Regression analysis of longitudinal data with irregular and informative observation times

In longitudinal data analyses, the observation times are often assumed to be independent of the outcomes. In applications in which this assumption is violated, the standard inferential approach of using the generalized estimating equations may lead to biased inference. Current methods require the correct specification of either the observation time process or the repeated measure process with a correct covariance structure. In this article, we construct a novel pairwise likelihood method for longitudinal data that allows for dependence between observation times and outcomes. This method investigates the marginal covariate effects on the repeated measure process, while leaving the probability structure of the observation time process unspecified. The novelty of this method is that it yields consistent estimator of the marginal covariate effects without specification of the observation time process or the covariance structure of the repeated measures process. Large sample properties of the regression coefficient estimates and a pairwise likelihood ratio test procedure are established. Simulation studies demonstrate that the proposed method performs well in finite samples. An analysis of weight loss data from a web-based program is presented to illustrate the proposed method.