UC Riverside

The transitional phase of menopause induces significant hormonal fluctuations, exerting a profound influence on women's long-term well-being. In the extensive longitudinal investigation of women's health during mid-life and beyond, known as the Study of Women's Health Across the Nation (SWAN), hormonal biomarkers are repeatedly assessed. However, these measurements follow an asynchronous schedule compared to other variables prone to errors, such as physical and cardiovascular measurements. To gain deeper insights into the diverse characteristics within the study population, we conducted a subgroup analysis employing a semiparametric mixture regression model. This approach allows us to explore how the relationship between hormonal responses and other time-varying or time-invariant covariates varies across subgroups. To address the challenges posed by asynchronous scheduling and measurement errors, we propose a novel strategy involving the modeling of time-varying covariate trajectories as functional data. This is achieved through the utilization of reduced rank Karhunen-Loève expansions, where splines are employed to capture the mean and eigenfunctions. Additionally, we introduce an Expectation-Maximization (EM) algorithm to effectively fit a joint model. This model simultaneously incorporates the mixture regression for the hormonal response and the functional principal component (FPC) model for the asynchronous, time-varying covariates. Importantly, we treat the latent subgroup membership and FPC scores as missing data in this framework. Furthermore, we explore data-driven methods to determine the optimal number of subgroups within the population. Through our comprehensive analysis of the SWAN data, we unveil a crucial subgroup structure within the aging female population, shedding light on important distinctions and patterns among women undergoing menopause.