Joint Modeling Methods for Individual-level Variances as Predictors of Health Outcomes

Abstract

Precision medicine has the potential to improve early health diagnostics and support individualized treatment plans. The study and identification of repeatedly measured biomarkers for diseases and health risks is essential to advance this field. Existing joint models developed for modeling longitudinal biomarkers have usually focused on estimating the means of the trajectories. However, the variabilities and covariabilities of these trajectories may be informative for health outcomes. This dissertation develops a family of Bayesian hierarchical models that model the individual-level variances and covariances of the trajectories and correlate them to outcomes of interest. The methods presented in this dissertation are designed to handle varying levels of data complexity such as multiple marker trajectories, repeatedly measured and cross-sectional outcomes, and individual time-varying (co-)variances. This body of work supports advances in personalized healthcare by modeling the complex interplay between biomarker means and variances, and corresponding health outcomes. In Chapter 2, I develop a joint model that links estimates of the individual means, variances and covariances of multiple biomarker trajectories to a cross-sectional outcome of interest. This framework can accommodate multiple individual markers by specifying individual variance-covariance matrices in the longitudinal submodel. I propose hierarchical priors on the individual variance-covariance matrices, which allow the model to flexibly capture between-subject differences and similarities in the residual variances and covariances. Simulations demonstrate that this joint model outperforms alternative two-stage approaches. In an application to women’s health, I find that higher individual variability of estradiol (E2) is associated with increased fat mass gain across the menopausal transition. This finding indicates that E2 variability may be protective against large increases in waist circumference in midlife women and raises new questions regarding the role ofE2 variability in predicting fat distribution changes during menopause. In Chapter 3, I examine the setting of simultaneously estimating multiple longitudinal trajectories, in order to understand associations between variables over time. I explore a linear parameterization of time-varying individual variances in the predictor model so that the individual variances, as well as the means, are used to predict the outcome at the same point in time. I demonstrate via simulation studies that this model is able to recover the true data generating parameters while maintaining low bias and proper coverage. I apply this method to women’s hormone markers and bone density measurements during the midlife and find that higher follicle-stimulating hormone (FSH) variability is associated with slower declines in bone density. Our findings suggest that FSH variability, but not E2 variability, is a more predictive measurement of bone health in midlife women. Chapter 4 introduces a joint model of individual-level mean and covariances trajectories of multiple markers for estimating a repeatedly measured health outcome. In the predictor submodel, the individual variance-covariance matrices comprised a shared residual covariance matrix and individual-specific regression coefficients that characterize the evolution of the variances and covariances over time. This method is applied to estimate the associations between FSH and testosterone variabilities and bone mineral content declines in women undergoing menopause. We find for the first time, high variability of testosterone is associated with faster declines in bone mineral content (BMC) for post-menopausal women. Conversely, higher covariability between FSH and testosterone post-FMP was also associated with slower declines in BMC. A simulation study validates that the model can recover the parameters of interest with low bias and high coverage.