panel data - Time-varying covariates in longitudinal analysis - Cross , Zeger S. Pepe xzt1@psu.edu PMID: 22103434 PMCID: PMC3288551 DOI: 10.1037/a0025814 Abstract PeerJ. I am looking for some help with my analysis of longitudinal data with time-varying covariates. Daniel RM, Cousens SN, De Stavola BL, et al. R01 CA090514/CA/NCI NIH HHS/United States, P50 DA010075/DA/NIDA NIH HHS/United States, R21 DA024260-01/DA/NIDA NIH HHS/United States, T32 CA009461/CA/NCI NIH HHS/United States, R21 DA024260/DA/NIDA NIH HHS/United States, P50 DA010075-14/DA/NIDA NIH HHS/United States, R01 DA022313/DA/NIDA NIH HHS/United States. We define. Secondly, if follow-up was stopped at a time later than the last visit, then additional rows capturing the censoring time must be added to the dataset. Please enable it to take advantage of the complete set of features! Stat. Glymour et al. endobj A 95% confidence interval for Y was estimated using 1,000 bootstrap samples, using the percentile method (22, 23). Daniel (2015). constant times, which is commonly assumed in longitudinal data analysis. Step 2. Regression analysis of longitudinal data with time-dependent covariates SCMMs give better precision even than stabilized weights in realistic scenarios. Hong SH, Chung HS, Seo IY, Kwon TG, Jeong H, Chung JI, Jeon SH, Park JY, Ha HK, Chung BH, Song W, Kim YJ, Kim SH, Lee JS, Lee J, Chung J. J Patient Rep Outcomes. Clipboard, Search History, and several other advanced features are temporarily unavailable. In: Seeber, G.U.H., et al. eCollection 2023 Mar. To subscribe to this RSS feed, copy and paste this URL into your RSS reader. Before Goetgeluk S, Vansteelandt S, Goetghebeur E. Estimation of controlled direct effects. endobj Asking for help, clarification, or responding to other answers. In practice, bias can also occur due to lack of positivity, which requires both exposed and unexposed individuals at every level of the confounders (13). The effect of blood cadmium levels on hypertension in male firefighters in a metropolitan city. Figure 1 visualizes the primary issues arising in a longitudinal observational setting, notably that prior exposure affects future outcome, prior outcome affects future exposure and covariates, and that there is time-dependent confounding by time-varying covariates Lt: Lt are confounders for the association between Xt and Yt, but on the pathway from Xt1 to Yt. Econometrica 50(4), 10291054 (1982), Hansen, L.P.: Generalized Method of Moments Estimation, pp. Data from the Comprehensive Dialysis Study motivate the proposed methods. , Daniel RM. In the numerator of the stabilized weights, we used a logistic model for Xt with Xt1 as the predictor. , Anderson G. Vansteelandt Fitted linear regression lines demonstrate the directionality and the extent of the association between negative affect and smoking urges. We considered two MSMs: 1) E(Ytxt)=0+X1xt; and 2) E(Ytxt)=0+X1xt+X2xt1. , Brumback B, Robins JM. 81, 11581168 (2007), CrossRef Econometrica 50, 569582 (1982), CrossRef The most commonly used is marginal structural models (MSM) estimated using inverse probability of treatment weights . <> Individuals are observed at T visits, t=1,,T, at which we observe the outcome Yt, the exposure Xt, and a vector of covariates Lt. Connect and share knowledge within a single location that is structured and easy to search. 14 0 obj The site is secure. Department of Medical Statistics, London School of Hygiene and Tropical Medicine, London, United Kingdom. Dziak JJ, Li R, Tan X, Shiffman S, Shiyko MP. Trent L. Lalonde . =HI8xFA n-.q4ZQLka([~3 -i|xJtNEP_7D$%"EAbjK]~] Z_qYDM:gRHE5w' `n,@z@3~oAppZG(d~IAGU|p#k5[yFj:=,00KFZh%tod>:Da{}CY4'!QqI(*og):`=X9#RjD+4 Wl xT mE/4M\v\ {Vd%H.fkcwk6? Unstabilized weights are most commonly used to estimate marginal effects, although they can also be used in fitting MSMs that condition on baseline variables. In model (2) X1 represents the total effect of Xta on Yt. . Assoc. Wiley, Hoboken (2008), Neuhaus, J.M., Kalbfleisch, J.D. LMM, GEE) that can analyze longitudinal data with: Unequal number of observations per person (ni) Unequally spaced observations (tij) Time-varying covariates (xij) Regression questions: i(t) =E[Yi(t)| Xi(t)] Innovative Statistical Methods for Public Health Data, https://doi.org/10.1007/978-3-319-18536-1_4, Tax calculation will be finalised during checkout. , Hernn MA. , Hotz J, Imbens I, et al. Interest may lie in studying the total effect of an exposure at a given time on a concurrent or subsequent outcome or in the effect of a pattern of exposures over time on a subsequent outcome. We outline this approach and describe how including propensity score adjustment is advantageous. : Analysis of Longitudinal Data, 2nd edn. During the last couple of decades statistical methods have been developed (ie. Figure 1 could be extended to allow non-time-varying covariates and more lagged effects, (e.g., an arrow from Xt2 to Yt). A review of the use of timevarying covariates in the FineGray In that case, the observed data may carry insufficient information to infer the average outcome if everyone versus no one were exposed, while there may be sufficient information to answer that question for subgroups where there is sufficient overlap (12, 19). 90(431), 845852 (1995), Fitzmaurice, G.M., Laird, N.M., Ware, J.H. endobj 2023 Jan 25;14:1051208. doi: 10.3389/fphys.2023.1051208. Association Between Dietary Potassium Intake Estimated From Multiple 24-Hour Urine Collections and Serum Potassium in Patients With CKD. This paper discusses estimation of causal effects from studies with longitudinal repeated measures of exposures and outcomes, such as when individuals are observed at repeated visits. Springer, New York (1995), Department of Applied Statistics and Research Methods, University of Northern Colorado, Greeley, CO, USA, You can also search for this author in B 69(1), 7999 (2007), Lalonde, T.L., Nguyen, A.Q., Yin, J., Irimate, K., Wilson, J.R.: Modeling correlated binary outcomes with time-dependent covariates. Understanding temporal change in human behavior and psychological processes is a central issue in the behavioral sciences. SCMMs estimate conditional effects, whereas MSMs are typically used to estimate marginal effects. To further assess the test for long-term direct effects we generated data under a second scenario in which there is no direct effect of Xt1 on Yt (Y=0 in model (14)), represented by a modification of Figure 1A with the arrows from Xt1 to Yt removed (simulation scenario 2). )W@p#jwZuV.vDfy]MOQs w`j'3h/J,pk,gD#@2C.)8zj,7g,|) zkLSla?#cCrg:yWJ/ &^$]7BZtQ~8;q/MfV\"FMUH)mf5ad4LKz"F s;Nyoah AEvi-1bZZMF9\DL%}9w'Lrt9aW[ 3) In scenario 2, the mean estimate of Y was 0.012 (standard deviation, 1.102), and 5.2% of the 95% confidence intervals for Y excluded 0, demonstrating approximately correct type I errors. However, I am happy to use Stata also. Using propensity scores gives two primary advantages (12). PMC The effect of Xt on Yt is confounded by prior exposure Xt1 and prior outcome Yt1 (via UY), implying that to obtain an unbiased effect estimate, the SCMM should either include Xt1 and Yt1, or it should include Xt1 and use an unstructured working correlation matrix. Arguello D, Rogers E, Denmark GH, Lena J, Goodro T, Anderson-Song Q, Cloutier G, Hillman CH, Kramer AF, Castaneda-Sceppa C, John D. Sensors (Basel). Statistical analysis of longitudinal data requires methods that can properly account for the intra-subject cor-relation of response measurements. 2023 Springer Nature Switzerland AG. , Wang Y, van der Laan MJ, et al. Chapman & Hall/CRC, Boca Raton (2006), Liang, K.Y., Zeger, S.L. , Vansteelandt S, Goetghebeur E. Naimi Innovative Statistical Methods for Public Health Data pp 5779Cite as, Part of the ICSA Book Series in Statistics book series (ICSABSS). 2013;32(9):15841618. S We outlined a new test for existence of long-term direct effects, which may be used as a simple alternative to the direct effect g-null test. To estimate causal effects, we assume no unmeasured confounding. Chapman & Hall, New York (2003), Hedeker, D., Gibbons, R.D. We refer to the resulting estimation approach as sequential conditional mean models (SCMMs), which can be fitted using generalized estimating equations . Comput. In this chapter a discussion is presented of analysis options for longitudinal data with time-dependent covariates. There is a large literature on adjustment for baseline outcomes in studies of the relationship between an exposure and a follow-up outcome or change in outcome. : Hierarchical generalised linear models: a synthesis of generalised linear models, random-effect models and structured dispersions. : Models for longitudinal data: a generalized estimating equation approach. 3pm}^9F%]pL7. There is some small finite sample bias using unstabilized weights. An official website of the United States government. 26(3), 947957 (2014), Wooldridge, J.M. How do I model these variables in my mixed effect model? ILD offer unique opportunities to describe temporal behavioral changes in detail and identify related environmental and psychosocial antecedents and consequences. Using the model from step 1, obtain the predicted outcomes Yt when Xt=0(t=1,,T) (i.e., when we force no effect of Xt on Yt). In this paper we propose joint modeling and analysis of longitudinal data with time-dependent covariates in the presence of informative observation and censoring times via a latent variable, and the distribution of the latent variable is left unspecified. : A cautionary note on inference for marginal regression models with longitudinal data and general correlated response data. Site design / logo 2023 Stack Exchange Inc; user contributions licensed under CC BY-SA. PMC Disclaimer. A time-varying effect model for intensive longitudinal data Authors Xianming Tan 1 , Mariya P Shiyko , Runze Li , Yuelin Li , Lisa Dierker Affiliation 1 The Methodology Center, The Pennsylvania State University, 204 East Calder Way, Suite 400, State College, PA 16801, USA. Hypertension is the diagnosis of hypertension at each wave (timepoint) - once a person has been diagnosed they cannot go back to being non-hypertensive, the same is true for the variable diabetes. Guidelines for multiple imputations in repeated measurements with time R.M.D. Our approach, stemming from functional principal component analysis, calibrates the unobserved synchronized covariate values from the observed asynchronous and error-prone covariate values, and is broadly applicable to asynchronous longitudinal regression with time-invariant or time-varying coefficients. Unstabilized weights are not recommended because they are known to be highly variable, but we include them for comparison. Sharma N, Moffa G, Schwendimann R, Endrich O, Ausserhofer D, Simon M. BMC Health Serv Res. In the SCMMs, model i fails to account for confounding by Xt1 and Yt1, and model ii fails to account for confounding by Xt1; in neither case can this by accounted for using an unstructured working correlation matrix, which only handles confounding by Yt1. : A caveat concerning independence estimating equations with multiple multivariate binary data. The https:// ensures that you are connecting to the The set of measures up to time t is indicated using a bar (e.g., Xt=(X1,,Xt1,Xt)). The .gov means its official. Good introductions to these methods are available (2, 3), and while the other g-methods are still not widely used, IPW estimation of MSMs is becoming more commonplace. Cannabis Use Is Associated With Decreased Antiretroviral Therapy Adherence Among Older Adults With HIV. , Joffe M. Vansteelandt Unauthorized use of these marks is strictly prohibited. The PubMed wordmark and PubMed logo are registered trademarks of the U.S. Department of Health and Human Services (HHS). Estimation of causal effects of time-varying exposures using longitudinal data is a common problem in epidemiology. However, there are variables such as smoking that can differ and change over the different waves. We therefore propose using bootstrapping. We recommend adjustment for prior outcomes in the SCMM. S QE( (\'Jya8nkR"kh#`;XAMtmm`qH:Z^;wX6l|0q|wO\ ksk5m''oAQHaEPEP^oiXZFN +c1-5fsg{?W/H:hr5K'[J]?cT9$VZH76~{wITy{W=j4K\[HZWl:U49]oG+2k!Go>jMpkO\k6bGiq9b6:g\~j -z}XD[DHh\MT[wag_~z`)$iaz hoZ|TgBLy~l`QkgQBkd"$v"5WOjz`^#O(GkrKj$ Methods such as inverse probability weighted estimation of marginal structural models have been developed to address this problem. Bethesda, MD 20894, Web Policies , Glymour M, Weuve J, et al. The COVID-19 pandemic has affected us in numerous ways and may consequently impact our relationships with pet dogs and cats. See this image and copyright information in PMC. Springer, Cham. While standard regression adjustment is often employed in studies using longitudinal measures, issues of potential biases due to time-dependent confounding are not always carefully considered and do indeed result in bias if prior values of the exposure and outcome are not controlled for. That is, we provide a reminder that it is not always necessary to default to using IPW estimation of MSMs or g-methods when there are time-varying confounders. Anyone you share the following link with will be able to read this content: Sorry, a shareable link is not currently available for this article. Psychol Methods. Why do men's bikes have high bars where you can hit your testicles while women's bikes have the bar much lower? Is there additional value of using repeated measurements in this specific case? However, HA-MSMs have not been much used in practice, and their validity remains in question (18). Modeling options for time-dependent covariate data are presented in two general classes: subject-specific models and population-averaged models. Step 3. Prev Sci. Multiscale Adaptive Marginal Analysis of Longitudinal Neuroimaging Data I would differentiate between time-varying covariates, such as smoking, and intermediate events, such as hypertension in your example. Amemiya, T.: Advanced Econometrics. This is an area for further work. The propensity score model for Xt included Yt1 and Xt1. In addition to their simplicity and familiarity, SCMMs extend more easily to accommodate continuous exposures, drop-out, and missing data (see Web Appendix 5). Is a downhill scooter lighter than a downhill MTB with same performance? Biometrics 51, 309317 (1995), Fitzmaurice, G.M., Laird, N.M.: Regression models for a bivariate discrete and continuous outcome with clustering. MP Fit a SCMM for Yt given Xt and the covariate history up to time t, including prior exposures and outcomes. Estimation of the causal effects of time-varying exposures. Unsynchronized longitudinal data refer to the timedependent response and covariate measurements for each individual measured at distinct time points. Also Taking ACE inhibitors: someone can take this drug in one wave but then in others, they might not. R.H.K. For linear models X1, X1, and X1 all represent the same estimand, provided the MSMs and SCMM are correctly specified. : Generalized Estimating Equations. This occurs particularly in studies with many visits or continuous exposures (4, 5). : Generalized Linear Models, 2nd edn. Making statements based on opinion; back them up with references or personal experience. Clipboard, Search History, and several other advanced features are temporarily unavailable. In: Chen, DG., Wilson, J. Epub 2015 Sep 21. c Monte Carlo 95% confidence interval corresponding to the bias. Precision was improved under truncation but comes at a cost of bias, which is small using MSM 2 but quite large using MSM 1. Data were simulated according to Figure 1A, using n=200 individuals observed at T=5 visits (simulation scenario 1). The site is secure. <>/Font<>/ProcSet[/PDF/Text/ImageB/ImageC/ImageI] >>/MediaBox[ 0 0 720 540] /Contents 19 0 R/Group<>/Tabs/S/StructParents 2>> , Rose S, Mortimer KM. B (Methodological) 58(4), 619678 (1996), Lee, Y., Nelder, J.A. Why the obscure but specific description of Jane Doe II in the original complaint for Westenbroek v. Kappa Kappa Gamma Fraternity? Soc. In linear models, our propensity score adjusted estimates are equivalent to efficient g-estimates in a SNMM for short-term effects (27). The analysis of longitudinal data requires a model which correctly accounts for both the inherent correlation amongst the responses as a result of the repeated measurements, as well as the feedback between the responses and predictors at different time points. 2012 Jun;13(3):288-99. doi: 10.1007/s11121-011-0264-z. See this image and copyright information in PMC. Often public health data contain variables of interest that change over the course of longitudinal data collection. Time varying covariates in longitudinal mixed effect models, Analysis of Longitudinal Data, 2nd Edition, New blog post from our CEO Prashanth: Community is the future of AI, Improving the copy in the close modal and post notices - 2023 edition, Testing simultaneous and lagged effects in longitudinal mixed models with time-varying covariates, When parameters are dropped from fixed effects in lmer, drop corresponding random effects, Time-varying covariates in longitudinal analysis, Interpretation and Prediction in Longitudinal Models with an Interaction between a Time-Varying Predictor and Time Itself, Mixed effects modeling using R with time varying predictors, Changing the time metric for longitudinal data. Interestingly, this holds even if the functional form of the propensity score used in the SCMM is misspecified, provided the exposure effect is the same across all levels of the propensity score and the remaining predictors in the model (12). The methods described in this paper are based on sequential conditional mean models (SCMMs) for the repeated outcome measures, fitted using generalized estimating equations (GEEs). Accessibility Challenges that arise with time-varying covariates are missing data on the covariate at different time points, and a potential bias in estimation of the hazard if the time-varying covariate is actually a mediator. Is there a generic term for these trajectories? x]k0 R.D%MAYv1va'&+)9)!e&7=}*p WW7 &8 B*% GEE for Repeated Measures Analysis | Columbia Public Health , Petersen M, Joffe M. Robins is supported by a Sir Henry Dale Fellowship jointly funded by the Wellcome Trust and the Royal Society (award 107617/Z/15/Z). <> Smoking urges for the same individual are plotted in the middle graph. Reger E, Javet M, Born DP, Heyer L, Romann M. Front Physiol. endobj Published by Oxford University Press on behalf of the Johns Hopkins Bloomberg School of Public Health. Our method categorizes covariates into types to determine the valid moment conditions to combine during estimation. KY Accessibility The 5. M Ser. 12 0 obj . <> . 15 0 obj Ogata S, Akashi Y, Kato S, Oka Y, Suda A, Yoshizaki S, Maeda Y, Nishimura K, Maeda K, Nakai S. Kidney Int Rep. 2022 Dec 11;8(3):584-595. doi: 10.1016/j.ekir.2022.12.005. This is a preview of subscription content, access via your institution. However, in this paper we show how standard regression methods can be used, even in the presence of time-dependent confounding, to estimate the total effect of an exposure on a subsequent outcome by controlling appropriately for prior exposures, outcomes, and time-varying covariates. Longitudinal Data Analysis - Harvard University Browse other questions tagged, Start here for a quick overview of the site, Detailed answers to any questions you might have, Discuss the workings and policies of this site. This site needs JavaScript to work properly. Vansteelandt A) Without time-varying confounders. In each simulated data set under scenario 1, we fitted SCMMs and MSMs using GEEs with independent and unstructured working correlation matrices. Analysis of Longitudinal Studies With Repeated Outcome Measures Associations between an exposure Xt and outcome Yt measured longitudinally, with random effects UX and UY (circles indicate that these are unobserved). xMK1N&n"E!`[jzBf23[89n!)% *DDX@A"itc+>|]F:U4K8)~t? J. Roy. There are several important considerations for time-varying covariates for longitudinal outcomes: If the time-varying covariate is exogenous or endogenous: That is, if the value of the covariate at a time point t is associated only with its history or it is also with the history of the outcome before t. 2023 Feb 7. Methods such as inverse probability Biometrika 88(4), 9871006 (2001), Lee, Y., Nelder, J.A. This paper does not consider another type of causal effectthe joint effect of a particular pattern of exposures over a series of time points on a subsequent outcome (e.g., the joint effect of Xt1 and Xt on Yt). We recommend adjustment for the outcome history and propensity scores, and estimation using independence GEE. . Conditional effects may be more realistic for interpretation, in particular when the exposed and unexposed have quite different covariate histories. Methods such as inverse probability weighted estimation of marginal structural models have been developed to address this problem. Ser. We set out the important considerations for securing results against bias due to model misspecification and compare the effects that can be estimated using SCMMs and IPW estimation of MSMs, as well as comparing the methods in simulation studies. Am. Stat. M ?crl8mu=GwyhSxGkeL|S :GN*OQh--@7S Causal inference in survival analysis using longitudinal observational The usual estimate of the standard error of Y will be erroneously small because it ignores that the Yt are predicted values. Disclaimer. endobj Biometrics 54, 638645 (1998), CrossRef AI Biometrics 44(4), 10491060 (1988), CrossRef In contrast, in SCMM (, Because SCMMs estimate conditional effects, they extend straightforwardly to allow interactions between exposure and time-dependent covariates. h (t) = exp {.136*age - .532*c + .003*c*time} * h0 (t) The problem is that this regression includes the (continously varying) time-varying regressor c*time . Since every observation gets a row, any two observations can have a different value of the treatment variable, even for the same subject.