Analysing bivariate survival data with interval sampling and application to cancer epidemiology

In biomedical studies, ordered bivariate survival data are frequently encountered when bivariate failure events are used as outcomes to identify the progression of a disease. In cancer studies, interest could be focused on bivariate failure times, for example, time from birth to cancer onset and time from cancer onset to death. This paper considers a sampling scheme, termed interval sampling, in which the first failure event is identified within a calendar time interval, the time of the initiating event can be retrospectively confirmed and the occurrence of the second failure event is observed subject to right censoring. In a cancer data application, the initiating, first and second events could correspond to birth, cancer onset and death. The fact that the data are collected conditional on the first failure event occurring within a time interval induces bias. Interval sampling is widely used for collection of disease registry data by governments and medical institutions, though the interval sampling bias is frequently overlooked by researchers. This paper develops statistical methods for analysing such data. Semiparametric methods are proposed under semi-stationarity and stationarity. Numerical studies demonstrate that the proposed estimation approaches perform well with moderate sample sizes. We apply the proposed methods to ovarian cancer registry data.