Abstract: Here we develop methods for applications where random change points are known to be present a priori and the interest lies in their estimation and investigating risk factors that influence them. A simple least square method estimating each individual’s change point based on one’s own observations is first proposed. An easy-to-compute empirical Bayes type shrinkage is then proposed to pool information from separately estimated change points. A method to improve the empirical Bayes estimates is developed. Simulations are conducted to compare least-square estimates and Bayes shrinkage estimates. The proposed methods are applied to the Berkeley Growth Study data to estimate the transition age of the puberty height growth.
Abstract: It is known that “standard methods for estimating the causal effect of a time-varying treatment on the mean of a repeated measures outcome (for example, GEE regression) may be biased when there are time-dependent variables that are simultaneously confounders of the effect of interest and are predicted by previous treatment” (Hern´an et al. 2002). Inverse-probability of treatment weighted (IPTW) methods are developed in the literature of causal inference. In genetic studies, however, the main interest is to estimate or test the genetic effect rather than the treatment effect. In this work, we describe an IPTW method that provides unbiased estimate for the genetic effect, and discuss how to develop a family-based association test using IPTW for family-based studies. We apply the developed methods to systolic blood pressure data in Framingham Heart Study, where some subjects took antihypertensive treatment during the course of study.