# Turnbull's Nonparametric Estimator for Interval-Censored Data

### Suely Ruiz Giolo

### Federal University of Paraná, Brazil

## Summary

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.

### Keywords:

nonparametric estimator, interval censoring, survival.