A note on the applicability of the standard nonparametric maximum likelihood estimator for combined incident and prevalent cohort data

Abstract

Nonparametric estimation of the survival function for either incident or prevalent cohort failure time data, exclusively, has been well studied in the literature; the Kaplan‐Meier (KM) estimator is routinely used for right‐censored incident cohort failure time data, whereas a modified form of the KM estimator, sometimes referred to as the Tsai–Jewell–Wang (TJW) estimator, is the default estimator used for prevalent cohort data with follow‐up. Often, failure time data comprise observations from a combination of incident and prevalent cohorts. In this note, we justify the use of the TJW estimator for a combined sample of incident and prevalent cohort data with follow‐up. We suggest how the TJW estimator forms the basis for density estimation and hypothesis testing problems, when incident and prevalent cohorts are combined.