Innovative Statistical Models for Inference from Complex Design Surveys and Longitudinal Studies.

Abstract

Bayesian inference is a method of statistical inference which combines two sources of information, prior information and data, into the posterior distribution. It is widely applied in different areas and has the advantage of being "data driven". This dissertation develops Bayesian statistical models in complex design surveys and women’s reproductive study.

Highly disproportional sample designs have large weights, which can introduce undesirable variability in estimates of population statistics. Previous work developed Bayesian "weight smoothing" or "weight pooling" models to produce general model-based weight trimming estimators of population statistics, but application has been limited to the context of stratified and post-stratified sample designs. In the first part of this dissertation, we extend "weight smoothing" estimators to a more general class of complex sample designs that include multi-stage cluster samples and/or strata that "cross" the weight strata.

As women mature, menstrual cycles typically begin to decline slowly in length and stabilize until a point at which the hormone cycles begin to break down, leading to a rapid increase in variability and a concomitant increase in cycle length until the onset of menopause. In order to study the structure of menstrual cycle lengths, we build a Bayesian change point model for the mean and variability of cycle lengths for data from the TREMIN cohort, a 70-year long longitudinal study of multiple cohorts of women’s reproductive life. This Bayesian hierarchical model summarizes the cycle length profiles at both a subject and population level. We integrate multiple imputation in our Bayesian estimation procedure to deal with different forms of missingness. Based on results from this analysis, menstrual patterns are classified into subgroups using a K-medoids algorithm. We then relate these subgroups to age of menopause, age at menarche, number of births, as well as to existing standard menopausal transition markers. Our results suggest mean and variance changepoints, which are identified using data throughout women’s late reproductive life, provide more comprehensive information about menopausal transition than previously defined transition markers.