Analyzing multiple cross-sectional samples with application to hospitalization time after surgeries

Repeated cross-sectional sampling results in multiple biased samples with possibly different weight functions. The standard non-parametric maximum likelihood estimator for the lifetime distribution of interest solves a set of nonlinear equations, and its variance has a very complicated form. We suggest a simple closed-form estimator for the case where entrances to the population of interest follow a Poisson model. The variance of the estimator and confidence intervals are easily calculated. Our motivating example concerns a series of cross-sectional surveys conducted in Israeli hospitals. We discuss the bias mechanism in our data and suggest a simple design plan that provides valid estimators even when the weight functions are unknown. The new method is applied to estimate the distribution of hospitalization time after bowel and hernia surgeries.