Turnbull's Nonparametric Estimator for Interval-Censored Data

Suely Ruiz Giolo

Federal University of Paraná, Brazil


In most applications, the data may be interval-censored. By interval-censored data, we mean that a random variable of interest is known only to lie in an interval, instead of being observed exactly. In such cases, the only information we have for each individual is that their event time falls in an interval, but the exact time is unknown. A nonparametric estimate of the survival function can also be found in such interval- censored situations. The survival function is perhaps the most important function in medical and health studies. In this work we describe and illustrate the iterative procedure proposed by Turnbull (1976) to estimate such function. This procedure has been implemented in the software R and the code used is provided in this work.


nonparametric estimator, interval censoring, survival.

Available as PDF, R code, Breast cancer data