Analytic methods geared toward more precise and accurate exposure assessments, and toward ensuring validity in the estimation of exposure-response associations, are critical to epidemiologic studies. Given the scientific questions to be addressed and the often complex structure and nature of the data obtained, this fact is particularly pertinent to environmental and reproductive studies. This application draws specific motivation from two such studies, the Michigan Female Health Study (MFHS) and the Mount Sinai Study of Women Office Workers (MSSWOW). Hypotheses arising in these studies require research into improved and targeted methods for predicting random effects in mixed linear models, into methods for associating environmental exposures to reproductive outcomes while adjusting for measurement error, and into the modeling of longitudinal menstrual cycle length data. Using data collected on female MFHS participants who were exposed to polybrominated biphenyls (PBB) in the mid-1970s, we propose a linear mixed model to describe the decay of serum PBB levels over time while accounting for important fixed and time-dependent covariates (e.g., intervening pregnancies). This model forms the basis for research into optimal criteria for predicting the residual PBB level for each eligible woman at the time of an index pregnancy. These methods will be extended to account for PBB measurements that are below assay detection limits. Secondly, we propose simultaneous modeling of PBB measurements and reproductive health outcomes among MFHS participants and/or their daughters to obtain valid and consistent estimation of exposure-response associations while accounting for measurement error. Finally, we propose mixture models to describe the distribution of standard and non-standard menstrual cycle lengths using data from the MSSWOW, and we describe novel approaches to account for random within-woman heterogeneity and the effects of covariates in this context. This application is designed to improve analytic methods for epidemiologic research by incorporating current developments in statistical theory, by developing new methodology, and by targeting this effort toward important scientific studies. These developments will directly benefit environmental and reproductive studies, but they are ubiquitous enough to be generally useful contributions to statistical practice.
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