Estimating Knots in Bilinear Spline Growth Mixture Models with Time-Invariant Covariates in the Framework of Individual Measurement Occasions

• Activity Number: 343 - Longitudinal Analysis, Clinical Trial Design, and Other Topics in Biopharmaceutical Statistics
• Type: Contributed
• Date/Time: Wednesday, August 5, 2020 : 10:00 AM to 2:00 PM
• Sponsor: Biopharmaceutical Section
• Author(s): Jin Liu* and Robert A Perera and Le Kang and Roy T Sabo
• Companies: and Virginia Commonwealth University Dept of Biostatistics and Virginia Commonwealth University and Virginia Commonwealth University
• Keywords: Linear spline growth mixture models; Unknown knots; Individually-varying time points; Time-invariant covariates; Simulation studies

Abstract

The linear spline growth mixture model is a tool for analyzing longitudinal data that come from a mixture of at least two latent classes where the underlying trajectories within each class are nonlinear. For each latent class, it approximates complex patterns by attaching at least two linear pieces. It poses interesting statistical challenges, such as estimating the location of a change point (or knot), grouping individuals into latent classes, associating those latent groups to baseline characteristics, and analyzing data with individually-varying measurement occasions. We developed a two-step bilinear spline growth mixture model (BLSGMM) to cluster these linear piecewise individual trajectories and associate time-invariant covariates (TICs) into latent classes. Our simulation studies demonstrate that the proposed BLSGMM-TICs can cluster the nonlinear trajectories well and estimate the parameters unbiasedly, precisely, and exhibit appropriate confidence interval coverage. An empirical example using longitudinal math scores shows that the model helps identify latent groups of nonlinear trajectories and associate the classes with baseline characteristics.