Methods for interval-censored data

In standard time-to-event or survival analysis, occurrence times of the event of interest are observed exactly or are right-censored, meaning that it is only known that the event occurred after the last observation time. There are numerous methods available for estimating the survival curve and for testing and estimation of the effects of covariates in this context. In some situations, however, the times of the events of interest may only be known to have occurred within an interval of time. In clinical trials, for example, patients are often seen at pre-scheduled visits but the event of interest may occur in between visits. These data are interval-censored. Owing to the lack of well-known statistical methodology and available software, a common ad hoc approach is to assume that the event occurred at the end (or beginning or midpoint) of each interval, and then apply methods for standard time-to-event data. However, this approach can lead to invalid inferences, and in particular will tend to underestimate the standard errors of the estimated parameters. The purpose of this tutorial is to illustrate and compare available methods which correctly treat the data as being interval-censored. It is not meant to be a full review of all existing methods, but only those which are available in standard statistical software, or which can be easily programmed. All approaches will be illustrated on two data sets and compared with methods which ignore the interval-censored nature of the data. We hope this tutorial will allow those familiar with the application of standard survival analysis techniques the option of applying appropriate methods when presented with interval-censored data.