The statistical analysis of consecutive survival data under serial dependence

Abstract

In the analysis of medical data, one often encounters data that are observed sequentially over time. For example in AIDS studies, let $X_1$ denote the time of infection, $X_2$ the time when antibodies occur and $X_3$ the time when AIDS is diagnosed for the first time. Typically, the variables of interest are the lifetimes $U_1 = X_2 - X_1$ and $U_2 = X_3 - X_2$, which may be dependent. While in applications, $U_1$ is often truncated from the right, $U_2$ may be censored due to time limitations. It is the aim of this paper to statistically analyse the joint distribution of the pair $(U_1,U_2)$.