Mixed Effects Logistic Regression Models for Longitudinal Ordinal Functional Response Data with Multiple‐Cause Drop‐Out from the Longitudinal Study of Aging

Summary. In the context of analyzing ordinal functional limitation responses from the Longitudinal Study of Aging, we investigate the association between current functional limitation and previous year's limitation and its modification by physical activity and multiple causes of drop‐out. We accommodate the longitudinal nature of the multiple causes of informative drop‐out (death and unknown loss‐to‐follow‐up) with a mixed effects logistic model. Under the proposed model with a random intercept and slope, the ordinal functional outcome and multiple discrete time survival profiles share a common random effect structure. This shared parameter selection model assumes that the multiple causes of drop‐out are conditionally independent of the functional limitation outcome given the underlying random effect representing an individual's trajectory of general health status across time. Although it is not possible to fully assess the adequacy of this assumption, we assess the robustness of the approach by varying the assumptions underlying the proposed model, such as the random effects distribution and the drop‐out component. It appears that between‐subject differences in initial functional limitation are strongly associated with future functional limitation and that this association is stronger for those who do not have physical activity regardless of the random effects and informative dropout specifications. In contrast, the association between current functional limitation and previous trajectory of functional status within an individual is weaker and more sensitive to changes in the random effects and drop‐out assumptions.