Estimation from cross-sectional samples under bias and dependence

A population can be entered at a known sequence of discrete times; it is sampled cross-sectionally, and the sojourn times of individuals in the sample are observed. It is well known that cross-sectioning leads to length-bias, but less well known and often ignored that it may also result in dependence among the observations. We show that observed sojourn times are independent only under a multinomial entrance process. We study asymptotic properties of parametric and nonparametric estimators of the sojourn time distribution using the product of marginals in spite of dependence, and provide conditions under which this approach results in proper or improper and wrong inference. We apply the proposed methods to data on hospitalization time after bowel and hernia surgeries collected by a cross-sectional design.