A Bayesian joint model of multiple longitudinal and categorical outcomes with application to multiple myeloma using permutation-based variable importance

TL;DR

This paper introduces a Bayesian joint model for analyzing multiple longitudinal and categorical outcomes, specifically applied to multiple myeloma data, incorporating nonlinear biomarker trajectories and a variable importance method for prognostic factor ranking.

Contribution

The paper develops a novel Bayesian joint modeling framework for longitudinal and categorical data with nonlinear trajectories, tailored for clinical prognosis and variable importance assessment.

Findings

Effective modeling of nonlinear biomarker trajectories in multiple myeloma.

Successful application of the model to real clinical data.

Enhanced identification of prognostic factors through variable importance.

Abstract

Joint models have proven to be an effective approach for uncovering potentially hidden connections between various types of outcomes, mainly continuous, time-to-event, and binary. Typically, longitudinal continuous outcomes are characterized by linear mixed-effects models, survival outcomes are described by proportional hazards models, and the link between outcomes are captured by shared random effects. Other modeling variations include generalized linear mixed-effects models for longitudinal data and logistic regression when a binary outcome is present, rather than time until an event of interest. However, in a clinical research setting, one might be interested in modeling the physician's chosen treatment based on the patient's medical history to identify prognostic factors. In this situation, there are often multiple treatment options, requiring the use of a multiclass classification approach. Inspired by this context, we develop a Bayesian joint model for longitudinal and categorical data. In particular, our motivation comes from a multiple myeloma study, in which biomarkers display nonlinear trajectories that are well captured through bi-exponential submodels, where patient-level information is shared with the categorical submodel. We also present a variable importance strategy to rank prognostic factors. We apply our proposal and a competing model to the multiple myeloma data, compare the variable importance and inferential results for both models, and illustrate patient-level interpretations using our joint model.