A Semiparametric Marginalized Model for Longitudinal Data with Informative Dropout

We propose a marginalized joint-modeling approach for marginal inference on the association between longitudinal responses and covariates when longitudinal measurements are subject to informative dropouts. The proposed model is motivated by the idea of linking longitudinal responses and dropout times by latent variables while focusing on marginal inferences. We develop a simple inference procedure based on a series of estimating equations, and the resulting estimators are consistent and asymptotically normal with a sandwich-type covariance matrix ready to be estimated by the usual plug-in rule. The performance of our approach is evaluated through simulations and illustrated with a renal disease data application. 1. Introduction Longitudinal studies often encounter data attrition because subjects drop out before the designated study end. Both statistical analysis and practical interpretation of longitudinal data can be complicated by dropouts. For example, in the Modification of Diet in Renal Disease (MDRD) study [1, 2], one main interest was to investigate the efficacy of interventions of blood pressure control and diet modification on patients with impaired renal functions. The primary outcome was glomerular filtration rate (GFR), which measured filtering capacity of kidneys, and was repeatedly measured over the study period. However, some patients could leave the study prematurely for kidney transplant or dialysis, which precluded further GFR measurements. This resulted in a dropout mechanism that could relate to patients’ kidney function and correlate with their GFR values. Other patients were followed to the end of the study or dropped out due to independent reasons. Thus, statistical analysis of longitudinal GFR needs to take into consideration the presence of mixed types of informative and independent dropouts. Many statistical models and inference approaches have been proposed to accommodate the nonignorable missingness into modeling longitudinal data (see reviews [3–8]). According to the target of inference and the interpretation of model parameters, existing methods can be classified into three categories: subject-specific inference, event-conditioning inference, and marginal inference. First, a widely used modeling strategy for longitudinal data with informative dropouts is to specify their joint distribution via shared or correlated latent variables. Under such model assumptions, the longitudinal parameters have a conditional, subject-specific interpretation (e.g., [9–11]). But the interpretation of longitudinal parameters usually changes