Bayesian consensus clustering for multivariate longitudinal data

Abstract

In clinical and epidemiological studies, there is a growing interest in studying the heterogeneity among patients based on longitudinal characteristics to identify subtypes of the study population. Compared to clustering a single longitudinal marker, simultaneously clustering multiple longitudinal markers allow additional information to be incorporated into the clustering process, which reveals co‐existing longitudinal patterns and generates deeper biological insight. In the current study, we propose a Bayesian consensus clustering (BCC) model for multivariate longitudinal data. Instead of arriving at a single overall clustering, the proposed model allows each marker to follow marker‐specific local clustering and these local clusterings are aggregated to find a global (consensus) clustering. To estimate the posterior distribution of model parameters, a Gibbs sampling algorithm is proposed. We apply our proposed model to the primary biliary cirrhosis study to identify patient subtypes that may be associated with their prognosis. We also perform simulation studies to compare the clustering performance between the proposed model and existing models under several scenarios. The results demonstrate that the proposed BCC model serves as a useful tool for clustering multivariate longitudinal data.

Joint clustering multiple longitudinal features: A comparison of methods and software packages with practical guidance

“…However, the BMM allows modeling the joint distribution of random effects of all features, while the BCC model further assumes that features are independent if given the latent class membership. Of note, Lu and Lou 44 compared the performance of the BCC model with and without such an independence assumption and found that clustering results are similar. Furthermore, while it is true that there are no formal statistical tests to detect whether a random effect is needed (eg, whether LCMM or GBTM is more appropriate), models incorporating random effects provide estimates of the variance of the random effects ($$$ {\Sigma}_{kr} $$$) which can serve as an indication of whether random effects are needed or not.…”

“…We refer readers to a recent study 77 for a comparison of these methods in latent variable models. In particular, when fitting a BCC model, a heuristic method using mean adjusted adherence is proposed 72 and has been used in practice 44 . The mean adjusted adherence (MAA) selects a model with feature‐specific clusterings contributing the most information to the global clustering.…”

“…72 Recently, this model is extended to cluster multivariate longitudinal data. 44,45 Unlike other methods which provide an overall clustering that utilizes information from all features (known as global clustering), the BCC model provides both feature-specific clustering and global clustering. Feature-specific clustering is also known as local clustering as it is based on each feature alone.…”

A Joint Modeling Approach for Clustering Mixed-Type Multivariate Longitudinal Data: Application to the CHILD Cohort Study

“…both continuous and discrete). For the former, example include multivariate model-based clustering using mixed effect models for continuous markers (Marshall et al, 2006;Villarroel et al, 2009;Proust-Lima et al, 2017), multivariate functional clustering for continuous (Jacques and Preda, 2014b) or discrete markers (Lim et al, 2020), Bayesian finite mixtures for continuous markers (Leiby et al, 2009;Frühwirth-Schnatter and Pyne, 2010) and hidden Markov models for continuous markers (Xia and Tang, 2019;Lu and Lou, 2021c). For the latter, examples include group-based multi-trajectory analysis (Nagin et al, 2018), which is an extension of the group-based single trajectory analysis (Nagin, 1999), and Bayesian mixture modeling for discrete and continuous longitudinal data (BMM) (Komárek et al, 2013(Komárek et al, , 2014.…”

Subgroup analysis for longitudinal data based on a partial linear varying coefficient model with a change plane

“…Various statistical methods have been proposed to identify subgroups for independent data and subsequently extended to longitudinal setting. For example, tree-based method 4,12 recursively partitions the covariate space using splitting criteria, mixture model 13,14 assumes that data comes from the mixture of subgroups, concave fusion penalty 15,16 allows clustering, Bayesian inference 17,18 assigns prior probabilities to possible subgroup effects, and some personalized modeling 19,20 provides optimal treatment regime. Some of these methods are poorly interpretable, some lack discussion on theoretical properties.…”