Using events from dropouts in nonparametric survival function estimation with application to incubation of AIDS

Often postdropout responses (PDR) in study dropouts are identified from death/disease registries or other medical records. If all dropout is random, then use of postdropout responses while censoring other subjects at date of dropout (CDO/PDR) will bias non-parametric survival probability estimates downward. Censoring all individuals at the last date of study contact, ignoring postdropout information (CDO) will produce unbiased nonparametric survival estimates. As onset of the response sometimes incapacitates the individual, preventing further study participation, dropout is often positively correlated with response. In this case CDO/PDR tends to prevent nonparametric survival overestimation but could lead to underestimation. When all of the responses in dropouts are identified, then regardless of dropout cause, use of all postdropout information, together with censoring all other subjects at time of analysis (CTA/PDR) will produce unbiased minimum variance estimates. We analyze the bias properties of nonparametric survival estimates produced using CDO/PDR, CDO, and CTA/PDR censoring mechanisms under various causes of study dropout and degrees of postdropout response recovery. The goal is to identify which of these censoring methods best incorporates postdropout information. Postdropout information may create interval-censored data. To facilitate statistical analysis of such data, the likelihood function is formulated in terms of the hazard. This results in computationally simple nonparametric estimates and covariances for interval-censored and left-truncated data. An application to estimation of acquired immune deficiency (AIDS)-free time after human immunodeficiency virus (HIV)-l seroconversion using data from a long-term cohort study with considerable dropout is presented. Upper and lower bound estimates for AIDS-free survival probabilities derived using CDO and CDO/PDR are shown to be quite close when compared to the underlying variance of these estimates. KEY WORDS: Censoring method; Dropout; Interval censoring; Nonparametric survival analysis; Postdropout response; Truncation.
Accurate projection of the future impact of the acquired immune deficiency (AIDS) epidemic requires knowledge of the hazard of AIDS as a function of time elapsed from human immunodeficiency virus [...]