Regression analysis of asynchronous longitudinal data with informative observation processes

Abstract

A great deal of literature has been established for regression analysis of longitudinal data but most of the existing methods assume that covariates can be observed completely or at the same observation times for the response variable, and the observation process is independent of the response variable completely or given covariates. As pointed out by many authors, in practice, one may face the situation where the response variable and covariates are observed intermittently at different time points, leading to sparse asynchronous longitudinal data, or the observation process may be related to the response variable even given covariates. It is apparent that sometimes both issues can occur in the same time and although some literature has been developed to address each of the two issues, it does not seem to exist an established approach that can deal with both together. To address this, in this paper, a flexible semiparametric transformation conditional model is presented and for estimation, a kernel-weighted estimating equation-based approach is proposed. The proposed estimators of regression parameters are shown to be consistent and asymptotically follow the normal distribution. For the assessment of the finite sample performance of the method, an extensive simulation study is carried out and suggests that it performs well for practical situations. The approach is applied to a prospective HIV study that motivated this investigation.