Methods for analyzing nonstandard longitudinal datasets

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Longitudinal data analysis is an important and now well-studied subject in biostatistics with several excellent texts providing various viewpoints on the subject. However, there are three topics that we wish to emphasize in the current proposal and which are neither part of the focus of these texts nor of the biostatistical and statistical literature. The first is the modeling of longitudinal data when the response and any time-dependent covariate(s) are not measured at the same time points. A smoothing step is required, and we will focus upon a binning approach to handle this atypical data structure and allow for longitudinal modeling using traditional mixed effects models. The second topic is joint modeling of longitudinal and survival data when the longitudinal response is measured both retrospectively and prospectively, whereas the typical arrangement is that the longitudinal response is measured only prospectively, i.e., when the start of the clock of the survival process begins. A number of issues need to be addressed with this type of data, especially as regard to estimation bias when the amount of retrospective data differs between study participants. The third topic focuses on implementing a flexible model for longitudinal data that exhibit a gradual change from an increasing to decreasing trajectory over time (or vice versa). The challenge is to try to obtain a reasonably realistic model for the mean trajectory while not overfitting the data with a high number of difficult to interpret parameters, something that may occur with a nonparametric curve-based approach. We discuss the mixed-effects bent cable regression model to achieve this often satisfying compromise. This model will also allow us to account for between-subject heterogeneity in the trajectories including where the changes occur. HQP (graduate students) will be heavily involved in attempting to address all three of these topics in this proposal.