collapse), ametropic amblyopia from high-frequency spatial training to reduce neural noise 16 , and anisometropic amblyopia from contrast-balanced binocular approaches 8 , 30 . (3) Prognostic value: Fixation stability could serve as a biomarker of disease severity and treatment responsiveness, aligning with recent efforts to incorporate oculomotor endpoints in amblyopia trials 27 , 31 . 5. Methodological Advances This study introduces several methodological strengths. First, binocular eye-tracking captures naturalistic fixation control, addressing limitations of earlier monocular paradigms 9 . Second, GAMs reveal nonlinear threshold effects that conventional regression approaches cannot detect 32 . Third, interaction modeling demonstrated for the first time that refractive error modulates fixation instability in a subtype-dependent manner (P interaction < 0.01). Together, these advances support the utility of nonlinear modeling in pediatric vision science. 6. Limitations and Future Directions Several limitations warrant consideration. The cross-sectional design precludes causal inference regarding whether acuity decline precedes fixation collapse. Longitudinal data from the ongoing CABC study will be essential to address temporal dynamics. In addition, the relatively small strabismic sample (n = 32) requires replication in larger cohorts, although bootstrap validation supports robustness. Finally, the current study only utilized a spatial dispersion metric TD (to quantify binocular fixation instability), which provides a limited view of oculomotor function. To generate a more comprehensive oculomotor profile and refine mechanistic interpretations, future work should incorporate additional oculomotor metrics such as microsaccade frequency and drift velocity to refine mechanistic interpretation. Declarations Conflicts of Interest The author(s) declare that there are no potential conflicts of interest with respect to the research, authorship, and/or publication of this article. Funding This study was supported by the Guangxi Key Research and Development Program (No. Guike AB23026047), Guangxi Natural Science Foundation (2024GXNSFAA010262), Guangdong Basic and Applied Basic Research Foundation (2021A1515011822), Guangxi Medical and Health Appropriate Technology Research and Development Project (2023003), and Guangxi Clinical Ophthalmic Research Center (No. Guike AD19245193). All funding parties did not have any role in the study design, conduct of this research, data analysis, or decisions in preparation or publishing of the manuscript. Author Contribution Statement Conceptualization: J.L., J.Z., X.X.; Methodology:J.L., J.Z., X.X.; Formal analysis: M.R.; Investigation: L.P., Y.H., W.L., L.L., Y.L., E.L., M.K., Q.C., Y.L.; Data curation: L.P., M.R., Y.H., L.L., Y.L., Q.C., Y.L.,E.L.; Validation: W.L., M.K., Q.C.; Writing-original draft: All authors; Writing-review & editing:J.L., J.Z., X.X.; Funding acquisition:J.L., J.Z., X.X References Levi DM. Rethinking amblyopia 2020. Vision research 2020; 176: 118–129. Kates MM, Beal CJ. Amblyopia. Jama 2021; 325(4): 408. Cruz OA, Repka MX, Hercinovic A, Cotter SA, Lambert SR, Hutchinson AK et al. Amblyopia Preferred Practice Pattern. Ophthalmology 2023; 130(3): P136-p178. Birch EE. Amblyopia and binocular vision. Progress in retinal and eye research 2013; 33: 67–84. Randhawa S, Griffiths N, O'Brien P, Panter C, Boparai K, Harrad R et al. Qualitative Exploration of the Visual Function Impairments and Health-Related Quality of Life Impacts of Amblyopia in Adult and Pediatric Populations. Ophthalmol Ther 2023; 12(5): 2505–2528. Subramanian V, Jost RM, Birch EE. A quantitative study of fixation stability in amblyopia. Investigative ophthalmology & visual science 2013; 54(3): 1998–2003. Kelly KR, Cheng-Patel CS, Jost RM, Wang YZ, Birch EE. Fixation instability during binocular viewing in anisometropic and strabismic children. Exp Eye Res 2019; 183: 29–37. Aizenman AM, Levi DM. Fixational stability as a measure for the recovery of visual function in amblyopia. Proceedings Eye Tracking Research & Applications Symposium 2021; 2021. Shaikh AG, Otero-Millan J, Kumar P, Ghasia FF. Abnormal Fixational Eye Movements in Amblyopia. PloS one 2016; 11(3): e0149953. Zhou Y, Bian H, Yu X, Wen W, Zhao C. Quantitative assessment of eye movements using a binocular paradigm: comparison among amblyopic, recovered amblyopic and normal children. BMC ophthalmology 2022; 22(1): 365. Altinbay D, Sahli E, Bingol Kiziltunc P, Atilla H. Evaluation of fixation characteristics in amblyopia using microperimetry. International ophthalmology 2023; 43(9): 3403–3412. Zhou Y, Yu W, Ye Q, Xu Z, He Y, Yao Y et al. Fixation Stability Deficits in Anisometropic Amblyopia. Investigative ophthalmology & visual science 2025; 66(1): 14. Haraguchi Y, Cakir GB, Shaikh A, Ghasia F. Binocular and Fellow Eye Acuity Deficits in Amblyopia: Impact of Fixation Instability and Sensory Factors. Journal of eye movement research 2025; 18(3): 20. Gonzalez EG, Wong AM, Niechwiej-Szwedo E, Tarita-Nistor L, Steinbach MJ. Eye position stability in amblyopia and in normal binocular vision. Investigative ophthalmology & visual science 2012; 53(9): 5386–5394. Ghasia FF, Shaikh AG. Uncorrected Myopic Refractive Error Increases Microsaccade Amplitude. Investigative ophthalmology & visual science 2015; 56(4): 2531–2535. Wahl S, Dragneva D, Rifai K. The limits of fixation-Keeping the ametropic eye on target. Journal of vision 2019; 19(13): 8. Niechwiej-Szwedo E, Colpa L, Wong AMF. Visuomotor Behaviour in Amblyopia: Deficits and Compensatory Adaptations. Neural plasticity 2019; 2019: 6817839. [Expert consensus on prevention and treatment of amblyopia in children]. [Zhonghua yan ke za zhi] Chinese journal of ophthalmology 2021; 57(5): 336–340. Ghasia FF, Otero-Millan J, Shaikh AG. Abnormal fixational eye movements in strabismus. The British journal of ophthalmology 2018; 102(2): 253–259. Cohen J, Cohen J, Cohen JW, Cohen J, Cohen J, Cohen J et al. Statistical power analysis for the behavioral science. Technometrics 1988; 31(4): 499–500. Holmqvist K, Nyström M, Andersson R, Dewhurst R, Jarodzka H, van de Weijer J Eye Tracking: A comprehensive guide to methods and measures . OUP Oxford; 2011. . Identifying fixations and saccades in eye-tracking protocols. Eye Tracking Research & Application 2000. Lan J, Li Y, Pang S, Zhang G, Wu D, Yang C et al. Targeting displacement as an indicator of binocular fixation in normal Chinese adults. Frontiers in neuroscience 2023; 17: 1124034. Wang Y, Wu Y, Luo L, Li F. Structural and functional alterations in the brains of patients with anisometropic and strabismic amblyopia: a systematic review of magnetic resonance imaging studies. Neural regeneration research 2023; 18(11): 2348–2356. Huang Y, Liu Z, Zhan Z, Zhang X, Gao L, Wang M et al. Interactions between excitatory neurons and parvalbumin interneurons in V1 underlie neural mechanisms of amblyopia and visual stimulation treatment. Communications biology 2024; 7(1): 1564. Wang H, Crewther SG, Liang M, Laycock R, Yu T, Alexander B et al. Impaired Activation of Visual Attention Network for Motion Salience Is Accompanied by Reduced Functional Connectivity between Frontal Eye Fields and Visual Cortex in Strabismic Amblyopia. Frontiers in human neuroscience 2017; 11: 195. Scaramuzzi M, Murray J, Otero-Millan J, Nucci P, Shaikh AG, Ghasia FF. Fixation instability in amblyopia: Oculomotor disease biomarkers predictive of treatment effectiveness. Progress in brain research 2019; 249: 235–248. Kelly KR, Jost RM, Wang YZ, Dao L, Beauchamp CL, Leffler JN et al. Improved Binocular Outcomes Following Binocular Treatment for Childhood Amblyopia. Investigative ophthalmology & visual science 2018; 59(3): 1221–1228. Tilia D, Bakaraju RC, Asper LJ, Papas EB. Associations between Binocular Vision Disorders and Contact Lens Dissatisfaction. Optometry and vision science: official publication of the American Academy of Optometry 2021; 98(10): 1160–1168. Ghasia F, Tychsen L. Inter-Ocular Fixation Instability of Amblyopia: Relationship to Visual Acuity, Strabismus, Nystagmus, Stereopsis, Vergence, and Age. American journal of ophthalmology 2024; 267: 230–248. Ghasia F, Wang J. Amblyopia and fixation eye movements. Journal of the neurological sciences 2022; 441: 120373. Chiang AY. Generalized Additive Models: An Introduction With R. Technometrics 2007; 49: 360–361. Additional Declarations There is no conflict of interest Cite Share Download PDF Status: Under Review Version 1 posted Reviewers invited by journal 04 May, 2026 Editor assigned by journal 30 Apr, 2026 Submission checks completed at journal 23 Apr, 2026 First submitted to journal 21 Apr, 2026 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-9490101","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":632505053,"identity":"739ea14e-f2b9-4984-a347-9b4af27cd25c","order_by":0,"name":"Xin Xiao","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA0UlEQVRIie2RPQoCMRBGAwPRYjSdbFDcK4wExMLDbG4g2FoIW9hYWCpeQm+wMqClB7BR9gKpxMLCbCuyP51FXjHV9xjmGyECgX8EikGLoQLIMveqr5yNXkl72q0b7LKHKxpuyxpZusAjx5k0xOhYoIhVLytXdCrNaEuDoebOgWcTMdrtk3JFgRhHjqTpFsoWRUK3CkVC6xklBHbJeGeUNRQFWGwBu2EU9RSd4tzf4ktOJfmSo+pb6Ho55vj2r1ScO/eaxqpfoXwTNYsHAoFA4DcfhoQ+3ZtIN6cAAAAASUVORK5CYII=","orcid":"https://orcid.org/0000-0003-1107-6521","institution":"the People's Hospital of Guangxi Zhuang Autonomous Region","correspondingAuthor":true,"prefix":"","firstName":"Xin","middleName":"","lastName":"Xiao","suffix":""},{"id":632505054,"identity":"24d72655-ff50-4b27-bb9f-2e4aca1b5efa","order_by":1,"name":"Lu Pan","email":"","orcid":"","institution":"","correspondingAuthor":false,"prefix":"","firstName":"Lu","middleName":"","lastName":"Pan","suffix":""},{"id":632505055,"identity":"46aa3a51-82da-4d36-b8b8-5c0d87faddb9","order_by":2,"name":"Meng Ru","email":"","orcid":"","institution":"","correspondingAuthor":false,"prefix":"","firstName":"Meng","middleName":"","lastName":"Ru","suffix":""},{"id":632505056,"identity":"2d0f7fa1-84cc-4e47-974f-c639bf057881","order_by":3,"name":"Yuxing Huang","email":"","orcid":"","institution":"","correspondingAuthor":false,"prefix":"","firstName":"Yuxing","middleName":"","lastName":"Huang","suffix":""},{"id":632505057,"identity":"0e749c3d-114e-431d-8cf9-cffc93818e19","order_by":4,"name":"Wuqiang Luo","email":"","orcid":"","institution":"","correspondingAuthor":false,"prefix":"","firstName":"Wuqiang","middleName":"","lastName":"Luo","suffix":""},{"id":632505058,"identity":"5ec7c8f0-56c6-4a6a-8fbc-4c2b0435e512","order_by":5,"name":"Lili Li","email":"","orcid":"","institution":"","correspondingAuthor":false,"prefix":"","firstName":"Lili","middleName":"","lastName":"Li","suffix":""},{"id":632505059,"identity":"fcf9772f-d97f-4c14-b795-43b7c78b2351","order_by":6,"name":"Yan Luo","email":"","orcid":"","institution":"","correspondingAuthor":false,"prefix":"","firstName":"Yan","middleName":"","lastName":"Luo","suffix":""},{"id":632505060,"identity":"738c176f-aaf5-45a6-adcf-a78c2b9bb2eb","order_by":7,"name":"Enwei Lin","email":"","orcid":"","institution":"","correspondingAuthor":false,"prefix":"","firstName":"Enwei","middleName":"","lastName":"Lin","suffix":""},{"id":632505061,"identity":"ba2fbbca-2f92-4e66-85a2-dd0edff912d1","order_by":8,"name":"Min Kong","email":"","orcid":"","institution":"","correspondingAuthor":false,"prefix":"","firstName":"Min","middleName":"","lastName":"Kong","suffix":""},{"id":632505062,"identity":"6c4ca379-511a-4f98-a0a3-79b5914f6a8e","order_by":9,"name":"Qi Chen","email":"","orcid":"","institution":"","correspondingAuthor":false,"prefix":"","firstName":"Qi","middleName":"","lastName":"Chen","suffix":""},{"id":632505063,"identity":"978eb60c-ba21-440f-ae24-6ba678d7d018","order_by":10,"name":"Yali Luo","email":"","orcid":"","institution":"","correspondingAuthor":false,"prefix":"","firstName":"Yali","middleName":"","lastName":"Luo","suffix":""},{"id":632505064,"identity":"1ca858a8-954f-44af-a8ed-b2e612d6cee5","order_by":11,"name":"Jianqing Lan","email":"","orcid":"","institution":"","correspondingAuthor":false,"prefix":"","firstName":"Jianqing","middleName":"","lastName":"Lan","suffix":""},{"id":632505065,"identity":"35874c6e-ef86-4546-83fd-4a80e00c1413","order_by":12,"name":"Jin Zeng","email":"","orcid":"","institution":"","correspondingAuthor":false,"prefix":"","firstName":"Jin","middleName":"","lastName":"Zeng","suffix":""}],"badges":[],"createdAt":"2026-04-22 03:10:37","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-9490101/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-9490101/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":109101667,"identity":"e55e88be-745f-4eb8-833f-025da0e6c579","added_by":"auto","created_at":"2026-05-12 14:29:32","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":500384,"visible":true,"origin":"","legend":"\u003cp\u003eFlowchart of participant enrollment in the China Amblyopia Behavior Cohort (CABC).\u003c/p\u003e\n\u003cp\u003e\u003cem\u003eThis flow diagram illustrates the recruitment and selection of children with ametropic, anisometropic, and strabismic amblyopia, as well as control participants, included in the final analysis.\u003c/em\u003e\u003c/p\u003e","description":"","filename":"floatimage1.png","url":"https://assets-eu.researchsquare.com/files/rs-9490101/v1/51a77b14ef7a0aa8b793603d.png"},{"id":109101733,"identity":"ffbf0ed2-7779-42a3-95f8-2fec4279f819","added_by":"auto","created_at":"2026-05-12 14:29:35","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":129201,"visible":true,"origin":"","legend":"\u003cp\u003eDistribution of fixation instability across study groups.\u003c/p\u003e\n\u003cp\u003e\u003cem\u003eBox plots show targeting displacement (TD) during sustained fixation tasks across amblyopia subtypes and controls. TD = average offset between gaze position and target center. Higher TD indicates greater fixation instability.\u003c/em\u003e\u003c/p\u003e","description":"","filename":"floatimage2.png","url":"https://assets-eu.researchsquare.com/files/rs-9490101/v1/ddd415998a629a49247e5369.png"},{"id":109101610,"identity":"9da49b5d-9e92-4256-b75f-7440fce55a9e","added_by":"auto","created_at":"2026-05-12 14:29:13","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":152810,"visible":true,"origin":"","legend":"\u003cp\u003eNonlinear associations between BCVA and fixation instability.\u003c/p\u003e\n\u003cp\u003e\u003cem\u003eLOESS smoothing plots of TD (targeting displacement) against BCVA (best-corrected visual acuity) across groups. A threshold-like nonlinear increase in TD is observed only in the strabismic amblyopia group.\u003c/em\u003e\u003c/p\u003e","description":"","filename":"floatimage3.png","url":"https://assets-eu.researchsquare.com/files/rs-9490101/v1/26ecc46bd7c676e64948f18c.png"},{"id":109101787,"identity":"788397ed-dff5-472f-907b-9f75ece13326","added_by":"auto","created_at":"2026-05-12 14:29:38","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":452336,"visible":true,"origin":"","legend":"\u003cp\u003eInteraction between BCVA and refractive error in predicting fixation instability.\u003c/p\u003e\n\u003cp\u003e\u003cem\u003eGeneralized additive model (GAM) interaction surfaces depicting the moderating effect of spherical equivalent (SE) on the relationship between BCVA and TD (targeting displacement) in (a) ametropic amblyopia, (b) anisometropic amblyopia, (c) strabismic amblyopia, and (d) controls. Warmer colors indicate higher TD values.\u003c/em\u003e\u003c/p\u003e","description":"","filename":"floatimage4.png","url":"https://assets-eu.researchsquare.com/files/rs-9490101/v1/a89ca981e01b47dbe4643ebd.png"},{"id":109101825,"identity":"9a87610b-73cc-4fa5-bb74-9b5517c28edb","added_by":"auto","created_at":"2026-05-12 14:29:46","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":183938,"visible":true,"origin":"","legend":"\u003cp\u003ePredicted fixation instability across levels of visual acuity in strabismic amblyopia.\u003c/p\u003e\n\u003cp\u003e\u003cem\u003eMarginal effect curves from GAM analysis. Below the threshold of 0.321 logMAR, fixation stability remains relatively preserved. Beyond this threshold, targeting displacement (TD) escalates sharply, indicating collapse of binocular fixation control.\u003c/em\u003e\u003c/p\u003e","description":"","filename":"floatimage5.png","url":"https://assets-eu.researchsquare.com/files/rs-9490101/v1/f66a982c0bb6ba22894bb59f.png"},{"id":109102084,"identity":"5a114193-c526-4a56-8fdc-cc96c698b2ab","added_by":"auto","created_at":"2026-05-12 14:31:06","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1828623,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9490101/v1/ee3416e1-d42a-4d6e-a9d8-f029e9c8f3f6.pdf"}],"financialInterests":"There is no conflict of interest","formattedTitle":"Critical BCVA Threshold and Refractive Error Modulation for Fixation Instability in Strabismic Amblyopia: Revealed by Eye-Tracking and GAM Modeling","fulltext":[{"header":"Introduction","content":"\u003cp\u003eAmblyopia, a neurodevelopmental disorder affecting 2%\u0026ndash;4% of children worldwide, is characterized by reduced best-corrected visual acuity (BCVA) in the absence of structural ocular abnormalities and despite optimal optical correction \u003csup\u003e\u003cspan additionalcitationids=\"CR2\" citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e\u003c/sup\u003e. Beyond impairing spatial vision and stereopsis, amblyopia is increasingly recognized as a disorder of oculomotor control. Binocular fixation instability\u0026mdash;quantified as targeting displacement (TD) during sustained gaze\u0026mdash;has emerged as a key biomarker of sensory\u0026ndash;motor dysfunction \u003csup\u003e\u003cspan additionalcitationids=\"CR5\" citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e\u003c/sup\u003e. Importantly, fixation instability manifests in a subtype-specific manner: strabismic amblyopia is associated with excessive fixation drift due to ocular misalignment, while anisometropic amblyopia shows a progressive increase in TD with declining acuity \u003csup\u003e\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e, \u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e\u003c/sup\u003e. Such instability exacerbates visual blur, impedes information acquisition, and correlates strongly with poor stereopsis and reading performance \u003csup\u003e\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e, \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e\u003c/sup\u003e, underscoring its clinical relevance for prognosis and rehabilitation \u003csup\u003e\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eDespite these insights, several knowledge gaps remain. First, most prior studies have relied on monocular recordings \u003csup\u003e\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e, \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e, \u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e\u003c/sup\u003e, thereby neglecting natural binocular viewing conditions in which interocular interactions strongly influence fixation control \u003csup\u003e\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e\u003c/sup\u003e. Second, the relationship between BCVA and fixation instability has often been modeled as linear \u003csup\u003e\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e, \u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e\u003c/sup\u003e, overlooking potential threshold effects suggested in strabismic amblyopia \u003csup\u003e\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e\u003c/sup\u003e. Third, the role of refractive error, particularly spherical equivalent (SE), as a moderator of sensory\u0026ndash;motor coupling remains poorly understood. Evidence indicates that uncorrected refractive error alters microsaccade dynamics and spatial processing \u003csup\u003e\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e, \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e\u003c/sup\u003e, but whether SE interacts with BCVA to drive fixation collapse in different amblyopia subtypes is unknown.\u003c/p\u003e \u003cp\u003eTo address these gaps, we leveraged data from the China Amblyopia Behavior Cohort (CABC) to investigate binocular fixation stability using high-resolution eye-tracking. We applied generalized additive models (GAMs) to: (1) identify a critical BCVA threshold associated with fixation instability in strabismic amblyopia; and (2) test whether refractive error modulates sensory-motor coupling (BCVA\u0026ndash;TD association) in a subtype-specific manner.\u003c/p\u003e \u003cp\u003eWe hypothesized that: BCVA degradation beyond a functional threshold would disproportionately disrupt fixation stability in strabismic amblyopia due to compromised cortical integration of misaligned inputs \u003csup\u003e\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e, \u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e\u003c/sup\u003e; Higher SE would amplify BCVA-driven TD increases in ametropic and strabismic subtypes by exacerbating optical defocus and neural noise \u003csup\u003e\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e, \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e\u003c/sup\u003e. Therefore, this study aims to delineate the precise, potentially non-linear, relationship between BCVA and fixation instability under binocular viewing conditions, and to elucidate how refractive error modulates this sensory-motor coupling across different amblyopia subtypes. These findings aim to inform subtype-stratified rehabilitation targeting both sensory and motor deficits.\u003c/p\u003e "},{"header":"Methods","content":"\n\u003ch3\u003e1. Study Design and Participants\u003c/h3\u003e\n\u003cp\u003eThis multicenter case-control study analyzed baseline data from the China Amblyopia Behavior Cohort (CABC, 2024\u0026ndash;2025). A total of 536 children with clinically confirmed amblyopia (303 ametropic, 201 anisometropic, 32 strabismic) and 159 sex-matched controls were recruited from three tertiary eye hospitals in Guangxi, Guangdong, and Sichuan, China.\u003c/p\u003e \u003cp\u003eAmblyopia subtypes were defined according to the Chinese Ophthalmological Society guidelines \u003csup\u003e\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e\u003c/sup\u003e: (1) Ametropic amblyopia: Bilateral BCVA reduction with interocular SE difference\u0026thinsp;\u0026lt;\u0026thinsp;0.75 D; (2) Anisometropic amblyopia: Interocular SE difference\u0026thinsp;\u0026ge;\u0026thinsp;1.50 D or cylindrical difference\u0026thinsp;\u0026ge;\u0026thinsp;1.00 D; (3) Strabismic amblyopia: amblyopia associated with manifest strabismus, confirmed by prism cover test (\u0026gt;\u0026thinsp;8Δ) \u003csup\u003e19\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eControl participants had normal BCVA (logMAR\u0026thinsp;\u0026le;\u0026thinsp;0.10 in both eyes), no history of amblyopia, ocular surgery, or neurological disease. Sample size was determined using a priori power analysis (target power 0.90, α\u0026thinsp;=\u0026thinsp;0.05, effect size f\u0026sup2; = 0.05), Specifically, the effect size f\u0026sup2; = 0.05 was determined based on relevant literature, indicating a minimum of 335 participants to detect nonlinear effects in GAMs \u003csup\u003e\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003e The study adhered to the Declaration of Helsinki and was approved by the Ethics Committee of the People's Hospital of Guangxi Zhuang Autonomous Region (KY-KJT-2023-285). Written informed consent was obtained from all legal guardians.\u003c/p\u003e\n\u003ch3\u003e2. Ophthalmic Examination Protocol\u003c/h3\u003e\n \u003cp\u003eAll participants underwent standardized ophthalmic examinations and stereoacuity assessment (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e). BCVA was measured using a standard logarithmic visual acuity chart at 5 m, the result was recorded via the LogMAR scale. Anterior segment and fundus evaluation were examined using slit-lamp biomicroscopy and ophthalmoscopy. Ocular alignment was assessed using prism cover test (strabismus: median 19.69Δ, range from 8.75\u0026thinsp;~\u0026thinsp;43.75Δ) and fixation behavior assessment. Cycloplegic refraction was performed 30\u0026ndash;40 min after instillation of 1% atropine sulfate (three drops at 10-min intervals). SE was calculated as sphere\u0026thinsp;+\u0026thinsp;0.5 \u0026times; cylinder.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eFine stereoacuity was measured with the Brain Imaging Bio-Stimulation Training System (National Engineering Research Center for Medical Devices, China). Participants, seated 80 cm from the display and wearing polarized glasses, identified the orientation of E-shaped targets (3\u0026deg; \u0026times; 3\u0026deg;). Fine stereoacuity thresholds were graded logarithmically: grade 0 (2.90), grade 1 (2.60), grade 2 (2.48), grade 3 (2.30), grade 4 (2.00), with higher grades indicating better fine stereoacuity.\u003c/p\u003e\n\u003ch3\u003e3. Binocular Fixation Stability Assessment\u003c/h3\u003e\n\u003cdiv id=\"Sec5\" class=\"Section2\"\u003e \u003ch2\u003e3.1 Eye-Tracking System\u003c/h2\u003e \u003cp\u003eBinocular fixation stability was measured using the Tobii Eye Tracker 4 (Tobii 4C, Sweden), sampling at 133 Hz with average spatial accuracy of 0.5\u0026ndash;1.0\u0026deg; and precision of 0.03\u0026deg; RMS. Participants were seated 80 cm from a 23-inch monitor (1920\u0026times;1080 pixels) in a dimly lit, sound-attenuated room. A nine-point binocular calibration was performed prior to each task, with calibration error required to be \u0026lt;\u0026thinsp;0.5\u0026deg;.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec6\" class=\"Section2\"\u003e \u003ch2\u003e3.2 Sustained Fixation Task\u003c/h2\u003e \u003cp\u003eA high-contrast yellow circular target (10\u0026deg; diameter) was presented sequentially at eight peripheral locations (\u0026plusmn;\u0026thinsp;5\u0026deg; horizontally and vertically) and centrally. Each stimulus lasted 2 s, with 0.5 s transition intervals. Participants were instructed to maintain fixation while minimizing head movement. Gaze coordinates were recorded in pixels.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec7\" class=\"Section2\"\u003e \u003ch2\u003e3.3 Targeting Displacement (TD)\u003c/h2\u003e \u003cp\u003eBinocular fixation stability was quantified as TD. TD is calculated as the average offset from the fixation point to the target center per frame, yielding horizontal (Fix_X), vertical (Fix_Y), and average TD values for each trial (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e). Targeting Displacement (TD) Calculated using the formula:\u003c/p\u003e \u003cp\u003eTD=\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\frac{1}{\\text{N}}{\\sum\\:}_{i=1}^{N}\\sqrt{{{\\left({x}_{i}-{x}_{c}\\right)}^{2}+({y}_{i}-{y}_{c})}^{2}}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003cp\u003eWhere (x\u003csub\u003ei\u003c/sub\u003e, y\u003csub\u003ei\u003c/sub\u003e) represents the binocular gaze coordinates for sample i, and (x\u003csub\u003ec\u003c/sub\u003e, y\u003csub\u003ec\u003c/sub\u003e) denotes the coordinates of the target center. This metric is a standard measure of fixation dispersion \u003csup\u003e\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e, \u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e\u003c/sup\u003e. Data segments with an eye tracking loss rate\u0026thinsp;\u0026gt;\u0026thinsp;20% are excluded from analysis to ensure data quality \u003csup\u003e\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e\u003c/sup\u003e.TD represents spatial dispersion of binocular gaze points, conceptually similar to the dispersion component of the bivariate contour ellipse area (BCEA). Unlike BCEA, which models a 68\u0026ndash;95% probability ellipse based on variance and covariance, TD reflects frame-wise Euclidean deviation and has been widely used in pediatric and low-vision eye-tracking studies. As BCEA requires longer stable fixation intervals, TD was selected for the current design involving brief multi-position fixations.\u003c/p\u003e \u003c/div\u003e\n\u003ch3\u003e4. Statistical Modeling of Sensory-Motor Coupling\u003c/h3\u003e\n\u003cp\u003eLOESS smoothing (span\u0026thinsp;=\u0026thinsp;0.75) was used for exploratory visualization of BCVA\u0026ndash;TD relationships by subtype. Nonlinear effects were tested using GAMs with thin-plate regression splines:\u003c/p\u003e \u003cp\u003eTD\u0026thinsp;~\u0026thinsp;s (BCVA, by =\u0026thinsp;subtype)\u0026thinsp;+\u0026thinsp;age\u0026thinsp;+\u0026thinsp;sex\u0026thinsp;+\u0026thinsp;SE\u0026thinsp;+\u0026thinsp;stereoacuity\u003c/p\u003e \u003cp\u003eTo assess moderation by refractive error, tensor product interactions were modeled:\u003c/p\u003e \u003cp\u003eTD\u0026thinsp;~\u0026thinsp;ti (BCVA, SE, by =\u0026thinsp;subtype) + covariates\u003c/p\u003e \u003cp\u003eSignificance of smooth and interaction terms was determined using false discovery rate (FDR)\u0026ndash;corrected P values. Threshold identification was using first-derivative analysis of marginal effects. Robustness was validated through bootstrap resampling (n\u0026thinsp;=\u0026thinsp;1,000) in the strabismic subgroup, 95% CI for effective degrees of freedom (edf), proportion of P\u0026thinsp;\u0026lt;\u0026thinsp;0.01 resamples were reported. Analyses were conducted in R (version 4.5.1; mgcv package), \u003cem\u003eβ\u003c/em\u003e coefficients and 95% CIs reported for all models.\u003c/p\u003e"},{"header":"Results","content":"\n\u003ch3\u003e1. Clinical Characteristics\u003c/h3\u003e\n\u003cp\u003eA total of 695 participants were included: 536 children with amblyopia (303 ametropic, 201 anisometropic, 32 strabismic) and 159 controls. Demographic and clinical data are summarized in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e. Significant group differences were observed for age, SE, BCVA, stereoacuity, and fixation stability (all P\u0026thinsp;\u0026lt;\u0026thinsp;0.001). Children with strabismic amblyopia exhibited the poorest BCVA (median logMAR 0.60) and highest SE (median\u0026thinsp;+\u0026thinsp;4.8 D).\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eDemographic and Clinical Characteristics of Amblyopia Subtypes and Controls\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"7\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eVariable\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eTotal (N\u0026thinsp;=\u0026thinsp;695).\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eAmetropic (n\u0026thinsp;=\u0026thinsp;303)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eAnisometropic (n\u0026thinsp;=\u0026thinsp;201)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eStrabismic (n\u0026thinsp;=\u0026thinsp;32)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eControl (159)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003eP value\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eGender, n (%)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.760\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eBoys\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e339 (48.8)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e154 (50.8)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e97 (48.3)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e14 (43.8)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e74 (46.5)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eGirls\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e356 (51.2)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e149 (49.2)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e104 (51.7)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e18 (56.2)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e85 (53.5)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAge, Median (IQR)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e6.0 (5.0, 7.0)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e6.0 (5.0, 6.0)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e6.0 (5.0, 6.0)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e6.0 (5.0, 6.0)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e7.0 (6.0, 9.0)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e\u0026lt;\u0026thinsp;0.001\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSE, Median (IQR)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.6 (0.0, 3.5)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.9 (-0.2, 3.5)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e2.5 (0.4, 4.5)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e4.8 (0.9, 6.7)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.0 (0.0, 0.0)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e\u0026lt;\u0026thinsp;0.001\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eBCVA, Median (IQR)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.3 (0.2, 0.4)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.3 (0.2, 0.4)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.4 (0.2, 0.5)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.4 (0.3, 0.5)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.0 (0.0, 0.1)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e\u0026lt;\u0026thinsp;0.001\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eFine stereopsis Median (IQR)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e2.3 (2.0, 2.9)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e2.3 (2.0, 2.9)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e2.9 (2.3, 2.9)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e2.9 (2.6, 2.9)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e2.0 (2.0, 2.0)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e\u0026lt;\u0026thinsp;0.001\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eFix_X Median (IQR)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e116.7 (61.8, 216.7)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e133.4 (70.7, 233.8)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e115.2 (69.9, 197.7)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e301.7 (142.0, 643.6)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e76.3 (45.4, 154.3)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e\u0026lt;\u0026thinsp;0.001\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eFix_Y, Median (IQR)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e116.4 (75.7, 176.8)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e130.0 (81.7, 189.3)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e123.0 (82.4, 175.6)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e160.0 (111.4, 208.8)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e83.3 (59.3, 131.6)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e\u0026lt;\u0026thinsp;0.001\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eFixation_TD, Median (IQR)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e121.4 (72.2, 198.4)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e141.1 (81.8, 212.0)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e124.9 (81.8, 189.3)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e257.9 (143.8, 487.7)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e84.9 (58.0, 144.2)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e\u0026lt;\u0026thinsp;0.001\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003ctfoot\u003e \u003ctr\u003e\u003ctd colspan=\"7\"\u003e\u003cem\u003eValues are presented as median (interquartile range, IQR) or number (percentage). SE\u0026thinsp;=\u0026thinsp;spherical equivalent; BCVA\u0026thinsp;=\u0026thinsp;best-corrected visual acuity; Fix_X\u0026thinsp;=\u0026thinsp;horizontal targeting displacement; Fix_Y\u0026thinsp;=\u0026thinsp;vertical targeting displacement; TD\u0026thinsp;=\u0026thinsp;targeting displacement. P values are from Kruskal\u0026ndash;Wallis or χ\u0026sup2; tests as appropriate.\u003c/em\u003e\u003c/td\u003e\u003c/tr\u003e \u003c/tfoot\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e\n\u003ch3\u003e2. Subtype-Specific Fixation Instability\u003c/h3\u003e\n\u003cp\u003eBinocular fixation instability, quantified as TD, was significantly greater in all amblyopia subtypes compared with controls (all P\u0026thinsp;\u0026lt;\u0026thinsp;0.001). The magnitude of instability differed by subtype, median TD difference was +\u0026thinsp;40.3px [95% CI: 25.7\u0026ndash;55.7] in ametropic amblyopia, +\u0026thinsp;32.1px [19.6\u0026ndash;45.6] in anisometropic amblyopia, and +\u0026thinsp;149.3px [92.7\u0026ndash;213.5] in strabismic amblyopia respectively (all P\u0026thinsp;\u0026lt;\u0026thinsp;0.001; Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e). The largest effect was observed in strabismic amblyopia, which showed marked deficits in horizontal (Fix_X), vertical (Fix_Y), and mean TD (all P\u0026thinsp;\u0026lt;\u0026thinsp;0.001 vs. other subtypes).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e\n\u003ch3\u003e3. Nonlinear BCVA–TD Association in Strabismic Amblyopia\u003c/h3\u003e\n\u003cp\u003eLOESS plots revealed a distinct threshold-dependent relationship exclusively in strabismic amblyopia (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e). While ametropic, anisometropic, and control groups showed flat BCVA\u0026ndash;TD curves, strabismic cases exhibited accelerated TD escalation when BCVA exceeded 0.3 logMAR.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e\n\u003ch3\u003e4. GAMs Ananlysis and Threshold Identification\u003c/h3\u003e\n\u003cp\u003eGAM analysis confirmed a significant nonlinear association between BCVA and TD in strabismic amblyopia (edf\u0026thinsp;=\u0026thinsp;4.46, P\u0026thinsp;=\u0026thinsp;0.002). Marginal effect analysis identified a critical inflection point at 0.321 logMAR (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003eA), beyond which TD increase sharply. Specifically, each 0.1 logMAR decrease in acuity was associated with an additional 38.2 px increase in TD (95% CI: 25.7\u0026ndash;50.7; Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e\n\u003ch3\u003e5. Refractive Error Modulation\u003c/h3\u003e\n\u003cp\u003eTensor product interactions indicated that higher SE amplification BCVA-related increases in fixation instability (TD) in ametropic amblyopia (\u003cem\u003eβ\u003c/em\u003e = +17.3 px/D per logMAR unit, P\u0026thinsp;=\u0026thinsp;0.013) and strabismic (\u003cem\u003eβ\u003c/em\u003e = +42.6 px/D per logMAR unit, P\u0026thinsp;=\u0026thinsp;0.004). The interaction model explained 27.9% of TD variance (adjusted R\u0026sup2; = 0.251), outperforming the main-effect model (Δdeviance explained\u0026thinsp;=\u0026thinsp;4.6%, P\u0026thinsp;\u0026lt;\u0026thinsp;0.001; Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e).\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eComparison of Parametric and Smooth Effects Between the Main Effect and Interaction Models\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"7\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eVariable\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c4\" namest=\"c3\"\u003e \u003cp\u003eModel1\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c7\" namest=\"c6\"\u003e \u003cp\u003eModel2\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eParametric Terms\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eEstimate\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003ep-value\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eEstimate\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003ep-value\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e(Intercept)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e103.490\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.003\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e110.071\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.001\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAge\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-11.250\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u0026lt;\u0026thinsp;0.001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-10.551\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u0026lt;\u0026thinsp;0.001\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eGender\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eBoys\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0(ref)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0(ref)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eGirls\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-23.728\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.004\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-21.803\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.008\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSE\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e2.341\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.155\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u0026mdash;\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u0026mdash;\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eFine stereopsis\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e57.987\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u0026lt;\u0026thinsp;0.001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e52.618\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u0026lt;\u0026thinsp;0.001\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eType_group\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAmetropic\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0(ref)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0(ref)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAnisometropic\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-28.015\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.057\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-23.129\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.111\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eStrabismic\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e199.350\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u0026lt;\u0026thinsp;0.001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e215.116\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u0026lt;\u0026thinsp;0.001\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eControl\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-22.227\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.268\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-19.070\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.334\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSmooth Terms\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eedf\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003ep-value\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eedf\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003ep-value\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003es(BCVA): Ametropic\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e3.764\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.404\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e3.732\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.228\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003es(BCVA): Anisometropic\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1.001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.472\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e1.001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.610\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003es(BCVA): Strabismic\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e4.460\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.002\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e4.473\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.002\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003es(BCVA): Control\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1.002\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.472\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e1.001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.622\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003es(SE)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u0026mdash;\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u0026mdash;\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e1.585\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.524\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eInteraction Terms\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eedf\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003ep-value\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eedf\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003ep-value\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eti(BCVA, SE): Ametropic\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u0026mdash;\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u0026mdash;\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e2.708\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.013\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eti(BCVA, SE): Anisometropic\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u0026mdash;\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u0026mdash;\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e1.001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.977\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eti(BCVA, SE): Strabismic\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u0026mdash;\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u0026mdash;\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e4.703\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.004\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eti(BCVA, SE): Control\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u0026mdash;\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u0026mdash;\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.977\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eR-sq.(adj)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.213\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.251\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eDeviance explained\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e23.3%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e27.9%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003ctfoot\u003e \u003ctr\u003e\u003ctd colspan=\"7\"\u003e\u003cem\u003eParametric terms represent fixed effects. Smooth terms are modeled using thin-plate regression splines. Interaction terms represent tensor product interactions between BCVA (best-corrected visual acuity) and SE (spherical equivalent). Model 1\u0026thinsp;=\u0026thinsp;main-effect model; Model 2\u0026thinsp;=\u0026thinsp;interaction model. Adjusted R\u0026sup2; and deviance explained reflect overall model performance. Significant effects are bolded.\u003c/em\u003e\u003c/td\u003e\u003c/tr\u003e \u003c/tfoot\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e\n\u003ch3\u003e6. Bootstrap Validation of Nonlinear Effects\u003c/h3\u003e\n\u003cp\u003eIn the strabismic subgroup (n\u0026thinsp;=\u0026thinsp;32), bootstrap resampling (n\u0026thinsp;=\u0026thinsp;1,000 iterations) confirmed robustness of nonlinear effect: the 95% CI for edf of the BCVA smooth term ranged from 3.1\u0026ndash;7.2, and 38.7% of resamples showed P\u0026thinsp;\u0026lt;\u0026thinsp;0.01 for nonlinearity.\u003c/p\u003e\n\u003ch3\u003e7. Sensory-Motor Decoupling Beyond the Threshold\u003c/h3\u003e\n\u003cp\u003eMarginal effect curves illustrated an abrupt shift in fixation stability in strabismic amblyopia at the identified BCVA threshold (Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e). Below 0.321 logMAR, TD remained stable (slope = -5.2 px/logMAR). Above the threshold, TD increased steeply (slope\u0026thinsp;=\u0026thinsp;+\u0026thinsp;49.1 px/logMAR, 95% CI: +32.7\u0026ndash;+65.5), consistent with a collapse of binocular fixation control.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e"},{"header":"Discussions","content":"\n\u003ch3\u003e1. Principal Findings\u003c/h3\u003e\n\u003cp\u003eThis study identified a critical BCVA threshold of 0.321 logMAR (\u0026asymp;\u0026thinsp;20/42 Snellen), beyond which binocular fixation stability deteriorated sharply in children with strabismic amblyopia. Refractive error further amplified this sensory\u0026ndash;motor decoupling in both ametropic and strabismic subtypes. These findings extend previous work by demonstrating that fixation instability is not merely proportional to acuity loss, but instead follows a threshold-dependent trajectory in strabismus.\u003c/p\u003e\n\u003ch3\u003e2. Integration with Previous Research\u003c/h3\u003e\n\u003cp\u003eOur results confirm and refine prior observations that fixation instability is a hallmark of amblyopia \u003csup\u003e\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e, \u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e\u003c/sup\u003e. Subramanian et al. \u003csup\u003e6\u003c/sup\u003e reported reduced fixation stability in amblyopic children using monocular recordings, while Kelly et al.\u003csup\u003e7\u003c/sup\u003e demonstrated greater instability in binocular conditions. By applying nonlinear modeling, we show that strabismic amblyopia is uniquely characterized by an abrupt inflection point, consistent with Birch's hypothesis of cortical integration failure when acuity loss surpasses a functional limit \u003csup\u003e\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e\u003c/sup\u003e. This may explain why some smaller studies failed to detect clear associations between acuity and fixation \u003csup\u003e\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e\u003c/sup\u003e\u0026mdash;linear models likely masked threshold effects.\u003c/p\u003e \u003cp\u003eWe also found that higher SE exacerbates fixation instability in ametropic and strabismic amblyopia, consistent with Wahl et al.'s proposal that optical defocus increases neural noise and disrupts microsaccade control \u003csup\u003e\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e\u003c/sup\u003e. In contrast, anisometropic amblyopia showed little BCVA\u0026ndash;TD coupling, unlike strabismic amblyopia caused by ocular misalignment and abnormal dorsal oculomotor circuits, anisometropic amblyopia is mainly characterized by interocular aniseikonia and asymmetric retinal image quality, rather than strabismus \u003csup\u003e\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e\u003c/sup\u003e. Long-term binocular perceptual imbalance during visual development leads to specific cortical remodeling and compensatory fixation control in anisometropic amblyopia \u003csup\u003e\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e\u003c/sup\u003e. instead of increased neural noise in oculomotor pathways. Combined with preserved ocular alignment \u003csup\u003e\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e\u003c/sup\u003e, this subtype-specific mechanism may explain the weak BCVA\u0026ndash;TD coupling in anisometropic amblyopia. Taken together, these findings indicate that fixation instability in amblyopia is not uniform, but varies by subtype, acuity threshold, and refractive factors; this threshold-dependent pattern likely reflects underlying cortical and oculomotor mechanisms.\u003c/p\u003e\n\u003ch3\u003e3. Neurobiological Interpretation\u003c/h3\u003e\n\u003cp\u003eBuilding on the threshold-dependent pattern observed in strabismic amblyopia, the identified threshold at 0.321 logMAR likely reflects a transition in cortical control of fixation. Below this level, residual binocular input may stabilize gaze through dorsal stream regulation of the superior colliculus \u003csup\u003e\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e\u003c/sup\u003e. Beyond the threshold, imbalanced input to V1/V2 disrupts efferent copy signals to frontal eye fields, precipitating fixation collapse \u003csup\u003e\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e, \u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e\u003c/sup\u003e. Functional MRI studies in amblyopia have documented abnormal parvocellular pathway activation and impaired integration across extrastriate areas \u003csup\u003e\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e, \u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e\u003c/sup\u003e, supporting this interpretation.\u003c/p\u003e\n\u003ch3\u003e4. Clinical Translation and Rehabilitation Implications\u003c/h3\u003e\n\u003cp\u003eThese findings have several clinical applications. (1) Threshold-Guided Intervention: For strabismic amblyopia with BCVA worse than 0.321 logMAR, early refractive correction is critical to mitigate SE-related amplification of instability (\u003cem\u003eβ\u003c/em\u003e = +42.6 px/D), followed by binocular integration training (e.g., dichoptic motion tasks) to restore sensory\u0026ndash;motor integration \u003csup\u003e\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e\u003c/sup\u003e. (2) Subtype-Specific strategies: Strabismic amblyopia may benefit from gaze stabilization therapy (Counteracts threshold-triggered collapse), ametropic amblyopia from high-frequency spatial training to reduce neural noise \u003csup\u003e\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e\u003c/sup\u003e, and anisometropic amblyopia from contrast-balanced binocular approaches \u003csup\u003e\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e, \u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e\u003c/sup\u003e. (3) Prognostic value: Fixation stability could serve as a biomarker of disease severity and treatment responsiveness, aligning with recent efforts to incorporate oculomotor endpoints in amblyopia trials \u003csup\u003e\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e, \u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e\n\u003ch3\u003e5. Methodological Advances\u003c/h3\u003e\n\u003cp\u003eThis study introduces several methodological strengths. First, binocular eye-tracking captures naturalistic fixation control, addressing limitations of earlier monocular paradigms \u003csup\u003e\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e\u003c/sup\u003e. Second, GAMs reveal nonlinear threshold effects that conventional regression approaches cannot detect \u003csup\u003e\u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e\u003c/sup\u003e. Third, interaction modeling demonstrated for the first time that refractive error modulates fixation instability in a subtype-dependent manner (P\u003csub\u003einteraction\u003c/sub\u003e \u0026lt; 0.01). Together, these advances support the utility of nonlinear modeling in pediatric vision science.\u003c/p\u003e\n\u003ch3\u003e6. Limitations and Future Directions\u003c/h3\u003e\n\u003cp\u003eSeveral limitations warrant consideration. The cross-sectional design precludes causal inference regarding whether acuity decline precedes fixation collapse. Longitudinal data from the ongoing CABC study will be essential to address temporal dynamics. In addition, the relatively small strabismic sample (n\u0026thinsp;=\u0026thinsp;32) requires replication in larger cohorts, although bootstrap validation supports robustness. Finally, the current study only utilized a spatial dispersion metric TD (to quantify binocular fixation instability), which provides a limited view of oculomotor function. To generate a more comprehensive oculomotor profile and refine mechanistic interpretations, future work should incorporate additional oculomotor metrics such as microsaccade frequency and drift velocity to refine mechanistic interpretation.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eConflicts of Interest\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe author(s) declare that there are no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eFunding\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThis study was supported by the Guangxi Key Research and Development Program (No. Guike AB23026047), Guangxi Natural Science Foundation (2024GXNSFAA010262), Guangdong Basic and Applied Basic Research Foundation (2021A1515011822), Guangxi Medical and Health Appropriate Technology Research and Development Project (2023003), and Guangxi Clinical Ophthalmic Research Center (No. Guike AD19245193). All funding parties did not have any role in the study design, conduct of this research, data analysis, or decisions in preparation or publishing of the manuscript.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAuthor Contribution Statement\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eConceptualization: J.L., J.Z., X.X.; Methodology:J.L., J.Z., X.X.; Formal analysis: M.R.; Investigation: L.P., Y.H., W.L., L.L., Y.L., E.L., M.K., Q.C., Y.L.; Data curation: L.P., M.R., Y.H., L.L., Y.L., Q.C., Y.L.,E.L.; Validation: W.L., M.K., Q.C.; Writing-original draft: All authors; Writing-review \u0026amp; editing:J.L., J.Z., X.X.; Funding acquisition:J.L., J.Z., X.X\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eLevi DM. Rethinking amblyopia 2020. \u003cem\u003eVision research\u003c/em\u003e 2020; 176: 118\u0026ndash;129.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eKates MM, Beal CJ. Amblyopia. \u003cem\u003eJama\u003c/em\u003e 2021; 325(4): 408.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eCruz OA, Repka MX, Hercinovic A, Cotter SA, Lambert SR, Hutchinson AK \u003cem\u003eet al.\u003c/em\u003e Amblyopia Preferred Practice Pattern. \u003cem\u003eOphthalmology\u003c/em\u003e 2023; 130(3): P136-p178.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eBirch EE. Amblyopia and binocular vision. \u003cem\u003eProgress in retinal and eye research\u003c/em\u003e 2013; 33: 67\u0026ndash;84.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eRandhawa S, Griffiths N, O'Brien P, Panter C, Boparai K, Harrad R \u003cem\u003eet al.\u003c/em\u003e Qualitative Exploration of the Visual Function Impairments and Health-Related Quality of Life Impacts of Amblyopia in Adult and Pediatric Populations. \u003cem\u003eOphthalmol Ther\u003c/em\u003e 2023; 12(5): 2505\u0026ndash;2528.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eSubramanian V, Jost RM, Birch EE. A quantitative study of fixation stability in amblyopia. \u003cem\u003eInvestigative ophthalmology \u0026amp; visual science\u003c/em\u003e 2013; 54(3): 1998\u0026ndash;2003.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eKelly KR, Cheng-Patel CS, Jost RM, Wang YZ, Birch EE. Fixation instability during binocular viewing in anisometropic and strabismic children. \u003cem\u003eExp Eye Res\u003c/em\u003e 2019; 183: 29\u0026ndash;37.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eAizenman AM, Levi DM. Fixational stability as a measure for the recovery of visual function in amblyopia. \u003cem\u003eProceedings Eye Tracking Research \u0026amp; Applications Symposium\u003c/em\u003e 2021; 2021.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eShaikh AG, Otero-Millan J, Kumar P, Ghasia FF. Abnormal Fixational Eye Movements in Amblyopia. \u003cem\u003ePloS one\u003c/em\u003e 2016; 11(3): e0149953.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eZhou Y, Bian H, Yu X, Wen W, Zhao C. Quantitative assessment of eye movements using a binocular paradigm: comparison among amblyopic, recovered amblyopic and normal children. \u003cem\u003eBMC ophthalmology\u003c/em\u003e 2022; 22(1): 365.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eAltinbay D, Sahli E, Bingol Kiziltunc P, Atilla H. Evaluation of fixation characteristics in amblyopia using microperimetry. \u003cem\u003eInternational ophthalmology\u003c/em\u003e 2023; 43(9): 3403\u0026ndash;3412.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eZhou Y, Yu W, Ye Q, Xu Z, He Y, Yao Y \u003cem\u003eet al.\u003c/em\u003e Fixation Stability Deficits in Anisometropic Amblyopia. \u003cem\u003eInvestigative ophthalmology \u0026amp; visual science\u003c/em\u003e 2025; 66(1): 14.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eHaraguchi Y, Cakir GB, Shaikh A, Ghasia F. Binocular and Fellow Eye Acuity Deficits in Amblyopia: Impact of Fixation Instability and Sensory Factors. \u003cem\u003eJournal of eye movement research\u003c/em\u003e 2025; 18(3): 20.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eGonzalez EG, Wong AM, Niechwiej-Szwedo E, Tarita-Nistor L, Steinbach MJ. Eye position stability in amblyopia and in normal binocular vision. \u003cem\u003eInvestigative ophthalmology \u0026amp; visual science\u003c/em\u003e 2012; 53(9): 5386\u0026ndash;5394.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eGhasia FF, Shaikh AG. Uncorrected Myopic Refractive Error Increases Microsaccade Amplitude. \u003cem\u003eInvestigative ophthalmology \u0026amp; visual science\u003c/em\u003e 2015; 56(4): 2531\u0026ndash;2535.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eWahl S, Dragneva D, Rifai K. The limits of fixation-Keeping the ametropic eye on target. \u003cem\u003eJournal of vision\u003c/em\u003e 2019; 19(13): 8.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eNiechwiej-Szwedo E, Colpa L, Wong AMF. Visuomotor Behaviour in Amblyopia: Deficits and Compensatory Adaptations. \u003cem\u003eNeural plasticity\u003c/em\u003e 2019; 2019: 6817839.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003e[Expert consensus on prevention and treatment of amblyopia in children]. \u003cem\u003e[Zhonghua yan ke za zhi] Chinese journal of ophthalmology\u003c/em\u003e 2021; 57(5): 336\u0026ndash;340.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eGhasia FF, Otero-Millan J, Shaikh AG. Abnormal fixational eye movements in strabismus. \u003cem\u003eThe British journal of ophthalmology\u003c/em\u003e 2018; 102(2): 253\u0026ndash;259.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eCohen J, Cohen J, Cohen JW, Cohen J, Cohen J, Cohen J \u003cem\u003eet al.\u003c/em\u003e Statistical power analysis for the behavioral science. \u003cem\u003eTechnometrics\u003c/em\u003e 1988; 31(4): 499\u0026ndash;500.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eHolmqvist K, Nystr\u0026ouml;m M, Andersson R, Dewhurst R, Jarodzka H, van de Weijer J \u003cem\u003eEye Tracking: A comprehensive guide to methods and measures\u003c/em\u003e. OUP Oxford; 2011.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003e. Identifying fixations and saccades in eye-tracking protocols. \u003cem\u003eEye Tracking Research \u0026amp; Application\u003c/em\u003e2000.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eLan J, Li Y, Pang S, Zhang G, Wu D, Yang C \u003cem\u003eet al.\u003c/em\u003e Targeting displacement as an indicator of binocular fixation in normal Chinese adults. \u003cem\u003eFrontiers in neuroscience\u003c/em\u003e 2023; 17: 1124034.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eWang Y, Wu Y, Luo L, Li F. Structural and functional alterations in the brains of patients with anisometropic and strabismic amblyopia: a systematic review of magnetic resonance imaging studies. \u003cem\u003eNeural regeneration research\u003c/em\u003e 2023; 18(11): 2348\u0026ndash;2356.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eHuang Y, Liu Z, Zhan Z, Zhang X, Gao L, Wang M \u003cem\u003eet al.\u003c/em\u003e Interactions between excitatory neurons and parvalbumin interneurons in V1 underlie neural mechanisms of amblyopia and visual stimulation treatment. \u003cem\u003eCommunications biology\u003c/em\u003e 2024; 7(1): 1564.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eWang H, Crewther SG, Liang M, Laycock R, Yu T, Alexander B \u003cem\u003eet al.\u003c/em\u003e Impaired Activation of Visual Attention Network for Motion Salience Is Accompanied by Reduced Functional Connectivity between Frontal Eye Fields and Visual Cortex in Strabismic Amblyopia. \u003cem\u003eFrontiers in human neuroscience\u003c/em\u003e 2017; 11: 195.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eScaramuzzi M, Murray J, Otero-Millan J, Nucci P, Shaikh AG, Ghasia FF. Fixation instability in amblyopia: Oculomotor disease biomarkers predictive of treatment effectiveness. \u003cem\u003eProgress in brain research\u003c/em\u003e 2019; 249: 235\u0026ndash;248.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eKelly KR, Jost RM, Wang YZ, Dao L, Beauchamp CL, Leffler JN \u003cem\u003eet al.\u003c/em\u003e Improved Binocular Outcomes Following Binocular Treatment for Childhood Amblyopia. \u003cem\u003eInvestigative ophthalmology \u0026amp; visual science\u003c/em\u003e 2018; 59(3): 1221\u0026ndash;1228.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eTilia D, Bakaraju RC, Asper LJ, Papas EB. Associations between Binocular Vision Disorders and Contact Lens Dissatisfaction. \u003cem\u003eOptometry and vision science: official publication of the American Academy of Optometry\u003c/em\u003e 2021; 98(10): 1160\u0026ndash;1168.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eGhasia F, Tychsen L. Inter-Ocular Fixation Instability of Amblyopia: Relationship to Visual Acuity, Strabismus, Nystagmus, Stereopsis, Vergence, and Age. \u003cem\u003eAmerican journal of ophthalmology\u003c/em\u003e 2024; 267: 230\u0026ndash;248.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eGhasia F, Wang J. Amblyopia and fixation eye movements. \u003cem\u003eJournal of the neurological sciences\u003c/em\u003e 2022; 441: 120373.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eChiang AY. Generalized Additive Models: An Introduction With R. \u003cem\u003eTechnometrics\u003c/em\u003e 2007; 49: 360\u0026ndash;361.\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"eye","isNatureJournal":false,"hasQc":false,"allowDirectSubmit":false,"externalIdentity":"eye","sideBox":"Learn more about [Eye](http://www.nature.com/eye/)","snPcode":"41433","submissionUrl":"https://mts-eye.nature.com/cgi-bin/main.plex","title":"Eye","twitterHandle":"@eye_journal","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"ejp","reportingPortfolio":"Nature AJ","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"","lastPublishedDoi":"10.21203/rs.3.rs-9490101/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9490101/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003ch2\u003ePurpose\u003c/h2\u003e \u003cp\u003eTo determine the critical best-corrected visual acuity (BCVA) threshold associated with binocular fixation instability in children with strabismic amblyopia, and to evaluate the modulatory effect of refractive error on this sensory\u0026ndash;motor coupling using high-resolution eye tracking and nonlinear modeling.\u003c/p\u003e\u003ch2\u003eMethods\u003c/h2\u003e \u003cp\u003eIn this multicenter case-control study, 536 children with amblyopia and 159 sex-matched controls were enrolled from the China Amblyopia Behavior Cohort (CABC, 2024\u0026ndash;2025). Binocular fixation stability (primary outcome: targeting displacement [TD]) was measured with a 133 Hz Tobii Eye Tracker 4. LOESS smoothing and generalized additive models (GAMs) were applied to characterize nonlinear BCVA\u0026ndash;TD relationships. Tensor product interactions tested the moderating effect of spherical equivalent (SE).\u003c/p\u003e\u003ch2\u003eResults\u003c/h2\u003e \u003cp\u003eAll amblyopia subtypes exhibited significantly greater fixation instability compared with controls (all P\u0026thinsp;\u0026lt;\u0026thinsp;0.001). A nonlinear BCVA\u0026ndash;TD relationship was observed exclusively in strabismic amblyopia, with fixation instability increasing sharply beyond a BCVA threshold of 0.321 logMAR (effective degrees of freedom, 4.46; P\u0026thinsp;=\u0026thinsp;0.002). Higher SE amplified BCVA-related TD increases in ametropic (P\u0026thinsp;=\u0026thinsp;0.013) and strabismic (P\u0026thinsp;=\u0026thinsp;0.004) subtypes, demonstrating refractive error modulation of sensory-motor coupling. The interaction model explained 27.9% of TD variance (adjusted R\u0026sup2; = 0.251).\u003c/p\u003e\u003ch2\u003eConclusions\u003c/h2\u003e \u003cp\u003eStrabismic amblyopia shows abrupt fixation instability beyond 0.321 logMAR; refractive error exacerbates this in ametropic/strabismic subtypes. Fixation stability should be a routine biomarker, with optimized refractive correction before strabismic BCVA falls below this threshold.\u003c/p\u003e","manuscriptTitle":"Critical BCVA Threshold and Refractive Error Modulation for Fixation Instability in Strabismic Amblyopia: Revealed by Eye-Tracking and GAM Modeling","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-05-12 14:25:53","doi":"10.21203/rs.3.rs-9490101/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"reviewersInvited","content":"","date":"2026-05-04T06:50:35+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2026-04-30T13:47:39+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2026-04-23T13:55:46+00:00","index":"","fulltext":""},{"type":"submitted","content":"Eye","date":"2026-04-22T03:05:45+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"eye","isNatureJournal":false,"hasQc":false,"allowDirectSubmit":false,"externalIdentity":"eye","sideBox":"Learn more about [Eye](http://www.nature.com/eye/)","snPcode":"41433","submissionUrl":"https://mts-eye.nature.com/cgi-bin/main.plex","title":"Eye","twitterHandle":"@eye_journal","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"ejp","reportingPortfolio":"Nature AJ","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"76973116-4d4a-4d6c-a963-dca64fcbf459","owner":[],"postedDate":"May 12th, 2026","published":true,"recentEditorialEvents":[{"type":"reviewersInvited","content":"3","date":"2026-05-04T06:50:35+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2026-04-30T13:47:39+00:00","index":"","fulltext":""}],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[{"id":67325365,"name":"Health sciences/Diseases/Eye diseases/Refractive errors"},{"id":67325366,"name":"Health sciences/Medical research/Epidemiology"}],"tags":[],"updatedAt":"2026-05-12T14:25:56+00:00","versionOfRecord":[],"versionCreatedAt":"2026-05-12 14:25:53","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-9490101","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-9490101","identity":"rs-9490101","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}