Bayesian Variable Selection for Joint Models of Heterogeneous Longitudinal Variables and a Binary outcome

Music City Center 

Many biomedical studies collect longitudinal clinical and lifestyle data of mixed types (continuous and discrete) to examine their associations with key health outcomes. However, inconsistencies in measurement timing and missing follow-ups pose challenges in linking these predictors to a binary outcome at a specific time point, such as cancer diagnosis. While Lim et al. (2022) proposed a joint model to impute standardized longitudinal values for mixed-type covariates, their approach did not incorporate variable selection, limiting its ability to identify the most relevant predictors.

Building on this framework, we introduce two structured Bayesian variable selection strategies within a joint modeling framework.The first approach is a one-level strategy that identifies important covariates for the binary outcome, including higher-order interactions. We then extend this to a two-level strategy, which simultaneously selects covariates for both the outcome and longitudinal trajectories. The two-level approach allows for the inclusion of a large number of predictors, including higher-order interactions, without overfitting or excessive computational burden by leveraging a shrinkage-based selection method. Furthermore, it accounts for model uncertainty and facilitates model averaging, improving imputation accuracy and predictive performance.

We apply our method to the LILAC study, using longitudinal WHI data to identify factors associated with post-treatment insomnia among female cancer survivors. Our results demonstrate the benefits of integrating variable selection into joint modeling, offering a robust and interpretable framework for high-dimensional, time-dependent biomedical data analysis.

Bayesian joint models

variable selection

interaction

Bayesian lasso

imputation

Bayesian inference 

Biometrics Section