Development and validation of a machine learning-based model for predicting live birth outcomes in patients undergoing frozen-thawed embryo transfer.

This study employed a retrospective-prospective mixed cohort design. Retrospective data were collected from patients who underwent FET cycles at the Department of Reproductive Medicine, Affiliated Hospital of Zunyi Medical University, between January 2021 and December 2023 for model development and internal validation. Prospective data were collected from patients between January 2024 and December 2024 for external validation of the model. This study was approved by the Ethics Committee of the Affiliated Hospital of Zunyi Medical University (KLLY-2024-030). All procedures were conducted in accordance with relevant guidelines and regulations (Declaration of Helsinki). Inclusion criteria were: (1) patients undergoing an FET cycle; (2) age 20–42 years. Exclusion criteria were: (1) chromosomal abnormalities in either partner; (2) concurrent severe systemic diseases, such as hypertension, diabetes, or heart disease; (3) patients who had undergone preimplantation genetic diagnosis (PGD) or preimplantation genetic screening (PGS); (4) patients with missing data exceeding 20% in general or clinical records (Fig.  1 ). Fig. 1 Flow diagram Flow diagram According to the “events per variable” (EPV) criterion for clinical predictive models, each predictor variable required at least 10 outcome events (EPV ≥ 10). Relevant literature reported that the live birth rate for FET cycles ranged from 37.98% to 43.05% [ 15 ]. This study adopted the minimum value of 37.98% for a conservative estimate. After screening via LASSO regression, a total of 12 candidate predictor variables were retained, and the required minimum sample size was calculated to be 316 cases. Considering that data incompleteness could result in a 20% loss, the target sample size was set at 379 cases. We ultimately enrolled 3,470 patients in the retrospective cohort, which was randomly divided into training and testing sets at a 7:3 ratio. An additional 1,476 patients were enrolled in an independent prospective cohort for external validation. All eligible patients were enrolled during the study period to minimize selection bias and ensure the accuracy and reliability of the model development. All data were extracted from standardized clinical medical records. The analysis encompassed seven dimensions—patient demographics, medical history, ovarian reserve, ovulation induction-related factors, endometrial factors, embryo laboratory parameters, and endocrine and metabolic factors—comprising a total of 42 influencing indicators. Patient demographics included female age, body mass index (BMI), educational level, ethnicity, marital status, duration of infertility, type of infertility, cause of infertility, and method of fertilization. Medical history included history of alcohol consumption, smoking, cesarean section, intrauterine adhesions, insulin resistance, obstetric history (number of pregnancies and deliveries), history of miscarriage, history of syphilis infection, and history of FET (frozen-thawed embryo transfer). Ovarian reserve function included follicle-stimulating hormone (FSH), luteinizing hormone (LH), estradiol (E2), progesterone (P), anti-Müllerian hormone (AMH), and antral follicle count (AFC). Ovarian stimulation-related factors included P level on the day of human chorionic gonadotropin (hCG) administration, E2 level on the day of hCG administration, and endometrial thickness on the day of hCG administration. Endometrial factors included endometrial preparation protocol, duration of endometrial preparation, P level on the day of endometrial conversion, E2 level on the day of endometrial conversion, and endometrial thickness on the day before transfer. Embryology laboratory parameters included number of embryos transferred, number of high-quality embryos transferred, number of blastocysts transferred, embryo type, and duration of embryo cryopreservation. Endocrine and metabolic factors included basal prolactin, blood glucose, thyroid-stimulating hormone (TSH), and alanine aminotransferase (ALT) levels. Data cleaning and preprocessing involved standardization and converting textual descriptions into numerical values to ensure data quality and accuracy. Continuous variables retained their original numerical values. Binary variables, such as infertility type (primary infertility = 0, secondary infertility = 1) and live birth outcome (live birth = 1, stillbirth = 0), were coded accordingly. Multicategorical variables were processed using one-hot encoding. This study employed the K-Nearest Neighbors (KNN) interpolation method to impute missing values for all variables. KNN interpolation identified the K neighbors most similar to the missing sample and estimated the missing value using the weighted average (for continuous variables) or the mode (for categorical variables) of these neighbors. After KNN interpolation, missing values for all variables were fully imputed. Patients with more than 20% missing data were excluded. Endometrial preparation protocols included the following: For patients with a history of spontaneous ovulation, a natural cycle protocol was used. Starting from days 8–12 of the menstrual cycle, follicular and endometrial development was monitored via ultrasound. The timing of ovulation was determined based on serum LH, E2, and P levels (requiring endometrial thickness ≥ 8 mm and a dominant follicle diameter ≥ 18 mm). Subsequently, hCG was administered to induce ovulation, followed by intramuscular injections of 20 mg of progesterone every other day to promote endometrial conversion.For patients with delayed or absent ovulation, an ovulation induction protocol was selected. Clomiphene or letrozole was administered on days 2–5 of the menstrual cycle to stimulate ovulation. Follicular and endometrial development was monitored via ultrasound. When the dominant follicle reached a diameter of ≥ 18 mm and the endometrial thickness was ≥ 8 mm, hCG was administered to induce ovulation, followed by luteal phase support and embryo transfer.For patients with irregular menstrual cycles, a hormone replacement cycle protocol was used. Starting on day 3 of the menstrual cycle, oral estradiol/estradiol-dydrogesterone tablets or estradiol valerate were administered at 4 mg daily. On days 10–12 of the cycle, hormone levels and transvaginal ultrasound were monitored, and the estrogen dose was adjusted based on the results, with a maximum dose of 8 mg. Once the endometrial thickness reached ≥ 8 mm and no mature follicles were present in either ovary, an individualized dose of progesterone was administered via intramuscular injection, followed by embryo thawing and transfer.For patients with a history of recurrent miscarriage or endometriosis, a down-regulation plus artificial cycle protocol was used. Leuprolide acetate (3.75 mg) was administered intramuscularly on days 2–5 of the menstrual cycle. Hormone levels and transvaginal ultrasound were re-evaluated 28 days later. Once down-regulation criteria were met (LH < 5 mIU/mL, FSH < 5 mIU/mL, E2 < 183.5 pmol/L, endometrial thickness ≤ 5 mm), endometrial preparation was performed according to the hormone-suppressed cycle protocol. The primary clinical outcome of this study was live birth, defined as the delivery of at least one infant exhibiting cardiac activity, respiration, umbilical cord pulsation, or muscle tone at or after 28 weeks of gestation. This study retrospectively collected clinical data from January 2021 to December 2023. Using complete random sampling, the dataset was divided into training and testing sets at a 7:3 ratio for model construction and internal validation. Patients were prospectively enrolled from January 2024 to December 2024 for external model validation to assess the model’s generalization ability. During the model development phase, to optimize the ML models and mitigate the effects of multicollinearity, we first performed feature selection on the predictor variables in the training set using LASSO regression and multivariate logistic regression to optimize the model inputs. Based on the selected features, we constructed three supervised ML models: logistic regression (LR), random forest (RF), and XGBoost. LR is a generalized linear regression model suitable for binary and multi-class classification problems and offers good probabilistic interpretability [ 16 ]. RF is an ensemble learning algorithm whose basic building blocks are decision trees [ 17 ] As a non-parametric, non-linear statistical learning method, RF is versatile across various types of response variables, from classification to quantitative outcome prediction and survival analysis, and can improve predictive performance by combining multiple decision trees [ 18 ]. The XGBoost algorithm is based on gradient-boosted decision trees and uses the second-order Taylor expansion to compute the loss function. This method is renowned for its outstanding computational speed and predictive accuracy. XGBoost iteratively improves predictions by continuously splitting features to promote tree growth and fitting the residuals of previous models. Upon completion of training, K decision trees are generated. For a given sample, its features correspond to different leaves at the nodes of each decision tree; each leaf is assigned a score, and the final prediction is calculated by aggregating the scores from all trees [ 19 ]. XGBoost is an excellent robust classifier that offers advantages including effective handling of missing values, reduced risk of overfitting, and accelerated runtime via parallel and distributed computing strategies [ 20 ]. To mitigate the risk of overfitting, grid search combined with five-fold cross-validation was used for hyperparameter tuning, and performance was evaluated on an independent test set and an external validation set. For model evaluation, this study employed a comprehensive metric system to thoroughly assess predictive performance. First, discriminative ability was evaluated using the receiver operating characteristic (ROC) curve and the area under the curve (AUC). Second, predictive accuracy was analyzed using calibration curves, and the Brier score was calculated to quantify the overall accuracy of predicted probabilities. Additionally, clinical utility was assessed using decision curve analysis (DCA). Furthermore, we calculated multiple metrics, including sensitivity, specificity, accuracy, precision, positive predictive value (PPV), negative predictive value (NPV), and F1 score, to ensure comprehensiveness and reliability. To enhance model interpretability, this study introduced the SHAP analysis method [ 21 ]. This method quantifies the contribution of each feature to the model’s predictions and distinguishes between positive and negative effects, providing both global and local explanations. Through feature importance ranking plots and individual sample SHAP heatmaps, we identified the key features most influencing prediction results and provided personalized prediction explanations for specific samples. The SHAP method effectively enhanced model transparency, aiding clinical decision support and personalized risk assessment. All statistical analyses and data visualizations were performed using R 4.3.2 and SPSS 29.0. Mean ± standard deviation (SD) was used to describe normally distributed continuous data, and t-tests were used to compare differences between two groups. Median and quartiles [M(Q1, Q3)] were used for non-normally distributed continuous data, and the Wilcoxon signed-rank test was used to compare differences between groups. Categorical data were described using counts and proportions (n (%)), and differences between groups were compared using the chi-square test. All statistical tests were two-sided, and P-values < 0.05 were considered statistically significant.

The retrospective cohort included 3,470 patients, of whom 1,430 achieved live birth, resulting in a live birth rate of 41.21%. The prospective cohort included 1,467 patients, of whom 675 achieved live birth, resulting in a live birth rate of 46.01%. A summary of patient characteristics in the live birth and non-live birth groups is presented in Table  1 . Age, educational level, marital status, obstetric history, history of miscarriage, number of FET cycles, history of cesarean section, history of intrauterine adhesions, duration of infertility, type of infertility, AMH, AFC, FSH, LH, blood glucose level, endometrial thickness on the day of hCG administration, number of blastocysts transferred, number of high-quality embryos transferred, embryo type, and endometrial preparation protocol showed significant differences between the two groups ( P   0.05). Table 1 Baseline characteristics of patients in internal cohort Variable Live Birth Group ( n  = 1430) Non-live birth group ( n  = 2040) z/χ² P -value Female age (year) 31(28,34) 33(30,37) -10.939 <0.001 BMI(kg/m2) 22.03(20.20,24.24) 22.22(20.17,24.56) -1.424 0.154 Ethnicityn(% ) 0.241 0.624  Han 1253(87.6%) 1776(87.1%)  Other 177(12.4%) 264(12.9%) Educational Attainment(% ) 25.541 <0.001  Elementary school or below 57(4.0%) 162(7.9%)  Junior high school or vocational school 674(47.1%) 978(47.9%)  High school or junior college 334(23.4%) 415(20.3%)  Bachelor’s degree or higher 365(25.5%) 485(23.8%) Marital Status(% ) 6.297 0.012  First marriage 1113(77.8%) 1512(74.1%)  Remarriage 317(22.2%) 528(25.9%) Duration of infertility(year) 4(2,6) 4(2,7) -4.450 <0.001 Type of infertility(% ) 9.121 0.003  Primary infertility 589(41.2%) 737(36.1%)  Secondary infertility 841(58.8%) 1303(63.9%) Causes of infertility(% ) 4.100 0.251  Male 70(4.9%) 82(4.0%)  Female 955(66.8%) 1353(66.3%)  Both 369(25.8%) 566(27.7%)  Unknown 36(2.5%) 39(1.9%) AMH(ng/mL) 3.84(2.46,5.74) 2.94(1.65,4.91) -10.979 <0.001 AFC 18.00(13.00,23.00) 14.00(10.00,20.00) -10.928 <0.001 Baseline FSH(mIU/mL) 6.40(5.50,7.60) 6.70(5.70,8.20) -5.484 <0.001 Baseline LH(mIU/mL) 5.40(4.10,7.53) 5.40(3.90,7.26) -2.031 0.042 Baseline E2(pmol/L) 138.20(102.88,195.10) 141.20(105.70,195.03) -1.176 0.239 Baseline P(ng/mL) 1.15(0.71,2.90) 1.12(0.71,2.39) -1.073 0.283 Baseline PRL(mIu/L) 345.95(258.50,449.55) 348.70(252.20,461.40) -0.572 0.567 Smoking-female(% ) 0.282 0.595  Yes 34(2.4%) 43(2.1%)  No 1396(97.6%) 1997(97.9%) Alcohol consumption-female(% ) 0.256 0.613  Yes 4(0.3%) 4(0.2%)  No 1426(99.7%) 2036(99.8%) Reproductive history(% )  Pregnancy 1(0,2) 1(0,2) -4.076 <0.001  Parity 0(0,1) 0(0,1) -4.528 <0.001 History of miscarriage(% ) 12.033 <0.001  < 2 1242(86.9%) 1683(82.5%)  ≥ 2 188(13.1%) 357(17.5%) History of cesarean section(% ) 28.579 <0.001  Yes 198(13.8%) 427(20.9%)  No 1232(86.2%) 1613(79.1%) History of intrauterine adhesions(% ) 30.974 <0.001  Yes 65(4.5%) 196(9.6%)  No 1365(95.5%) 1844(90.4%) History of insulin resistance(% ) 0.516 0.473  Yes 205(14.3%) 275(13.5%)  No 1225(85.7%) 1765(86.5%) History of syphilis infection(% ) 1.872 0.171  Yes 38(2.7%) 71(3.5%)  No 1392(97.3%) 1969(96.5%) Blood glucose(mmol/L ) 4.83(4.48,5.12) 4.86(4.54,5.20) -2.647 0.008 TSH(mIU/L ) 2.12(1.49,2.77) 2.13(1.51,2.84) -0.771 0.441 ALT(U/L ) 21.00(18.00,25.00) 21.00(18.00,25.30) -1.233 0.218 Number of previous FET transfers 1(1,2) 2(1,3) -23.625 <0.001 Fertilization(% ) 1.256 0.262  IVF 1174(82.1%) 1644(80.6%)  ICSI 256(17.9%) 396(19.4%) E2 on HCG day(pg/mL) 9839.50(6744.00,21495.00) 8306.00(5575.50,18258.50) -8.375 <0.001 P on HCG day(ng/mL) 2.04(1.36,2.99) 1.93(1.27,2.85) -2.899 0.004 Endometrial thickness on HCG day(mm) 10.40(8.90,12.00) 9.90(8.10,11.70) -6.811 <0.001 Endometrial Preparation Time(day ) 12.00(10.00,14.00) 12.00(10.00,14.00) -0.530 0.596 FET protocol(% ) 15.474 0.001  NC 181(12.7%) 333(16.3%)  OS 43(3.0%) 89(4.4%)  HRT 1125(78.7%) 1492(73.1%)  GnRH-a-HRT 81(5.7%) 126(6.2%) E2 on endometrial conversion day (pmol/L) 739.50(550.55,1073.00) 667.25(517.08,952.30) -5.692 <0.001 P on endometrial conversion day (ng/mL) 0.51(0.24,0.87) 0.50(0.23,0.88) -0.330 0.742 Endometrial thickness on conversion day(mm) 8.60(8.10,9.50) 8.50(8.00,9.40) -4.283 <0.001 Endometrial thickness on the day before transfer(mm) 9.40(8.40,10.70) 9.20(8.20,10.50) -3.667 <0.001 Type of embryos transferred(% ) 133.115 <0.001  Cleavage 265(18.5%) 747(36.6%)  Blastocyst 1165(81.5%) 1293(63.4%) Number of transferred embryos(% ) 0.510 0.475  1 901(63.0%) 1261(61.8%)  2 529(37.0%) 779(38.2%) Number of blastocysts transferred 1(1,1) 1(0,1) -11.851 <0.001 Number of high-quality embryos transferred 1(0,1) 0(0,1) -3.666  1 ≤ 3years 147(10.30%) 239(11.7%)  > 3years 66(4.6%) 90(4.4%) Baseline characteristics of patients in internal cohort Endometrial thickness on HCG day(mm) Endometrial thickness on conversion day(mm) To mitigate the impact of multicollinearity, we employed LASSO combined with multivariate logistic regression to identify predictive variables. First, we used LASSO regression with 10-fold cross-validation to identify the optimal regularization parameter λ. Using λ1se (λ = 0.023619) as the selection criterion, we identified the 12 most predictive variables. Fig.  2 A and B illustrate the variable selection process based on LASSO regression. Next, the 12 predictive variables were incorporated into a multivariate logistic regression model for secondary screening. The features selected for the final model included age, AMH, duration of infertility, number of FET cycles, number of blastocysts transferred, number of high-quality embryos transferred, E2 on the day of hCG administration, endometrial thickness on the day of hCG administration, embryo type at transfer, and history of intrauterine adhesions (Table  2 ). Fig. 2 A LASSO coefficient path plot. B LASSO regularization path plot. When the regularization parameter lambda is set to 0.023619,the model retains predictive performance while using fewer features, selecting 12 variables: age, duration of infertility, AMH, AFC, FSH, E2 on HCG day, endometrial thickness on HCG day, number of blastocysts transferred, number of high-quality embryos transferred, embryo type, history of intrauterine adhesions, and number of FET cycles A LASSO coefficient path plot. B LASSO regularization path plot. When the regularization parameter lambda is set to 0.023619,the model retains predictive performance while using fewer features, selecting 12 variables: age, duration of infertility, AMH, AFC, FSH, E2 on HCG day, endometrial thickness on HCG day, number of blastocysts transferred, number of high-quality embryos transferred, embryo type, history of intrauterine adhesions, and number of FET cycles Table 2 Multivariate logistic regression of model variables Variables β SE Wald P OR(95%CI) Age −0.045 0.012 −3.721 < 0.001 0.956 (0.933, 0.979) Number of previous FET transfers −1.400 0.074 −18.872 < 0.001 0.247 (0.213, 0.285) Number of blastocysts transferred 0.866 0.142 6.081 < 0.001 2.378 (1.798, 3.144) Number of high-quality embryos transferred 1.017 0.106 9.584 < 0.001 2.765 (2.244, 3.407) AMH 0.050 0.022 2.256 0.024 1.051 (1.007, 1.097) AFC 0.013 0.009 1.584 0.113 1.014 (0.997, 1.031) FSH −0.039 0.021 −1.815 0.070 0.962 (0.923, 1.003) Type of embryos transferred −0.663 0.216 −3.073 0.002 0.515 (0.338, 0.787) Duration of infertility −0.039 0.014 −2.742 0.006 0.962 (0.936, 0.989) E2 on HCG day 0.000 0.000 4.747 < 0.001 1.000 (1.000, 1.000) Endometrial thickness on HCG day 0.043 0.020 2.214 0.027 1.044 (1.005, 1.085) History of intrauterine adhesions −0.772 0.237 −3.252 0.001 0.462 (0.290, 0.736) Multivariate logistic regression of model variables Endometrial thickness on HCG day The selected predictive factors were integrated into three different ML models to construct LR, RF, and XGBoost predictive models. To optimize predictive performance and prevent overfitting, hyperparameter tuning was performed on the training set using grid search combined with five-fold cross-validation. The results of these models on the test set are shown in Table  3 . As shown in Fig.  3 A, the XGBoost model achieved the best predictive performance on the test set, with an AUC of 0.843, significantly outperforming RF (AUC = 0.828) and LR (AUC = 0.818). Furthermore, the XGBoost model performed well on other metrics: precision = 0.786, specificity = 0.858, accuracy = 0.772, and F1 score = 0.725. Calibration curves and Brier scores were used to evaluate predictive calibration. As shown in Fig.  3 B, the calibration curve demonstrated good agreement between predicted probabilities of live birth and actual outcomes, and the calibration curve had the lowest Brier score (0.154), indicating more accurate predicted probabilities. Fig.  3 C, the DCA, showed that the XGBoost model provided the greatest net benefit within a threshold range of 20% to 70%. Table 3 Performance of three machine learning-based models for predicting live birth in the testing set Model AUC Accuracy Sensitivity Specificity Precision PPV NPV F1 score Brier score LR 0.818 0.774 0.663 0.851 0.758 0.758 0.782 0.707 0.166 RF 0.828 0.764 0.709 0.802 0.712 0.712 0.797 0.713 0.166 XGBoost 0.843 0.786 0.684 0.858 0.772 0.772 0.794 0.725 0.154 Performance of three machine learning-based models for predicting live birth in the testing set Fig. 3 A , B , and C show the ROC curve, calibration curve, and clinical decision curve of the model on the test set. D , E , and F show the ROC curve, calibration curve, and clinical decision curve of the model on the external validation set A , B , and C show the ROC curve, calibration curve, and clinical decision curve of the model on the test set. D , E , and F show the ROC curve, calibration curve, and clinical decision curve of the model on the external validation set A prospective cohort of 1,467 patients was used as an independent external validation set to validate the three predictive models. The results showed that the XGBoost model demonstrated the best predictive performance. As shown in Table  4 , this model had an AUC of 0.809, with a precision of 0.744, sensitivity of 0.744, and specificity of 0.768. The ROC curve in Fig.  3 D demonstrates that the XGBoost model maintained optimal discriminative performance in external validation. To further evaluate calibration and clinical utility, we plotted calibration curves and DCA curves. The calibration curve in Fig.  3 E indicated good agreement between predicted and observed outcomes, confirming predictive consistency and clinical relevance. Additionally, the Brier score of 0.175 further supported predictive reliability. As shown in Fig.  3 F, DCA indicated that within the threshold probability range of 20% to 80%, the XGBoost model provided higher clinical net benefit, supporting its value for real-world clinical decision-making. Table 4 Performance of three machine learning-based models for predicting live birth in the external validation set Model AUC Accuracy Sensitivity Specificity Precision PPV NPV F1 score Brier score LR 0.798 0.737 0.717 0.754 0.713 0.713 0.758 0.715 0.183 RF 0.796 0.709 0.757 0.668 0.660 0.660 0.763 0.705 0.191 XGBoost 0.809 0.744 0.744 0.768 0.724 0.724 0.760 0.720 0.175 Performance of three machine learning-based models for predicting live birth in the external validation set To further interpret the model’s predictions, we employed the SHAP method to assess the impact of each feature. Fig.  4 A presents the top 10 most influential factors, ranked by mean SHAP absolute value: number of FET cycles, number of blastocysts transferred, number of high-quality embryos transferred, AMH, E2 on the day of hCG administration, embryo type at transfer, age, endometrial thickness on the day of hCG administration, duration of infertility, and history of intrauterine adhesions. Fig.  4 B displays a SHAP summary plot, which visually analyzes the direction of each feature’s influence on live birth outcome. The y-axis represents the feature value, and the x-axis reflects the degree of influence on the probability of live birth. Overall, for patients undergoing FET, the probability of live birth decreased as the number of previous FET cycles increased, the number of high-quality embryos transferred decreased, AMH levels decreased, age increased, and duration of infertility increased.To demonstrate how the XGBoost model evaluated the contribution of individual patient features, we used SHAP plots to explain individual predictions for two representative cases. Fig.  4 C shows a patient who did not achieve a live birth, while Fig.  4 D shows a patient who achieved a live birth. The SHAP explanation process began with the baseline value E[f(x)], which represented the average predicted value across all samples. On this basis, each input feature increased or decreased the predicted probability for that sample according to its contribution. The length of the arrows reflected the absolute magnitude of the corresponding SHAP value for each feature, while the direction of the arrows indicated the direction of influence. Specifically, magenta indicated a negative impact on the prediction (arrow pointing left, SHAP value decreasing), and yellow indicated a positive impact (arrow pointing right, SHAP value increasing). The length of the color bar represented the intensity of the contribution. Ultimately, by summing the contributions of each feature, the model derived an individualized prediction result for a specific patient. Fig. 4 A , B SHAP variable importance plots, with features sorted by descending order of their average SHAP absolute values. C , D SHAP attempts to provide personalized feature attribution using two examples: the color indicates the contribution of each feature; magenta indicates that the feature has a negative impact on the prediction (arrow pointing left, SHAP value decreases), while yellow indicates that the feature has a positive impact on the prediction (arrow pointing right, SHAP value increases).The length of the color bars indicates the strength of the contribution; E[f(x)] represents the SHAP reference value, i.e., the model’s predicted mean. f(x) denotes the individual SHAP value A , B SHAP variable importance plots, with features sorted by descending order of their average SHAP absolute values. C , D SHAP attempts to provide personalized feature attribution using two examples: the color indicates the contribution of each feature; magenta indicates that the feature has a negative impact on the prediction (arrow pointing left, SHAP value decreases), while yellow indicates that the feature has a positive impact on the prediction (arrow pointing right, SHAP value increases).The length of the color bars indicates the strength of the contribution; E[f(x)] represents the SHAP reference value, i.e., the model’s predicted mean. f(x) denotes the individual SHAP value

Infertility has become an increasingly serious reproductive health issue worldwide, affecting approximately 15% of couples of childbearing age [ 1 ]. Currently, in vitro fertilization and embryo transfer (IVF-ET) is the primary treatment for infertility [ 2 ]. Since the first pregnancy resulting from a thawed embryo in 1983, frozen-thawed embryo transfer has become one of the most important technologies in assisted reproductive medicine [ 3 ]. With improvements in vitrification technology and the widespread adoption of whole-embryo freezing strategies, the proportion of FET cycles has increased rapidly. Currently, FET cycles account for over 60% of all transfer cycles [ 4 , 5 ]. Although the live birth rate (LBR) for FET has improved globally in recent years, it remains around 40%. Consequently, most women experience treatment failure and bear a significant physical, psychological, and financial burden [ 6 ]. Traditional predictive methods rely solely on clinicians’ clinical experience and patients’ past data. However, the successful delivery of at least one newborn depends on the effective establishment of pregnancy, which is influenced by numerous factors throughout the nearly ten-month gestation period. The complexity and multifactorial nature of this process limit the predictive accuracy of human judgment. Given these challenges, there is an urgent need in clinical practice for a personalized predictive tool to support clinical decision-making, thereby improving pregnancy outcomes and reducing the number of required treatment cycles. Machine learning (ML), a key branch of artificial intelligence (AI), is an emerging interdisciplinary field whose applications in healthcare have become a focal point in contemporary society [ 7 ]. Compared to traditional statistical methods, ML is better equipped to handle complex variable interactions and nonlinear relationships, enabling exceptional performance in areas such as disease diagnosis and clinical outcome prediction [ 8 ]. ML has emerged as an effective strategy for improving the prediction of assisted reproductive technology (ART) outcomes. In the field of reproductive medicine, ML algorithms have been applied to predict implantation success during IVF, guide more precise embryo selection, and assess treatment-related risks [ 9 – 11 ]. However, previous models have primarily been based on fresh embryo transfer cycles [ 12 , 13 ], lacking targeted predictions for live births in FET cycles. Furthermore, most existing models focus on the accuracy of global predictions, with limited attention paid to personalized interpretations that could inform patient-specific counseling or treatment. SHAP additive interpretation, as an advanced interpretability framework, provides intuitive and quantifiable explanations for the predictions of any ML model [ 14 ]. Therefore, this study aimed to explore the factors influencing live births after FET, construct an ML-based predictive model for live birth outcomes, and use the SHAP method to analyze and interpret the contribution of each predictive factor, thereby providing guidance for clinical treatment decisions and patient counseling.

In summary, this study developed an interpretable ML model to predict live birth following FET. The XGBoost model demonstrated high predictive performance in both internal and prospective validation, offering valuable insights for predicting live birth in FET patients and optimizing treatment strategies. Furthermore, the SHAP method was used to interpret the results generated by the ML model, providing data support for clinicians to formulate individualized treatment strategies and establish reasonable patient expectations. Future research should prioritize external validation using multicenter cohort data to further assess the model’s generalization ability, and develop web- or mobile-based applications to enhance the model’s clinical translation.

Recent studies indicate that ML methods are increasingly being applied in obstetrics and gynecology, including reproductive endocrinology, gynecological imaging, and obstetric risk prediction. For example, Zorlu et al. [ 22 ]combined ML with elastography to predict symptoms associated with adenomyosis; Gao et al. Gao [ 23 ] successfully applied an XGBoost model to predict preterm birth; Zorlu et al. [ 24 ]used first-trimester biomarkers to validate an ML-based model for predicting gestational diabetes. These recent studies support the view that enhanced ML models are gradually becoming essential tools for optimizing patient-centered care across the entire field of reproductive health. Live birth is the ultimate goal of ART treatment and the primary concern for patients undergoing FET and their physicians. Although several predictive models have been developed for assessing infertility and ART outcomes, existing studies [ 13 , 25 ] have focused on predicting live birth in patients undergoing fresh-cycle IVF, and predictive models for FET cycles remain relatively limited. Jin et al [ 26 ] constructed a nomogram model based on LASSO regression, demonstrating that maternal age, BMI, cesarean section history, number of high-quality embryos, and endometrial thickness were independent predictors of live birth in women undergoing FET for the first time; this model exhibited good predictive performance. Wang et al. [ 27 ] constructed a nomogram model to predict live births in women undergoing FET during the ovulation phase; however, predictive accuracy was limited, with an AUC of 0.648. In contrast, Liang et al. [ 28 ]utilized ML to develop a data-driven prediction (DDP) model combining random forest and genetic algorithm to predict the probability of live birth in FET patients, achieving superior performance with an accuracy exceeding 85% and an AUC of 0.83. However, most existing models focus on global prediction accuracy and lack interpretability regarding individual predictions, which to some extent limits their practical application in clinical decision-making. Therefore, this study is the first to adopt the SHAP explainable ML method, successfully constructing and validating three ML models for predicting live birth outcomes after FET. In both the internal and external validation sets, all models demonstrated good predictive performance, with the XGBoost model performing best. The XGBoost model captured complex interactions among multiple features and possessed unique advantages in handling categorical features, nonlinear relationships, and complex dependencies, thereby enabling a more comprehensive assessment of the combined effects of patient-specific and treatment-related factors on live birth outcomes. Calibration curve and ROC curve analyses indicated that the model’s predicted probabilities aligned closely with observed probabilities and demonstrated clinical net benefit across a wide range of thresholds. To further elucidate the model’s predictive mechanisms and assess individual contributions of each predictor, this study applied SHAP analysis to the best-performing XGBoost model. SHAP values quantified the positive or negative impact of each feature on live birth outcomes after FET. The SHAP analysis revealed that the most important features, in descending order, were the number of FET cycles, number of blastocysts transferred, number of high-quality embryos transferred, AMH, E2 on the day of hCG administration, embryo type at transfer, age, endometrial thickness on the day of hCG administration, duration of infertility, and history of intrauterine adhesions. Through SHAP analysis, this study significantly enhanced model interpretability, enabling visual demonstration of each feature’s contribution to individual predictions and providing more actionable, personalized data support for clinical decision-making and patient counseling. This study used SHAP analysis to reveal the contribution of each feature to the model’s predictions. The results showed that, among the predictive factors, the number of FET cycles contributed most significantly to the model’s predictions, which may reflect cumulative embryo quality, endometrial receptivity status, or underlying pathological factors. This variable is a non-modifiable historical factor and cannot be directly used to guide initial treatment decisions; however, its clinical value lies in patient counseling and expectation management. For example, for patients who have experienced multiple FET failures, clinicians can use the model’s predictions to help them establish reasonable expectations for live birth and discuss alternative strategies. A study by Vaegter et al. [ 29 ]involving 8,400 single-embryo transfer cycles found that patients who had never undergone IVF and had never achieved a live birth had better pregnancy outcomes than those who had undergone 1–6 IVF cycles and had achieved one live birth. Similarly, Peng et al. [ 30 ], using multi-model ML algorithms to predict cumulative live birth rates in IVF, demonstrated that the number of IVF failures was the most significant factor affecting live birth rates. A higher SHAP score indicated that for each additional IVF failure, the patient’s probability of achieving a live birth decreased significantly. Therefore, in clinical practice, patients undergoing multiple transfers require more in-depth exploration of underlying causes and individualized intervention strategies. Previous studies have shown that the number of embryos transferred and the number of high-quality embryos transferred significantly influence pregnancy outcomes. A large randomized controlled trial involving women aged ≤ 35 years demonstrated that the number of frozen embryos transferred, rather than embryo quality, was significantly associated with live birth [ 31 ]. However, in our study, embryo quality was an important predictor of FET outcomes. Transferring two or at least one high-quality embryo significantly increased the likelihood of live birth, consistent with previous findings [ 32 ]. SHAP analysis further indicated that transferring two blastocysts increased the likelihood of live birth. It should be noted that although twin blastocyst transfer yields higher pregnancy rates compared with single blastocyst transfer, existing studies and consensus guidelines emphasize that twin blastocyst transfer increases the risk of multiple pregnancies, associated pregnancy complications, and adverse perinatal outcomes. Therefore, patient selection should be strictly controlled, and single blastocyst transfer should be prioritized [ 33 ], to ensure maternal and fetal safety while improving live birth rates. A history of intrauterine adhesions was identified as another important predictive factor. The development of intrauterine adhesions is a complex, multifactorial process involving multiple stages; with diverse triggering factors and pathogenic mechanisms, it is one of the major causes of reduced fertility or infertility [ 34 ]. Intrauterine adhesions interfere with sperm transport through the reproductive tract (cervix, uterus, and fallopian tubes) and lead to endometrial ischemia, reduced receptivity, and decreased endometrial thickness, thereby severely disrupting the microenvironment essential for embryo implantation [ 35 ]. In one study comparing endometrial receptivity on the day of ovulation between patients with and without a history of intrauterine adhesions, the live birth rate was significantly higher in patients without a history of intrauterine adhesions [ 36 ]. This finding suggests that patients with a history of intrauterine adhesions should undergo thorough evaluation and intervention prior to FET. This study used SHAP waterfall plots to visually demonstrate the model’s predictive process for individual patients, providing clinicians with an actionable tool for personalized patient interpretation. Taking Fig.  4 C as an example, the model predicted a live birth probability of 29.3% for this patient, which was significantly lower than the population average predicted probability of 41.6% (E[f(x)] = 0.416). SHAP analysis clearly identified the primary negative factors contributing to the reduced predicted probability: a history of two previous failed FETs (-0.154), absence of blastocyst transfer (-0.0645), and low AMH level (2.04, -0.0638). Conversely, the transfer of two high-quality embryos was a positive contributing factor (+ 0.183). Based on this analysis, clinicians could provide the following personalized counseling: “Your two previous unsuccessful FETs are the primary factors affecting the predicted success rate for this cycle. Additionally, your ovarian reserve (AMH) is low, and the embryos transferred this time are cleavage-stage rather than blastocysts. However, both embryos transferred are of high quality, which is a favorable factor. Overall, the current predicted probability of live birth is approximately 30%. We recommend further evaluation of your endometrial condition and embryo quality, and consider adjusting the transfer protocol if necessary.” This SHAP-based personalized interpretation offers the following clinical value. First, it clearly distinguishes between modifiable and non-modifiable factors: for non-modifiable factors such as a history of previous FET failure, clinicians can use this information for patient expectation management to help establish realistic expectations for live birth; for modifiable factors such as embryo type and endometrial thickness, it serves as a reference for treatment adjustments. Second, by comparing the differences in feature contributions between Fig.  4 C (no live birth) and Fig.  4 D (live birth), clinicians can intuitively understand which factors play a critical role in successful pregnancy, thereby adopting differentiated intervention strategies in various clinical scenarios. Overall, the SHAP method not only enhances model interpretability but also provides valuable insights into the factors influencing the model’s decision-making process. Compared with other studies, the strengths of this study are primarily reflected in the following aspects. First, the use of LASSO regression for variable selection effectively reduced the number of variables, which improved the model’s clinical utility and mitigated the risk of overfitting. Second, the use of the SHAP method to interpret the model not only assessed the importance of each variable at the global level but also utilized SHAP plots to identify primary predictors of live birth at the individual level, thereby enhancing interpretability and practical value. However, this study also has certain limitations. First, model development and validation primarily relied on retrospective data and a prospective cohort from a single center, rather than multicenter big data, which may introduce inherent bias and limit generalizability. Specifically, the retrospective, single-center design may introduce selection bias; furthermore, external validation employed a time-segmented validation method, with both validation and development data originating from the same center, failing to conduct independent external geographic validation. Consequently, the model’s cross-center generalizability remains limited. Second, this study did not incorporate certain potentially important factors, such as novel biomarkers (e.g., endometrial gene expression profiles, microbiome characteristics, and blastocyst morphodynamic parameters) as well as clinical factors such as patients’ lifestyle, dietary habits, and psychological state. These factors may be closely associated with pregnancy outcomes after FET, and their omission may have, to some extent, affected the model’s predictive performance. Future studies should conduct independent external validation of this model through prospective, multicenter designs and attempt to incorporate a broader range of predictive factors. This is crucial for enhancing the model’s generalizability and clinical translational value.