In disease surveillance systems or registries, bivariate survival data are typically collected under interval sampling. It refers to a situation when entry into a registry is at the time of the first failure event (e.g., HIV infection) within a calendar time interval, the time of the initiating event (e.g., birth) is retrospectively identified for all the cases in the registry, and subsequently the second failure event (e.g., death) is observed during the follow-up. Sampling bias is induced due to the selection process that the data are collected conditioning on the first failure event occurs within a time interval. Consequently, the first failure time is doubly truncated, and the second failure time is informatively right censored. A copula model under semi-stationary condition is considered to assess the association between the bivariate survival times with interval sampling. Estimation and inference are carried out by a two-stage procedure. We first obtain bias-corrected estimators of marginal survival functions, then a pseudo conditional likelihood method is developed to study the association parameter. Asymptotic properties of the proposed estimators are established, and finite sample performance is evaluated by simulation studies. The method is applied to a motivating community-based AIDS study in Rakai to investigate the effect of age at infection on survival time of HIV seroconverters.


Epidemiology | Statistical Methodology | Statistical Models | Statistical Theory | Survival Analysis

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Supplementary Materials