Model-Based Clustering of High-Dimensional Longitudinal Data via Regularization

Abstract

We propose a model‐based clustering method for high‐dimensional longitudinal data via regularization in this paper. This study was motivated by the Trial of Activity in Adolescent Girls (TAAG), which aimed to examine multilevel factors related to the change of physical activity by following up a cohort of 783 girls over 10 years from adolescence to early adulthood. Our goal is to identify the intrinsic grouping of subjects with similar patterns of physical activity trajectories and the most relevant predictors within each group. The previous analyses conducted clustering and variable selection in two steps, while our new method can perform the tasks simultaneously. Within each cluster, a linear mixed‐effects model (LMM) is fitted with a doubly penalized likelihood to induce sparsity for parameter estimation and effect selection. The large‐sample joint properties are established, allowing the dimensions of both fixed and random effects to increase at an exponential rate of the sample size, with a general class of penalty functions. Assuming subjects are drawn from a Gaussian mixture distribution, model effects and cluster labels are estimated via a coordinate descent algorithm nested inside the Expectation‐Maximization (EM) algorithm. Bayesian Information Criterion (BIC) is used to determine the optimal number of clusters and the values of tuning parameters. Our numerical studies show that the new method has satisfactory performance and is able to accommodate complex data with multilevel and/or longitudinal effects.

Novel Clustering Methods Identified Three Caries Status-Related Clusters Based on Oral Microbiome in Thai Mother–Child Dyads

“…It is obvious that these other approaches fail to consider the relationship between the covariates and the outcome of interest during the clustering process as they only make such a connection after the clustering has been performed. In addition, limited work has been done on the clustering of longitudinal high-dimensional data [ 19 ]. The longitudinal latent class analysis may be used to consider the correlation inherent in time-dependent, repeated-measure observations, with the limitation that all time points must be identical across subjects.…”

“…In this paper, we consider the clustering of correlated observations with categorical outcomes and high-dimensional microbiome data. The method used here is a novel, non-trivial extension of the one detailed in Yang and Wu [ 19 ], which is a mixture-model-based clustering method for longitudinal data with regularization to enforce a variable selection of high-dimensional covariates. We extend this by considering categorical outcomes as opposed to Gaussian outcomes, which pose unique challenges of their own, as the Yang and Wu method only considers Gaussian outcomes.…”

Clustering of longitudinal physical activity trajectories among young females with selection of associated factors

“…A novel one-step procedure [ 33 ] was used to perform clustering and variable selection simultaneously via a mixture of linear mixed-effects models with shrinkage penalties on both fixed effects and random effects.…”

“…As one can see from the discussion above, post-selection inference in clustering methods is even more challenging than the inference problem for single models because one should consider not only the within-cluster but also between-cluster significance. In the paper of Yang and Wu [ 33 ], the authors proved that joint convergence rate of the fixed and random effects when both dimensions grow at an exponential rate of sample size within clusters (i.e., for a homogeneous population). Under the same setting, they also proved the sparsistency property.…”

Individual reference intervals in practice: A guide to personalise clinical and omics level data with IRIS

“…A simultaneous penalised linear mixed model (SP-LMM), as implemented in the splmm R package, was fitted for each dataset. This involves a feature selection in a high-dimensional longitudinal setting [14]. A few metabolites and proteins with the largest absolute effect size were considered to be potentially associated with the CVD onset.…”