The Impact of Dependency and Serial Correlation in Matched ITSA: Methodological Considerations

The Impact of Dependency and Serial Correlation in Matched ITSA: Methodological Considerations | 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 Research Article The Impact of Dependency and Serial Correlation in Matched ITSA: Methodological Considerations Rahim Moineddin This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7565524/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 7 You are reading this latest preprint version Abstract Interrupted Time Series Analysis (ITSA) is a widely used quasi-experimental method for evaluating the longitudinal impact of interventions. This study explores the methodological considerations of Matched Controlled Interrupted Time Series (MCITS) designs, particularly the effects of serial correlation and dependency between matched cases and controls on type I error and bias. Using a Monte Carlo simulation approach, we assess the accuracy, type I error and bias, of parameter estimates and compare single and joint segmented regression models. Results indicate that type I error is underestimated in separate models when intra-cluster correlation (ICC) is nonzero and serial correlation is negative, whereas joint modeling maintains appropriate error rates. Bias estimates remain minimal across scenarios, reinforcing the robustness of the joint model for analyzing intervention effects in matched controlled ITSA designs. These findings provide important insights for researchers conducting longitudinal evaluations of interventions in fields such as healthcare and public policy. Figures Figure 1 Figure 2 Figure 3 Figure 4 Introduction Interrupted Time Series Analysis (ITSA) design is a robust quasi-experimental method widely used to evaluate the longitudinal effects of interventions. This design is particularly valuable for assessing changes in the level, and slope of a time series following an intervention, enabling researchers to determine the statistical significance of intervention parameters 1 . Segmented regression analysis is a key statistical tool in ITSA studies, providing a powerful means of estimating intervention effects 2 , 3 . The single-group Interrupted Time Series Analysis design can address several threats to validity; however, some concerns remain: (i) external events unrelated to the intervention may influence the observed effects; (ii) changes in measurement tools, instruments, or methods over time can affect the data; (iii) if the time series is based on cross-sectional data, shifts in the composition of the study population before and after the intervention may introduce bias; and (iv) issues such as low statistical power, violated test assumptions, and measurement unreliability also pose threats. For a comprehensive overview of threats to validity in ITSA designs, see 4 , 5 and the sources cited therein. One approach to minimize the effects of these threats to validity of ITSA is to include a comparable control series, known as a comparative interrupted time series (CITS) analysis 4 . A well-selected control showing no effect can strengthen the case for a causal link between the intervention and the outcome. In contrast, if the control group also shows an effect, it suggests the observed change may be due to other factors 6 . Matching controls in interrupted time series analysis designs offer several advantages over non-matched controls including enhanced control for potential confounding factors, particularly those that occur concurrently with the intervention, like co-interventions or other historical events. This strengthens the causal inference by reducing the risk of misinterpreting the intervention's impact as due to these confounding factors. Linden 7 introduced a matching framework for creating a comparable control group as an alternative to multivariable regression and reweighting for estimating treatment effects in ITSA. Matching is often favoured over the statistical adjustment techniques when evaluating treatment effects for an intervention 7 . Interrupted Time Series Analysis (ITSA) designs are employed across diverse fields, with notable applications in healthcare—such as evaluating quality improvement initiatives, clinical practice guidelines, and the effects of major public health events like the COVID-19 pandemic. However, several methodological considerations are critical to the success of matched Controlled Interrupted Time Series studies. In particular, the effects of serial correlation and dependency among matched cases and controls on type I error and bias have not been fully explored. The purpose of this study is to assess the impact of serial correlation in time-ordered observations and the dependency between matched cases and controls on type I error and bias in the estimated level and slope changes—both within groups and in the differences between cases and controls—using a simulation study. Methods In the following sections, we use "matched cases and controls" and "cluster" interchangeably. Matched repeated measures over time have two sources of dependency: (i) matching/clustering, where each cluster contains multiple units that are more similar to one another than to units in other clusters; (ii) repeated measures, where repeated observations are taken over time. In this setup, the data exhibits both (i) within-cluster correlation among matched cases and controls and (ii) within-subject correlation over time. A suitable framework for modelling repeated matched cases and controls data is the linear mixed model which can be expressed as: Y = Xβ + Zu + ε where Y is the vector of observed responses, X is the design matrix for fixed effects, β is the vector of fixed-effect coefficients, Z is the design matrix for random effects, u is the vector of random effects, assumed to follow a multivariate normal distribution with mean zero and covariance matrix G , ε is the vector of residual errors, assumed to follow a multivariate normal distribution with mean zero and variance covariance matrix R 8 . This formulation allows for modeling both fixed effects and random effects, along with their respective variance-covariance structures, providing a flexible approach to analyzing data with complex correlation structures. Following Wagner et al.'s 3 framework, the proposed fixed-effect, \(\:X\beta\:,\) part of segmented regression model can be written as follows $$\:{\beta\:}_{0}+{\beta\:}_{1}{time}_{t}+{\beta\:}_{2}{intervention}_{t}+{\beta\:}_{3}{time-after}_{t}+{\beta\:}_{4}{case}_{t}+{\beta\:}_{5}{case}_{t}*{time}_{t}+{\beta\:}_{6}{case}_{t}*{intervention}_{t}+{\beta\:}_{7}{case}_{t}*{time-after}_{t}$$ Where time t is a continuous variable counting the time points from the start of the observation period; intervention t is a binary variable, taking the value 0 for time t before the intervention and 1 for time t after the intervention; time-after t is 0 for time t before the intervention and counts time t from the start of the intervention; case t is a dummy variable, taking the value 1 for cases and 0 for matched controls. The intercept before intervention, slope before intervention, intercept after intervention, and slope after intervention for the control group are β 0 , β 1 , β 0 + β 2 , β 1 + β 3 respectively. For cases, these β 0 + β 4 , β 1 + β 5 , β 0 + β 2 + β 4 + β 6 , and β 1 + β 3 + β 5 + β 7 respectively. Level and slope changes for the control group and cases are given by β 2 , β 3 , β 2 + β 6 , β 3 + β 7 respectively. The differences between cases and controls in intercept and slope before the intervention are β 4 and β 5 respectively. The differences in level changes and slope changes between cases and controls are β 6 and β 7 respectively. The covariance structure between cases and their matched controls is modeled by the G matrix, while the within-subject covariance structure due to repeated measures is modeled by the R matrix. The similarity between cases and their matched controls (within-cluster correlation) is typically measured using the intra-cluster correlation coefficient (ICC). A common assumption in matched case-control studies is that the correlation between any two matched cases and controls remains constant across all time points. When a random-effects regression model is used to analyze matched case-control data, an exchangeable correlation is obtained by including a random intercept for the matching of cases and controls. The ICC can then be estimated as the ratio of the between-case/control variance to the total variance of the outcome 9 . Simulation We generated 1,000 matched case-control datasets from the null model: \(\:{y}_{it}={b}_{i0}+{e}_{it}\) where \(\:{y}_{it}\) is the t th observation of the i th subject, b i0 follows a normal distribution with mean zero and standard deviation σ b and e it follows an autoregressive process of order 1 (AR(1)): \(\:{e}_{it}=\phi\:{e}_{i(t-1)}+{a}_{t}\) where \(\:{a}_{t}\) follows a normal distribution with mean zero and constant variance σ. The random intercept b i0 and e it are independent. The variance of \(\:{y}_{it}\) is the sum of variance of b i0 and e it . Variance of e it is \(\:\frac{V\left({a}_{t}\right)}{(1-{\phi\:}^{2})}\) thus \(\:ICC=\frac{{\sigma\:}_{b}^{2}}{\frac{V\left({a}_{t}\right)}{\left(1-{\phi\:}^{2}\right)}+{\sigma\:}_{b}^{2}}\) . In our simulation, we set σ = 1, φ in (-0.8, -0.4, 0, 0.4, 0.8), intra-cluster correlation coefficient (ICC) in (0, 0.2, 0.4), the number of time points before and after the intervention in ( 5, 10 ), and the number of cases with 1:1 matched controls in ( 25, 50, 100 ). For each scenario the standard deviation of b i0 is calculated using the formula \(\:ICC=\frac{{\sigma\:}_{b}^{2}}{\frac{{\sigma\:}^{2}}{\left(1-{\phi\:}^{2}\right)}+{\sigma\:}_{b}^{2}}\) . Models We fitted two separate segmented linear regression models of the form \(\:{y}_{t}={\beta\:}_{0}+{\beta\:}_{1}{time}_{t}+{\beta\:}_{2}{intervention}_{t}+{\beta\:}_{3}{time-after}_{t}+{\epsilon\:}_{t}\) to generated data for cases and control. The serial correlation is modeled as an autoregressive AR(1) process. The third model is the proposed segmented linear regression model that jointly is fitted to generated matched cases and control data. The serial correlation among the repeated measures is modelled as an autoregressive AR(1) process and the correlation between matched cases and controls is modelled as random intercept with variance component covariance structure. We used these 3 fitted regression models to calculate type I error and bias for interpret and slope of cases and controls before and after intervention, level and slope changes for cases and controls. Then we calculated the type I error and bias for difference between case and control level and slope change using the joint model. We also used Z-test to compare level and slope change differences between cases and controls using estimated level and slope changes calculated by separated segmented regression fitted to cases and control data separately. Type I error is estimated by the proportion of significant estimates at the level of 5 percent and Bias is estimated as the difference between the average of the estimated parameters and the true parameter. We also calculate and report estimated serial correlation and ICC. Results The simulation results are summarized in Table 1 and Table 2 given in appendix. Table 1 presents the bias and Type I error for regression lines before and after the intervention, as well as the level and slope changes estimated using separate and joint regression models. Table 2 shows the differences between the intervention and control regression lines, along with the differences in level and slope changes between the case and control groups, obtained through separate and joint regression modeling. Intercept and Slope Before and After Intervention and Level and Slope Changes When examining Type I error for the intercept and slope before and after the intervention and level and slope changes —across both cases and their matched controls—using regression models fitted separately and jointly, the following patterns emerge: i) When the intraclass correlation coefficient (ICC) is zero, Type I errors are close to 5%, ii) However, when ICC is non-zero and φ is negative, the Type I errors from separate models fitted to the generated case and control data tend to be underestimated, iii) - In contrast, the Type I errors from joint segmented regression models remain close to 5% across all combinations of φ and ICC. Figure 1: Plots showing Type I errors for estimated parameters of segmented regression lines, fitted separately and jointly, are presented here for simulated data where the number of time points before and after the intervention is 10. Difference in Level and Slope Changes We examined the difference between cases and controls level and slope changes using two separate segmented regression fitted to cases and controls simulated data and by proposed jointly modelling the data. When ICC is zero type I errors for both methods are very close to 5% level. When ICC is not zero and serial correlation is negative the type I error for joint model are close to 5% while for separated models are below 5% level. Figure 2: Plots showing Type I errors for differences (cases – controls) estimated level and slope changes fitted separately and jointly, are presented here for simulated data where the number of time points before and after the intervention is 10. Bias The estimated bias for estimated parameters is close to zero. More accurately they ranged between − 0.04 to 0.04 for entire scenarios. More than 99% of estimated biases were between − 0.02 and 0.02. Estimated ICC and φ The averages of the estimated ICC and φ across all scenarios are very close to the true values of ICC and φ. Figure 3 Estimated ICC and φ compared with true values Standard Errors We calculated the average standard errors of the estimated parameters using two approaches: (1) separate segmented regressions fitted to simulated data for cases and controls, and (2) a proposed joint model that simultaneously analyzes both datasets. When the intraclass correlation coefficient (ICC) is zero, the estimated standard errors from both methods are very similar. However, when ICC is non-zero and serial correlation is negative, the standard errors from the separate models tend to be larger than those obtained from the joint model, which accounts for the dependency between cases and their matched controls. Figure 4 Plots showing estimated standard errors for estimated parameters fitted separately and jointly, are presented here for simulated data where the number of time points before and after the intervention is 10. Discussion This study contributes to the growing body of research on Interrupted Time Series Analysis (ITSA) designs, particularly in the context of Matched Controlled Interrupted Time Series (MCITS) studies. Our findings highlight the importance of properly accounting for correlation structures within matched pairs to ensure accurate statistical inference. A key challenge in ITSA designs with matched controls is the presence of two sources of dependency: within-cluster correlation due to case-control matching and within-subject correlation over time. Failure to account for these dependencies may lead to biased estimates and incorrect conclusions regarding the impact of interventions. Our simulation study demonstrated that when intra-cluster correlation (ICC) is nonzero and serial correlation is negative, separate segmented regression models tend to underestimate type I error rates. This underestimation can have substantial implications for researchers relying on traditional ITSA approaches, as it may lead to incorrect conclusions about the significance of intervention effects. In contrast, the joint segmented regression model effectively controls type I error rates across various scenarios, ensuring more reliable inference. One of the fundamental advantages of the joint modeling approach is its ability to integrate both within-cluster and within-subject dependencies into a single analytical framework. By explicitly modeling the correlation between matched cases and controls, the joint model accounts for shared variance and improves precision in estimating intervention effects. This results in a more accurate assessment of level and slope changes before and after an intervention, strengthening causal interpretations. The study further emphasizes the need for researchers to carefully consider the impact of serial correlation and dependency structures when designing ITSA studies. While intra-cluster correlation is often treated as a nuisance factor, our findings suggest that failing to account for ICC can lead to erroneous conclusions. A key implication of this study is the recommendation for analysts to simultaneously model correlation due to matching using mixed-effects approach and to address serial correlation by explicitly modeling the covariance structure of the residuals. These approaches provide a flexible framework for handling complex correlation structures in matched interrupted time series analysis designs. Despite the strengths of this approach, several challenges remain. For example, the selection of an appropriate covariance structure is crucial in ensuring the validity of parameter estimates. While our joint model effectively controlled type I error rates, alternative modeling strategies—such as incorporating non-exchangeable correlation structures—should be explored in future research. Additionally, the findings are based on simulated data, and real-world applications may introduce additional complexities, such as unmeasured confounders or heterogeneity in intervention effects. Overall, this study underscores the methodological considerations necessary for robust ITSA designs with matched controls. The findings reinforce the importance of adopting joint modeling approaches to enhance causal inference and reduce bias in intervention effect estimates. Future research should aim to refine these techniques and extend their applications across diverse fields, ensuring that ITSA remains a powerful tool for evaluating intervention effectiveness in longitudinal studies. Conclusion This study underscores the critical importance of appropriately modeling correlation structures in matched controlled interrupted time series analyses. Specifically, failure to account for intra-cluster correlation and serial correlation can substantially distort Type I error rates, potentially undermining causal inference. By incorporating both correlation sources within a joint linear mixed-effects segmented regression framework, researchers can achieve more accurate and reliable inference. We recommend that applied researchers employing matched CITS designs use models that explicitly account for the dependencies within matched pairs and across repeated time points. As the use of matched CITS designs continues to expand in evaluating complex interventions—particularly in health policy, public health, and implementation science—ensuring valid statistical inference through robust modeling approaches is essential. Declarations Ethics approval and consent to participate Not Applicable Consent for publication Not Applicable Author Contribution RM wrote the main manuscript, performed data analysis, interpretation of results and reviewed the manuscript. Acknowledgements Not Applicable Data Availability The data that supports the findings of this study are not publicly available. References Cruz M, Bender M, Ombao H. A robust interrupted time series model for analyzing complex health care intervention data. Stat Med. 2017;36(29):4660–76. https://doi.org/10.1002/sim.7443 . Turner SL, Karahalios A, Forbes AB, Taljaard M, Grimshaw JM, McKenzie JE. Comparison of six statistical methods for interrupted time series studies: Empirical evaluation of 190 published series. BMC Med Res Methodol. 2021;21(1):134. 10.1186/s12874-021-01306-w . Wagner AK, Soumerai SB, Zhang F, Ross-Degnan D. Segmented regression analysis of interrupted time series studies in medication use research. J Clin Pharm Ther. 2002;27(4):299–309. https://doi.org/10.1046/j.1365-2710.2002.00430.x . Lopez Bernal J, Cummins S, Gasparrini A. The use of controls in interrupted time series studies of public health interventions. Int J Epidemiol. 2018;47(6):2082–93. 10.1093/ije/dyy135 . Linden A. Challenges to validity in single-group interrupted time series analysis. J Eval Clin Pract. 2017;23(2):413–8. https://doi.org/10.1111/jep.12638 . St.Clair T, Hallberg K, Cook TD. The validity and precision of the comparative interrupted time-series design: Three within-study comparisons. J educational Behav Stat. 2016;41(3):269–99. 10.3102/1076998616636854 . Linden A. A matching framework to improve causal inference in interrupted time-series analysis. J Eval Clin Pract. 2018;24(2):408–15. 10.1111/jep.12874 . Diggle P. Analysis of longitudinal data. 2nd ed. Oxford;: Oxford University Press; 2002. Ouyang Y, Kulkarni MA, Protopopoff N, Li F, Taljaard M. Accounting for complex intracluster correlations in longitudinal cluster randomized trials: A case study in malaria vector control. BMC Med Res Methodol. 2023;23(1):64. 10.1186/s12874-023-01871-2 . Tables Table 1 and 2 are available in the Supplementary Files section. Additional Declarations No competing interests reported. Supplementary Files AppendixTable1.xls AppendixTable2.xls Cite Share Download PDF Status: Under Review Version 1 posted Reviews received at journal 07 Nov, 2025 Reviewers agreed at journal 31 Oct, 2025 Reviewers invited by journal 24 Oct, 2025 Editor invited by journal 26 Sep, 2025 Editor assigned by journal 25 Sep, 2025 Submission checks completed at journal 25 Sep, 2025 First submitted to journal 08 Sep, 2025 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. 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04:21:11","extension":"png","order_by":15,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":22191,"visible":true,"origin":"","legend":"","description":"","filename":"OnlineFigure3.png","url":"https://assets-eu.researchsquare.com/files/rs-7565524/v1/9c23a2b5a077cb77222382a5.png"},{"id":95260682,"identity":"33d6e4f1-6a73-4153-9926-d1376f8da69a","added_by":"auto","created_at":"2025-11-06 04:21:12","extension":"png","order_by":16,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":40060,"visible":true,"origin":"","legend":"","description":"","filename":"OnlineFigure4.png","url":"https://assets-eu.researchsquare.com/files/rs-7565524/v1/280eb6c7278779698ffc5a57.png"},{"id":95260689,"identity":"94875f94-144d-4829-9e3e-be48a9e12672","added_by":"auto","created_at":"2025-11-06 04:21:13","extension":"xml","order_by":17,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":41827,"visible":true,"origin":"","legend":"","description":"","filename":"e262de44cb3f43a8b58abf3b573b02ee1structuring.xml","url":"https://assets-eu.researchsquare.com/files/rs-7565524/v1/c327fe79ba0ce652d65fd638.xml"},{"id":95260698,"identity":"8173d323-fe4e-48db-a86b-9df443b410a0","added_by":"auto","created_at":"2025-11-06 04:21:14","extension":"html","order_by":18,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":47133,"visible":true,"origin":"","legend":"","description":"","filename":"earlyproof.html","url":"https://assets-eu.researchsquare.com/files/rs-7565524/v1/1a925f89f1f0be2922af6bd3.html"},{"id":95260694,"identity":"3deceb50-e943-46e4-882a-f78df7847d77","added_by":"auto","created_at":"2025-11-06 04:21:13","extension":"jpg","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":109242,"visible":true,"origin":"","legend":"\u003cp\u003ePlots showing Type I errors for estimated parameters of segmented regression lines, fitted separately and jointly, are presented here for simulated data where the number of time points before and after the intervention is 10.\u003c/p\u003e","description":"","filename":"Figure1.jpg","url":"https://assets-eu.researchsquare.com/files/rs-7565524/v1/bf4f71abc772aaa81a2368e6.jpg"},{"id":95260706,"identity":"4d1cc136-8cf2-4efa-a918-522dc445a172","added_by":"auto","created_at":"2025-11-06 04:21:14","extension":"jpg","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":80852,"visible":true,"origin":"","legend":"\u003cp\u003ePlots showing Type I errors for differences (cases – controls) estimated level and slope changes fitted separately and jointly, are presented here for simulated data where the number of time points before and after the intervention is 10.\u003c/p\u003e","description":"","filename":"Figure2.jpg","url":"https://assets-eu.researchsquare.com/files/rs-7565524/v1/6ea117aac1b5d36df409e920.jpg"},{"id":95260708,"identity":"8f83a7f1-5e30-40a1-8c5c-dbc4e1f197b8","added_by":"auto","created_at":"2025-11-06 04:21:14","extension":"jpg","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":53186,"visible":true,"origin":"","legend":"\u003cp\u003eEstimated ICC and φ compared with true values\u003c/p\u003e","description":"","filename":"Figure3.jpg","url":"https://assets-eu.researchsquare.com/files/rs-7565524/v1/25a06362a6e46e8bbfd71ad6.jpg"},{"id":95260679,"identity":"081c6633-22d1-4a65-8dba-45063619c741","added_by":"auto","created_at":"2025-11-06 04:21:11","extension":"jpg","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":104744,"visible":true,"origin":"","legend":"\u003cp\u003ePlots showing estimated standard errors for estimated parameters fitted separately and jointly, are presented here for simulated data where the number of time points before and after the intervention is 10.\u003c/p\u003e","description":"","filename":"Figure4.jpg","url":"https://assets-eu.researchsquare.com/files/rs-7565524/v1/b20951f545e4977b6aeb9824.jpg"},{"id":95315788,"identity":"25cbce66-7f3c-4bf9-9439-ba8cf3accf4e","added_by":"auto","created_at":"2025-11-06 15:57:07","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":825313,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7565524/v1/c851e197-1f90-4b08-9f0e-ddf1615a77a2.pdf"},{"id":95260675,"identity":"c01ce3cc-b2d5-4c69-9e58-313431da42f4","added_by":"auto","created_at":"2025-11-06 04:21:10","extension":"xls","order_by":0,"title":"","display":"","copyAsset":false,"role":"supplement","size":140800,"visible":true,"origin":"","legend":"","description":"","filename":"AppendixTable1.xls","url":"https://assets-eu.researchsquare.com/files/rs-7565524/v1/3526ac700459955b93bf4d98.xls"},{"id":95260697,"identity":"c4ebb29e-6f1e-4c3b-9c39-f453461b52f3","added_by":"auto","created_at":"2025-11-06 04:21:14","extension":"xls","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":76800,"visible":true,"origin":"","legend":"","description":"","filename":"AppendixTable2.xls","url":"https://assets-eu.researchsquare.com/files/rs-7565524/v1/846cc1e77f34b2956d6056ba.xls"}],"financialInterests":"No competing interests reported.","formattedTitle":"The Impact of Dependency and Serial Correlation in Matched ITSA: Methodological Considerations","fulltext":[{"header":"Introduction","content":"\u003cp\u003eInterrupted Time Series Analysis (ITSA) design is a robust quasi-experimental method widely used to evaluate the longitudinal effects of interventions. This design is particularly valuable for assessing changes in the level, and slope of a time series following an intervention, enabling researchers to determine the statistical significance of intervention parameters \u003csup\u003e\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u003c/sup\u003e. Segmented regression analysis is a key statistical tool in ITSA studies, providing a powerful means of estimating intervention effects\u003csup\u003e\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e, 3\u003c/sup\u003e.\u003c/p\u003e\u003cp\u003eThe single-group Interrupted Time Series Analysis design can address several threats to validity; however, some concerns remain: (i) external events unrelated to the intervention may influence the observed effects; (ii) changes in measurement tools, instruments, or methods over time can affect the data; (iii) if the time series is based on cross-sectional data, shifts in the composition of the study population before and after the intervention may introduce bias; and (iv) issues such as low statistical power, violated test assumptions, and measurement unreliability also pose threats. For a comprehensive overview of threats to validity in ITSA designs, see\u003csup\u003e\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e,\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e\u003c/sup\u003e and the sources cited therein.\u003c/p\u003e\u003cp\u003eOne approach to minimize the effects of these threats to validity of ITSA is to include a comparable control series, known as a comparative interrupted time series (CITS) analysis\u003csup\u003e\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e\u003c/sup\u003e. A well-selected control showing no effect can strengthen the case for a causal link between the intervention and the outcome. In contrast, if the control group also shows an effect, it suggests the observed change may be due to other factors\u003csup\u003e\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e\u003cp\u003eMatching controls in interrupted time series analysis designs offer several advantages over non-matched controls including enhanced control for potential confounding factors, particularly those that occur concurrently with the intervention, like co-interventions or other historical events. This strengthens the causal inference by reducing the risk of misinterpreting the intervention's impact as due to these confounding factors. Linden\u003csup\u003e\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e\u003c/sup\u003e introduced a matching framework for creating a comparable control group as an alternative to multivariable regression and reweighting for estimating treatment effects in ITSA. Matching is often favoured over the statistical adjustment techniques when evaluating treatment effects for an intervention\u003csup\u003e\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e\u003cp\u003eInterrupted Time Series Analysis (ITSA) designs are employed across diverse fields, with notable applications in healthcare\u0026mdash;such as evaluating quality improvement initiatives, clinical practice guidelines, and the effects of major public health events like the COVID-19 pandemic. However, several methodological considerations are critical to the success of matched Controlled Interrupted Time Series studies. In particular, the effects of serial correlation and dependency among matched cases and controls on type I error and bias have not been fully explored. The purpose of this study is to assess the impact of serial correlation in time-ordered observations and the dependency between matched cases and controls on type I error and bias in the estimated level and slope changes\u0026mdash;both within groups and in the differences between cases and controls\u0026mdash;using a simulation study.\u003c/p\u003e"},{"header":"Methods","content":"\u003cp\u003eIn the following sections, we use \"matched cases and controls\" and \"cluster\" interchangeably. Matched repeated measures over time have two sources of dependency: (i) matching/clustering, where each cluster contains multiple units that are more similar to one another than to units in other clusters; (ii) repeated measures, where repeated observations are taken over time. In this setup, the data exhibits both (i) within-cluster correlation among matched cases and controls and (ii) within-subject correlation over time.\u003c/p\u003e\u003cp\u003eA suitable framework for modelling repeated matched cases and controls data is the linear mixed model which can be expressed as: \u003cb\u003eY\u0026thinsp;=\u0026thinsp;Xβ\u0026thinsp;+\u0026thinsp;Zu\u0026thinsp;+\u0026thinsp;ε\u003c/b\u003e where \u003cb\u003eY\u003c/b\u003e is the vector of observed responses, \u003cb\u003eX\u003c/b\u003e is the design matrix for fixed effects, \u003cb\u003eβ\u003c/b\u003e is the vector of fixed-effect coefficients, \u003cb\u003eZ\u003c/b\u003e is the design matrix for random effects, \u003cb\u003eu\u003c/b\u003e is the vector of random effects, assumed to follow a multivariate normal distribution with mean zero and covariance matrix \u003cb\u003eG\u003c/b\u003e, \u003cb\u003eε\u003c/b\u003e is the vector of residual errors, assumed to follow a multivariate normal distribution with mean zero and variance covariance matrix \u003cb\u003eR\u003c/b\u003e\u003csup\u003e8\u003c/sup\u003e.\u003c/p\u003e\u003cp\u003eThis formulation allows for modeling both fixed effects and random effects, along with their respective variance-covariance structures, providing a flexible approach to analyzing data with complex correlation structures. Following Wagner et al.'s\u003csup\u003e3\u003c/sup\u003e framework, the proposed fixed-effect, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:X\\beta\\:,\\)\u003c/span\u003e\u003c/span\u003e part of segmented regression model can be written as follows\u003cdiv id=\"Equa\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equa\" name=\"EquationSource\"\u003e\n$$\\:{\\beta\\:}_{0}+{\\beta\\:}_{1}{time}_{t}+{\\beta\\:}_{2}{intervention}_{t}+{\\beta\\:}_{3}{time-after}_{t}+{\\beta\\:}_{4}{case}_{t}+{\\beta\\:}_{5}{case}_{t}*{time}_{t}+{\\beta\\:}_{6}{case}_{t}*{intervention}_{t}+{\\beta\\:}_{7}{case}_{t}*{time-after}_{t}$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003eWhere time\u003csub\u003et\u003c/sub\u003e is a continuous variable counting the time points from the start of the observation period; intervention\u003csub\u003et\u003c/sub\u003e is a binary variable, taking the value 0 for time\u003csub\u003et\u003c/sub\u003e before the intervention and 1 for time\u003csub\u003et\u003c/sub\u003e after the intervention; time-after\u003csub\u003et\u003c/sub\u003e is 0 for time\u003csub\u003et\u003c/sub\u003e before the intervention and counts time\u003csub\u003et\u003c/sub\u003e from the start of the intervention; case\u003csub\u003et\u003c/sub\u003e is a dummy variable, taking the value 1 for cases and 0 for matched controls.\u003c/p\u003e\u003cp\u003eThe intercept before intervention, slope before intervention, intercept after intervention, and slope after intervention for the control group are β\u003csub\u003e0\u003c/sub\u003e, β\u003csub\u003e1\u003c/sub\u003e, β\u003csub\u003e0\u003c/sub\u003e\u0026thinsp;+\u0026thinsp;β\u003csub\u003e2\u003c/sub\u003e, β\u003csub\u003e1\u003c/sub\u003e\u0026thinsp;+\u0026thinsp;β\u003csub\u003e3\u003c/sub\u003e respectively. For cases, these β\u003csub\u003e0\u003c/sub\u003e\u0026thinsp;+\u0026thinsp;β\u003csub\u003e4\u003c/sub\u003e, β\u003csub\u003e1\u003c/sub\u003e\u0026thinsp;+\u0026thinsp;β\u003csub\u003e5\u003c/sub\u003e, β\u003csub\u003e0\u003c/sub\u003e\u0026thinsp;+\u0026thinsp;β\u003csub\u003e2\u003c/sub\u003e\u0026thinsp;+\u0026thinsp;β\u003csub\u003e4\u003c/sub\u003e\u0026thinsp;+\u0026thinsp;β\u003csub\u003e6\u003c/sub\u003e, and β\u003csub\u003e1\u003c/sub\u003e\u0026thinsp;+\u0026thinsp;β\u003csub\u003e3\u003c/sub\u003e\u0026thinsp;+\u0026thinsp;β\u003csub\u003e5\u003c/sub\u003e\u0026thinsp;+\u0026thinsp;β\u003csub\u003e7\u003c/sub\u003e respectively.\u003c/p\u003e\u003cp\u003eLevel and slope changes for the control group and cases are given by β\u003csub\u003e2\u003c/sub\u003e, β\u003csub\u003e3\u003c/sub\u003e, β\u003csub\u003e2\u003c/sub\u003e\u0026thinsp;+\u0026thinsp;β\u003csub\u003e6\u003c/sub\u003e, β\u003csub\u003e3\u003c/sub\u003e\u0026thinsp;+\u0026thinsp;β\u003csub\u003e7\u003c/sub\u003e respectively. The differences between cases and controls in intercept and slope before the intervention are β\u003csub\u003e4\u003c/sub\u003eand β\u003csub\u003e5\u003c/sub\u003e respectively. The differences in level changes and slope changes between cases and controls are β\u003csub\u003e6\u003c/sub\u003e and β\u003csub\u003e7\u003c/sub\u003e respectively.\u003c/p\u003e\u003cp\u003eThe covariance structure between cases and their matched controls is modeled by the G matrix, while the within-subject covariance structure due to repeated measures is modeled by the R matrix. The similarity between cases and their matched controls (within-cluster correlation) is typically measured using the intra-cluster correlation coefficient (ICC). A common assumption in matched case-control studies is that the correlation between any two matched cases and controls remains constant across all time points.\u003c/p\u003e\u003cp\u003eWhen a random-effects regression model is used to analyze matched case-control data, an exchangeable correlation is obtained by including a random intercept for the matching of cases and controls. The ICC can then be estimated as the ratio of the between-case/control variance to the total variance of the outcome\u003csup\u003e\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e\n\u003ch3\u003eSimulation\u003c/h3\u003e\n\u003cp\u003eWe generated 1,000 matched case-control datasets from the null model: \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{y}_{it}={b}_{i0}+{e}_{it}\\)\u003c/span\u003e\u003c/span\u003e where \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{y}_{it}\\)\u003c/span\u003e\u003c/span\u003e is the t\u003csub\u003eth\u003c/sub\u003e observation of the i\u003csub\u003eth\u003c/sub\u003e subject, b\u003csub\u003ei0\u003c/sub\u003e follows a normal distribution with mean zero and standard deviation σ\u003csub\u003eb\u003c/sub\u003e and e\u003csub\u003eit\u003c/sub\u003e follows an autoregressive process of order 1 (AR(1)): \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{e}_{it}=\\phi\\:{e}_{i(t-1)}+{a}_{t}\\)\u003c/span\u003e\u003c/span\u003e where \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{a}_{t}\\)\u003c/span\u003e\u003c/span\u003e follows a normal distribution with mean zero and constant variance σ. The random intercept b\u003csub\u003ei0\u003c/sub\u003e and e\u003csub\u003eit\u003c/sub\u003e are independent. The variance of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{y}_{it}\\)\u003c/span\u003e\u003c/span\u003eis the sum of variance of b\u003csub\u003ei0\u003c/sub\u003e and e\u003csub\u003eit\u003c/sub\u003e. Variance of e\u003csub\u003eit\u003c/sub\u003e is \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\frac{V\\left({a}_{t}\\right)}{(1-{\\phi\\:}^{2})}\\)\u003c/span\u003e\u003c/span\u003e thus \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:ICC=\\frac{{\\sigma\\:}_{b}^{2}}{\\frac{V\\left({a}_{t}\\right)}{\\left(1-{\\phi\\:}^{2}\\right)}+{\\sigma\\:}_{b}^{2}}\\)\u003c/span\u003e\u003c/span\u003e.\u003c/p\u003e\u003cp\u003eIn our simulation, we set σ\u0026thinsp;=\u0026thinsp;1, φ in (-0.8, -0.4, 0, 0.4, 0.8), intra-cluster correlation coefficient (ICC) in (0, 0.2, 0.4), the number of time points before and after the intervention in ( 5, 10 ), and the number of cases with 1:1 matched controls in ( 25, 50, 100 ). For each scenario the standard deviation of b\u003csub\u003ei0\u003c/sub\u003e is calculated using the formula \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:ICC=\\frac{{\\sigma\\:}_{b}^{2}}{\\frac{{\\sigma\\:}^{2}}{\\left(1-{\\phi\\:}^{2}\\right)}+{\\sigma\\:}_{b}^{2}}\\)\u003c/span\u003e\u003c/span\u003e .\u003c/p\u003e\n\u003ch3\u003eModels\u003c/h3\u003e\n\u003cp\u003eWe fitted two separate segmented linear regression models of the form \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{y}_{t}={\\beta\\:}_{0}+{\\beta\\:}_{1}{time}_{t}+{\\beta\\:}_{2}{intervention}_{t}+{\\beta\\:}_{3}{time-after}_{t}+{\\epsilon\\:}_{t}\\)\u003c/span\u003e\u003c/span\u003eto generated data for cases and control. The serial correlation is modeled as an autoregressive AR(1) process. The third model is the proposed segmented linear regression model that jointly is fitted to generated matched cases and control data. The serial correlation among the repeated measures is modelled as an autoregressive AR(1) process and the correlation between matched cases and controls is modelled as random intercept with variance component covariance structure.\u003c/p\u003e\u003cp\u003eWe used these 3 fitted regression models to calculate type I error and bias for interpret and slope of cases and controls before and after intervention, level and slope changes for cases and controls. Then we calculated the type I error and bias for difference between case and control level and slope change using the joint model. We also used Z-test to compare level and slope change differences between cases and controls using estimated level and slope changes calculated by separated segmented regression fitted to cases and control data separately.\u003c/p\u003e\u003cp\u003eType I error is estimated by the proportion of significant estimates at the level of 5 percent and Bias is estimated as the difference between the average of the estimated parameters and the true parameter. We also calculate and report estimated serial correlation and ICC.\u003c/p\u003e"},{"header":"Results","content":"\u003cp\u003eThe simulation results are summarized in Table\u0026nbsp;1 and Table\u0026nbsp;2 given in appendix.\u003c/p\u003e\u003cp\u003eTable\u0026nbsp;1 presents the bias and Type I error for regression lines before and after the intervention, as well as the level and slope changes estimated using separate and joint regression models.\u003c/p\u003e\u003cp\u003eTable\u0026nbsp;2 shows the differences between the intervention and control regression lines, along with the differences in level and slope changes between the case and control groups, obtained through separate and joint regression modeling.\u003c/p\u003e\n\u003ch3\u003eIntercept and Slope Before and After Intervention and Level and Slope Changes\u003c/h3\u003e\n\u003cp\u003eWhen examining Type I error for the intercept and slope before and after the intervention and level and slope changes \u0026mdash;across both cases and their matched controls\u0026mdash;using regression models fitted separately and jointly, the following patterns emerge: i) When the intraclass correlation coefficient (ICC) is zero, Type I errors are close to 5%, ii) However, when ICC is non-zero and φ is negative, the Type I errors from separate models fitted to the generated case and control data tend to be underestimated, iii) - In contrast, the Type I errors from joint segmented regression models remain close to 5% across all combinations of φ and ICC.\u003c/p\u003e\u003cp\u003eFigure 1: Plots showing Type I errors for estimated parameters of segmented regression lines, fitted separately and jointly, are presented here for simulated data where the number of time points before and after the intervention is 10.\u003c/p\u003e\u003cdiv id=\"Sec7\" class=\"Section2\"\u003e\u003ch2\u003eDifference in Level and Slope Changes\u003c/h2\u003e\u003cp\u003eWe examined the difference between cases and controls level and slope changes using two separate segmented regression fitted to cases and controls simulated data and by proposed jointly modelling the data. When ICC is zero type I errors for both methods are very close to 5% level. When ICC is not zero and serial correlation is negative the type I error for joint model are close to 5% while for separated models are below 5% level.\u003c/p\u003e\u003cp\u003eFigure 2: Plots showing Type I errors for differences (cases \u0026ndash; controls) estimated level and slope changes fitted separately and jointly, are presented here for simulated data where the number of time points before and after the intervention is 10.\u003c/p\u003e\u003c/div\u003e\n\u003ch3\u003eBias\u003c/h3\u003e\n\u003cp\u003eThe estimated bias for estimated parameters is close to zero. More accurately they ranged between \u0026minus;\u0026thinsp;0.04 to 0.04 for entire scenarios. More than 99% of estimated biases were between \u0026minus;\u0026thinsp;0.02 and 0.02.\u003c/p\u003e\n\u003ch3\u003eEstimated ICC and φ\u003c/h3\u003e\n\u003cp\u003eThe averages of the estimated ICC and φ across all scenarios are very close to the true values of ICC and φ.\u003c/p\u003e\u003cp\u003e\u003cstrong\u003eFigure 3\u003c/strong\u003e\u003cp\u003eEstimated ICC and φ compared with true values\u003c/p\u003e\u003c/p\u003e\u003cdiv id=\"Sec10\" class=\"Section2\"\u003e\u003ch2\u003eStandard Errors\u003c/h2\u003e\u003cp\u003eWe calculated the average standard errors of the estimated parameters using two approaches: (1) separate segmented regressions fitted to simulated data for cases and controls, and (2) a proposed joint model that simultaneously analyzes both datasets.\u003c/p\u003e\u003cp\u003eWhen the intraclass correlation coefficient (ICC) is zero, the estimated standard errors from both methods are very similar. However, when ICC is non-zero and serial correlation is negative, the standard errors from the separate models tend to be larger than those obtained from the joint model, which accounts for the dependency between cases and their matched controls.\u003c/p\u003e\u003cp\u003e\u003cstrong\u003eFigure 4\u003c/strong\u003e\u003cp\u003ePlots showing estimated standard errors for estimated parameters fitted separately and jointly, are presented here for simulated data where the number of time points before and after the intervention is 10.\u003c/p\u003e\u003c/p\u003e\u003c/div\u003e"},{"header":"Discussion","content":"\u003cp\u003eThis study contributes to the growing body of research on Interrupted Time Series Analysis (ITSA) designs, particularly in the context of Matched Controlled Interrupted Time Series (MCITS) studies. Our findings highlight the importance of properly accounting for correlation structures within matched pairs to ensure accurate statistical inference. A key challenge in ITSA designs with matched controls is the presence of two sources of dependency: within-cluster correlation due to case-control matching and within-subject correlation over time. Failure to account for these dependencies may lead to biased estimates and incorrect conclusions regarding the impact of interventions.\u003c/p\u003e\u003cp\u003eOur simulation study demonstrated that when intra-cluster correlation (ICC) is nonzero and serial correlation is negative, separate segmented regression models tend to underestimate type I error rates. This underestimation can have substantial implications for researchers relying on traditional ITSA approaches, as it may lead to incorrect conclusions about the significance of intervention effects. In contrast, the joint segmented regression model effectively controls type I error rates across various scenarios, ensuring more reliable inference.\u003c/p\u003e\u003cp\u003eOne of the fundamental advantages of the joint modeling approach is its ability to integrate both within-cluster and within-subject dependencies into a single analytical framework. By explicitly modeling the correlation between matched cases and controls, the joint model accounts for shared variance and improves precision in estimating intervention effects. This results in a more accurate assessment of level and slope changes before and after an intervention, strengthening causal interpretations.\u003c/p\u003e\u003cp\u003eThe study further emphasizes the need for researchers to carefully consider the impact of serial correlation and dependency structures when designing ITSA studies. While intra-cluster correlation is often treated as a nuisance factor, our findings suggest that failing to account for ICC can lead to erroneous conclusions. A key implication of this study is the recommendation for analysts to simultaneously model correlation due to matching using mixed-effects approach and to address serial correlation by explicitly modeling the covariance structure of the residuals. These approaches provide a flexible framework for handling complex correlation structures in matched interrupted time series analysis designs.\u003c/p\u003e\u003cp\u003eDespite the strengths of this approach, several challenges remain. For example, the selection of an appropriate covariance structure is crucial in ensuring the validity of parameter estimates. While our joint model effectively controlled type I error rates, alternative modeling strategies\u0026mdash;such as incorporating non-exchangeable correlation structures\u0026mdash;should be explored in future research. Additionally, the findings are based on simulated data, and real-world applications may introduce additional complexities, such as unmeasured confounders or heterogeneity in intervention effects.\u003c/p\u003e\u003cp\u003eOverall, this study underscores the methodological considerations necessary for robust ITSA designs with matched controls. The findings reinforce the importance of adopting joint modeling approaches to enhance causal inference and reduce bias in intervention effect estimates. Future research should aim to refine these techniques and extend their applications across diverse fields, ensuring that ITSA remains a powerful tool for evaluating intervention effectiveness in longitudinal studies.\u003c/p\u003e"},{"header":"Conclusion","content":"\u003cp\u003eThis study underscores the critical importance of appropriately modeling correlation structures in matched controlled interrupted time series analyses. Specifically, failure to account for intra-cluster correlation and serial correlation can substantially distort Type I error rates, potentially undermining causal inference. By incorporating both correlation sources within a joint linear mixed-effects segmented regression framework, researchers can achieve more accurate and reliable inference.\u003c/p\u003e\u003cp\u003eWe recommend that applied researchers employing matched CITS designs use models that explicitly account for the dependencies within matched pairs and across repeated time points. As the use of matched CITS designs continues to expand in evaluating complex interventions\u0026mdash;particularly in health policy, public health, and implementation science\u0026mdash;ensuring valid statistical inference through robust modeling approaches is essential.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eEthics approval and consent to participate\u003c/strong\u003e\u003cp\u003eNot Applicable\u003c/p\u003e\u003c/p\u003e\u003cp\u003e\u003cstrong\u003eConsent for publication\u003c/strong\u003e\u003cp\u003eNot Applicable\u003c/p\u003e\u003c/p\u003e\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\u003cp\u003eRM wrote the main manuscript, performed data analysis, interpretation of results and reviewed the manuscript.\u003c/p\u003e\u003ch2\u003eAcknowledgements\u003c/h2\u003e\u003cp\u003e Not Applicable\u003c/p\u003e\u003ch2\u003eData Availability\u003c/h2\u003e\u003cp\u003eThe data that supports the findings of this study are not publicly available.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eCruz M, Bender M, Ombao H. 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Oxford;: Oxford University Press; 2002.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eOuyang Y, Kulkarni MA, Protopopoff N, Li F, Taljaard M. Accounting for complex intracluster correlations in longitudinal cluster randomized trials: A case study in malaria vector control. BMC Med Res Methodol. 2023;23(1):64. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.1186/s12874-023-01871-2\u003c/span\u003e\u003cspan address=\"10.1186/s12874-023-01871-2\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"},{"header":"Tables","content":"\u003cp\u003eTable 1 and 2 are available in the Supplementary Files section.\u003c/p\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":"bmc-medical-research-methodology","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"bmrm","sideBox":"Learn more about [BMC Medical Research Methodology](http://bmcmedresmethodol.biomedcentral.com/)","snPcode":"","submissionUrl":"https://www.editorialmanager.com/bmrm/default.aspx","title":"BMC Medical Research Methodology","twitterHandle":"BMC_series","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"em","reportingPortfolio":"BMC Series","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"","lastPublishedDoi":"10.21203/rs.3.rs-7565524/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7565524/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eInterrupted Time Series Analysis (ITSA) is a widely used quasi-experimental method for evaluating the longitudinal impact of interventions. This study explores the methodological considerations of Matched Controlled Interrupted Time Series (MCITS) designs, particularly the effects of serial correlation and dependency between matched cases and controls on type I error and bias.\u003c/p\u003e\u003cp\u003eUsing a Monte Carlo simulation approach, we assess the accuracy, type I error and bias, of parameter estimates and compare single and joint segmented regression models.\u003c/p\u003e\u003cp\u003eResults indicate that type I error is underestimated in separate models when intra-cluster correlation (ICC) is nonzero and serial correlation is negative, whereas joint modeling maintains appropriate error rates. Bias estimates remain minimal across scenarios, reinforcing the robustness of the joint model for analyzing intervention effects in matched controlled ITSA designs.\u003c/p\u003e\u003cp\u003eThese findings provide important insights for researchers conducting longitudinal evaluations of interventions in fields such as healthcare and public policy.\u003c/p\u003e","manuscriptTitle":"The Impact of Dependency and Serial Correlation in Matched ITSA: Methodological Considerations","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-11-06 04:20:40","doi":"10.21203/rs.3.rs-7565524/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"editorInvitedReview","content":"","date":"2025-11-07T07:46:58+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"223752563038405506553604424948448605875","date":"2025-10-31T07:34:42+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2025-10-24T20:40:57+00:00","index":"","fulltext":""},{"type":"editorInvited","content":"","date":"2025-09-26T18:32:43+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2025-09-25T09:27:10+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2025-09-25T09:26:35+00:00","index":"","fulltext":""},{"type":"submitted","content":"BMC Medical Research Methodology","date":"2025-09-08T14:42:56+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"bmc-medical-research-methodology","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"bmrm","sideBox":"Learn more about [BMC Medical Research Methodology](http://bmcmedresmethodol.biomedcentral.com/)","snPcode":"","submissionUrl":"https://www.editorialmanager.com/bmrm/default.aspx","title":"BMC Medical Research Methodology","twitterHandle":"BMC_series","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"em","reportingPortfolio":"BMC Series","inReviewEnabled":true,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"1b06ed90-7005-4afa-8fb0-db53945a5641","owner":[],"postedDate":"November 6th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[],"tags":[],"updatedAt":"2025-11-06T04:20:40+00:00","versionOfRecord":[],"versionCreatedAt":"2025-11-06 04:20:40","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-7565524","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-7565524","identity":"rs-7565524","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}