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A Longitudinal Joint Cluster Regression model for Detecting Latent Group Structures
Farhad Hatami (Lancaster University)
Much of the current research in neurodegenerative diseases focuses on identifying biomarkers and risk factors for clinical progression. However, the heterogeneity of these diseases is a key confounding factor to treatment development, as study cohorts typically include multiple phenotypes presenting distinct disease trajectories. Therefore, identifying the predictive factors for a given patient is of great clinical importance to predict individual disease progression. This challenge can be addressed by determining the underlying latent subtypes. We are primarily interested in longitudinal datasets, where a cognitive outcome and relevant covariates are measured at repeated timepoints. Current biomedical technology enables the collection of high-dimensional covariates (genomics, proteomics, etc.), making model development challenging both in theory and practice.
We develop a scalable method that we name longitudinal joint cluster regression (LJCR), which allows us to jointly estimate a predictive regression model and identify latent subtypes within the data. Latent group structures are modelled using a class of Gaussian mixture models that couple together the multivariate distribution of the covariates and responses. We model the longitudinal dynamics of each individual using a random effects intercept and slope model (i.e. a subject-specific random intercept that quantifies the cross-sectional variability, and a subject-specific slope that quantifies the decrease in cognitive function over multiple timepoints). The inference is done via a profile likelihood approach that can handle high-dimensional covariates by incorporating sparsity assumptions via ridge penalization.
We show the performance of the method by applying it to two datasets; a simulation study where we have high-dimensional longitudinal data, and a dataset of amyotrophic lateral sclerosis (ALS) patients. We show that our model allows us to predict progression and identify subgroup-specific predictors.