Presentation: Cross-sectional Sampling and the Poisson Assumption
Speaker: Professor Micha Mandel, PhD, Department of Statistics, The Hebrew University of Jerusalem
Abstract: 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 designs result in multiple biased samples with possibly different weight functions, but it is often ignored that it may result in dependence among observations. We start with the single sample problem and show that observed sojourn times are independent only under a Poisson entrance process. For multiple independent samples and under a Poisson entrance process, we suggest simple closed-form estimators for the lifetime distribution and its variance. The 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.