A marginal model for analyzing discrete outcomes from longitudinal surveyswith outcomes subject to multiple-cause nonresponse

Techniques for analyzing categorical outcomes obtained from longitudinal su rvey samples, with outcomes subject to multiple-cause nonresponse, are deve loped within the framework, of weighted generalized estimating equations. D evelopment of these techniques was motivated by disability data obtained fr om the Longitudinal Study of Aging (LSOA), a longitudinal survey sample con taining missing follow-up for many elderly participants. We posit a model t hat combines different multivariate link functions to permit fitting Markov models to an outcome with categories represented by a mixture of ordinal s uccess states and multiple failure states. Extending the missing data appro ach of Robins, Rotnitzky, and Zhao to longitudinal survey sample settings, we use multiple-logit models to model the probability of multiple reasons f or missing success or failure outcomes. Given the assumption that the proba bility of nonresponse depends only on observed responses and covariates spe cified in the missing data model, weighted estimating equations that permit the incorporation of both survey and missing data weights are used in esti mation of parameters specified in the Markov models. Taylor series and jack knife variance estimators are developed for parameters estimated from these models and are presented within the context of adjusting for survey consid erations and multiple-cause nonresponse. The sensitivity of marginal model results to different features of the survey design and missing data conside rations are explored. Analyses of the LSOA suggest that participation in ph ysical activity may be an important predictor of transitions in functional limitations among older adults.