On the use of auxiliary data to estimate the survival function and its variance: an application to acquired...

Prospective studies have as their goal the estimation of the survival function when the time to the specified event may be censored due to loss to follow-up or to the termination of the study before the event of interest occurs. In such a study, information about an auxiliary event, correlated to the event of interest, is often available. An example of such an auxiliary event in cancer studies is remission or relapse. A stochastic model was proposed by Lagakos, which utilizes this type of information in the analysis of survival studies [1]. The primary objective of using an auxiliary information is to improve the estimation of survival. This article proposes a method to estimate the variance of the estimator of the survival function S(t) for the model including such auxiliary information. Thus, we compute for different situations the relative efficiency of the estimator of S(t) using the stochastic model to the estimator of S(t) using only survival data. The method is applied to data from a prospective study of 379 HIV-seropositive homosexual men, of whom 31 developed AIDS. In our example, the auxiliary event is defined by the level of CD4 lymphocyte counts using distinct threshold values, for instance 200 cells/mm3, while the event of interest is the time to development of AIDS.