Using subject-level variability to predict time-varying outcomes: investigating the association between hormone...

Women are at increased risk of bone loss during the menopausal transition; in fact, nearly 50% of women's lifetime bone loss occurs during this time. In addition to level and rate of change in estradiol (E2) and follicle-stimulating hormone (FSH), the variability of these hormones may be a key predictor of bone loss; however, this remains unexplored in the existing literature. We introduce a joint model that explicitly characterizes the uncertainty in the means and variances of the hormone trajectories. Our method estimates both the individual mean marker trajectories and the individual residual variances, and links these variances to bone trajectories. In our application, for the first time, higher FSH variance interacted with time was associated with declines in bone mineral density (BMD) across the menopausal transition. At the final menstrual period, higher individual FSH variance predicted an average 0.26% decline in BMD, but this effect is moderated over time. Our results suggest that the mean and variance of FSH, rather than E2, may be a stronger predictor of menopausal bone health. In a variety of simulation studies, our method achieves $>90\%$ interval coverage, whereas naive two-stage alternatives often fail to propagate uncertainty in the individual-level variance estimates.