Modeling time-varying effects with generalized and unsynchronized longitudinal data.

We propose novel estimation approaches for generalized varying coefficient models that are tailored for unsynchronized, irregular and infrequent longitudinal designs/data. Unsynchronized longitudinal data refer to the time-dependent response and covariate measurements for each individual measured at distinct time points. Data from the Comprehensive Dialysis Study motivate the proposed methods. We model the potential age-varying association between infection-related hospitalization status and the inflammatory marker, C-reactive protein, within the first 2 years from initiation of dialysis. We cannot directly apply traditional longitudinal modeling to unsynchronized data, and no method exists to estimate time-varying or age-varying effects for generalized outcomes (e.g., binary or count data) to date. In addition, through the analysis of the Comprehensive Dialysis Study data and simulation studies, we show that preprocessing steps, such as binning, needed to synchronize data to apply traditional modeling can lead to significant loss of information in this context. In contrast, the proposed approaches discard no observation; they exploit the fact that although there is little information in a single subject trajectory because of irregularity and infrequency, the moments of the underlying processes can be accurately and efficiently recovered by pooling information from all subjects using functional data analysis. We derive subject-specific mean response trajectory predictions and study finite sample properties of the estimators.