Finite Mixtures of Multivariate t Linear Mixed‐Effects Models for Censored Longitudinal Data With Concomitant Covariates

Clustering longitudinal biomarkers in clinical trials uncovers associations between clinical outcomes, disease progression, and treatment effects. Finite mixtures of multivariate <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics><mml:mrow><mml:mi>t</mml:mi></mml:mrow> <mml:annotation>$$ t $$</mml:annotation></mml:semantics> </mml:math> linear mixed-effects (FM-MtLME) models have proven effective for modeling and clustering multiple longitudinal trajectories that exhibit grouped patterns with strong within-group similarity. Motivated by an AIDS study with plasma viral loads measured under assay-specific detection limits, this article extends the FM-MtLME model to account for censored outcomes. The proposed model is called the FM-MtLME with censoring (FM-MtLMEC). To allow covariate-dependent mixing proportions, we further extend it with a logistic link, resulting in the EFM-MtLMEC model. Two efficient EM-based algorithms are developed for parameter estimation of both FM-MtLMEC and EFM-MtLMEC models. The utility of our methods is demonstrated through comprehensive analyses of the AIDS data and simulation studies.