Inference under biased sampling and right censoring for a change point in the hazard function

Abstract

Length-biased survival data commonly arise in cross-sectional surveys and prevalent cohort studies on disease duration. Ignoring biased sampling leads to bias in estimating the hazard-of-failure and the survival-time in the population. We address estimating the location of a possible change-point of an otherwise smooth hazard function when the collected data form a biased sample from the target population and the data are subject to informative censoring. We provide two estimation methodologies, for the location and size of the change-point, adapted to two scenarios of the truncation distribution: known and unknown. While the estimators in the first case show gain in efficiency as compared to those in the second case, the latter is more robust to the form of the truncation distribution. In both cases, the change-point estimators can achieve the rate $\mathcal{O}_{p}(1/n)$. We study the asymptotic properties of the estimates and devise interval-estimators for the location and size of the change, paving the way towards making statistical inference about whether or not a change-point exists. Several simulated examples are discussed to assess the finite sample behavior of the estimators. The proposed methods are then applied to analyze a set of survival data collected on elderly Canadian citizen (aged 65$+$) suffering from dementia.