Tutorial on methods for interval-censored data and their implementation in R

Interval censoring is encountered in many practical situations when the event of interest cannot be observed and it is only known to have occurred within a time window. The theory for the analysis of interval-censored data has been developed over the past three decades and several reviews have been written. However, it is still a common practice in medical and reliability studies to simplify the interval censoring structure of the data into a more standard right censoring situation by, for instance, imputing the midpoint of the censoring interval. The availability of software for right censoring might well be the main reason for this simplifying practice. In contrast, several methods have been developed to deal with interval-censored data and the corresponding algorithms to make the procedures feasible are scattered across the statistical software or remain behind the personal computers of many researchers. The purpose of this tutorial is to present, in a pedagogical and unified manner, the methodology and the available software for analyzing interval-censored data. The paper covers frequentist non-parametric, parametric and semiparametric estimating approaches, non-parametric tests for comparing survival curves and a section on simulation of interval-censored data. The methods and the software are described using the data from a dental study.