Gap time bias in incident and prevalent cohorts

Multiple event data are frequently encountered in incident and prevalent cohort studies when the multiple events are considered as the major outcomes. For incident cohorts, statistical analysis for the time to the first event, the first gap time, can be conducted using standard techniques in survival analysis under appropriate conditions. These techniques are, nevertheless, inappropriate for analyzing the second gap time because of the presence of induced informative censoring. For prevalent cohorts, because the sample is biased in general, standard methods do not apply to gap times of any order, but techniques for truncated data can be used for the analysis of the first gap time. It is shown that the combined incident and prevalent data form the usual survival data for analysis of the second gap time when certain stationarity conditions are satisfied. The problems are illustrated by a cohort example to study the natural history of Human Immunodeficiency Virus (HIV) and Acquired Immunodeficiency Syndrome (AIDS).