Thursday, June 14, 2018
4:00 pm – 5:00 pm
Micha Mandel, Ph.D.
Professor, Department of Statistics, Hebrew University of Jerusalem, Israel
Multiple Cross-sectional Samples and the Poisson Assumption
We consider a population that can be joined at a known sequence of discrete times. Data are collected using independent cross-sectional surveys, and the lifetimes of individuals in the sample are observed. It is well known that such sampling design results in multiple biased samples with possibly different weight functions, but less well known and often ignored that it may also result in dependence among the observations. We first show that observed sojourn times are independent (almost) only under a Poisson entrance process. Furthermore, assuming entrances according to a Poisson model, we suggest simple closed-form estimators for the lifetime distribution and its variance. Our motivating example concerns a series of cross-sectional surveys conducted in Israeli hospitals. We discuss the bias mechanism in our data and develop a simple design plan that provides valid estimators even when the weight functions are unknown. The method is applied to estimate the distribution of hospitalization time after bowel and hernia surgeries.