On the Nonparametric Estimation of A Distribution Function with Interval-censored and Truncated Observations

Abstract

We propose a new estimator for a distribution function F when the observed data is in the form of interval-censored and truncated as in Turnbull (1976) and Frydman (1994). The estimators proposed by these authors are based on characterizations of a reduced support of . In some cases the reduced supports are too restricted that these estimators provide little information about F. We discuss a new characterization of 's support that is more reflective of the observed support and show that the new estimator can be easily obtained with Turnbull's self-sufficient algorithm. We also show that the idea can be extended to a study with general censored and truncated data. The analysis of pregnancy data from a comparative trial of two spermicidal barrier methods is used to illustrate usefulness of the method. Models that incorporate covariates are also discussed.