In medical follow-up studies, ordered bivariate survival data are frequently encountered when bivariate failure events are used as the 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 where the ﬁrst failure event (cancer onset) is identiﬁed within a calendar time interval, the time of the initiating event (birth) can be retrospectively conﬁrmed, and the occurrence of the second event (death) is observed sub ject to right censoring. To analyze this type of bivariate failure time data, it is important to recognize the presence of bias arising due to interval sampling. In this paper, nonparametric and semiparametric methods are developed to analyze the bivariate survival data with interval sampling under stationary and semi-stationary conditions. Numerical studies demonstrate the proposed estimating approaches perform well with practical sample sizes in diﬀerent simulated models. We apply the proposed methods to SEER ovarian cancer registry data for illustration of the methods and theory.
Zhu, Hong and Wang, Mei-Cheng, "Analyzing Bivariate Survival Data with Interval Sampling and Application to Cancer Epidemiology" (November 2009). Johns Hopkins University, Dept. of Biostatistics Working Papers. Working Paper 201.