A Marginal Model for Analyzing Discrete Outcomes From Longitudinal Surveys With Outcomes Subject to Multiple-Cause Nonresponse

• Published in: Journal of the American Statistical Association Vol. 96; no. 455; pp. 844 - 857
• Main Authors: Miller, Michael E, Ten Have, Thomas R, Reboussin, Beth A, Lohman, Kurt K, Rejeski, W. Jack
• Format: Journal Article
• Language: English
• Published: Alexandria, VA Taylor & Francis 01.09.2001; American Statistical Association; Taylor & Francis Ltd
• Subjects: Analytical estimating; Applications and Case Studies; Categorical outcome model; Exact sciences and technology; Exercise; Experimental design; Generalized estimating equation; Markov models; Mathematical independent variables; Mathematics; Missing data; Modeling; Multivariate analysis; Musical intervals; Nonresponse model; Older adults; Parametric inference; Parametric models; Polls & surveys; Probability and statistics; Sampling; Sampling theory, sample surveys; Sciences and techniques of general use; Statistical methods; Statistical models; Statistical variance; Statistics; Survey data; Survey sample; Mixed distribution; Data analysis; Parameter estimation; Variance estimation; Taylor series; Probability distribution; Markov model; Multivariate analysis; Covariate; Missing data; Sampling theory; Model matching; Experimental design; Generalized equation; Marginal distribution; Bootstrap; Jackknife method; Estimating equation; Logit model; Sample survey; Resampling method
• ISSN: 0162-1459; 1537-274X
• DOI: 10.1198/016214501753208555

Techniques for analyzing categorical outcomes obtained from longitudinal survey samples, with outcomes subject to multiple-cause nonresponse, are developed within the framework of weighted generalized estimating equations. Development of these techniques was motivated by disability data obtained from the Longitudinal Study of Aging (LSOA), a longitudinal survey sample containing missing follow-up for many elderly participants. We posit a model that combines different multivariate link functions to permit fitting Markov models to an outcome with categories represented by a mixture of ordinal success states and multiple failure states. Extending the missing data approach of Robins, Rotnitzky, and Zhao to longitudinal survey sample settings, we use multiple-logit models to model the probability of multiple reasons for missing success or failure outcomes. Given the assumption that the probability of nonresponse depends only on observed responses and covariates specified in the missing data model, weighted estimating equations that permit the incorporation of both survey and missing data weights are used in estimation of parameters specified in the Markov models. Taylor series and jackknife variance estimators are developed for parameters estimated from these models and are presented within the context of adjusting for survey considerations and multiple-cause nonresponse. The sensitivity of marginal model results to different features of the survey design and missing data considerations are explored. Analyses of the LSOA suggest that participation in physical activity may be an important predictor of transitions in functional limitations among older adults.