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Mixed Effects Logistic Regression Models for Multiple Longitudinal Binary Functional Limitation Responses with Informative Drop-Out and Confounding by Baseline Outcomes

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In the context of analyzing multiple functional limitation responses collected longitudinally from the Longitudinal Study of Aging (LSOA), we investigate the heterogeneity of these outcomes with respect to their associations with previous functional status and other risk factors in the presence of informative drop-out and confounding by baseline outcomes. We accommodate the longitudinal nature of the multiple outcomes with a unique extension of the nested random effects logistic model with an autoregressive structure to include drop-out and baseline outcome components with shared random effects. Estimation of fixed effects and variance components is by maximum likelihood with numerical integration. This shared parameter selection model assumes that drop-out is conditionally independent of the multiple functional limitation outcomes given the underlying random effect representing an individual's trajectory of functional status across time. Whereas it is not possible to fully assess the adequacy of this assumption, we assess the robustness of this approach by varying the assumptions underlying the proposed model such as the random effects structure, the drop-out component, and omission of baseline functional outcomes as dependent variables in the model. Heterogeneity among the associations between each functional limitation outcome and a set of risk factors for functional limitation, such as previous functional limitation and physical activity, exists for the LSOA data of interest. Less heterogeneity is observed among the estimates of time-level random effects variance components that are allowed to vary across functional outcomes and time. We also note that, under an autoregressive structure, bias results from omitting the baseline outcome component linked to the follow-up outcome component by subject-level random effects.

Keywords: Autoregressive structure; Discrete-time survival; Nested random effects; Numerical integration; Shared parameter

Document Type: Research Article


Affiliations: 1: Department of Biostatistics and Epidemiology, University of Pennsylvania School of Medicine, Blockley Hall, 6th Floor, 423 Guardian Drive, Philadelphia, Pennsylvania 19104-6021, U.S.A. 2: Section on Biostatistics, Department of Public Health Sciences, Wake Forest University School of Medicine, Winston-Salem, North Carolina 27157, U.S.A. 3: Department of Health Evaluation Sciences, Pennsylvania State University School of Medicine, Hershey, Pennsylvania 17033, U.S.A.

Publication date: March 1, 2002


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