Analysis of Repeated Ordered Categorical Outcomes with Possibly Missing Observations and Time-Dependent Covariates

Abstract

This article describes a method for comparing responses in two groups of subjects observed repeatedly at a common set of observation times when the response is an ordered categorical outcome. The method, which allows both time-dependent covariates and missing observations, consists of two analytic steps. In the first step, the data are analyzed separately at each occasion using a regression model chosen from the class of models for ordinal data proposed by McCullagh (1980). The joint asymptotic distribution of the estimates of these occasion-specific regression coefficients and a consistent estimator of their asymptotic covariance matrix are obtained without imposing any parametric model of dependence on the repeated observations. In the second step, this asymptotic distribution, together with appropriate simultaneous inference procedures, is used to characterize the overall difference between groups and the variation in group differences over time. The missing-data process may differ between groups to be compared, but it must be independent of response given the covariate values. The new procedures are illustrated by an analysis of annual reports of severity of wheezing in a cohort of preadolescent children participating in a longitudinal study of air pollution and respiratory health.