Survival analysis with interval censored data

Censoring is the most important feature that distinguishes survival analysis from other statistical methods. Censored observation means incomplete observation and provides partial information about the time of failure. This means that even though a unit has been observed for a period of time, there is no failure in this process. In addition, a unit under observation may be excluded from the study for some reason or units may have been involved in research at different times. If the failure time is not completed due to such reasons, then censored observation occurs. In survival analysis, there are different types of censoring, however in practice the most common type is right censoring. Most of the methods used in survival analysis have been developed for right censored data sets. Studies on interval censoring gains speed in recent years. If the failure time of the unit occurs within a certain range, there are interval censoring observations. These data usually occur when observations of interest are not constantly monitored. It is only known that the event of interest takes place between two observation periods. Cox regression model and parametric survival models used commonly in survival analysis have been developed for interval censored data. In this study, survival models for interval censored data is examined theoretically and primary biliary cirrhosis data is used in the application section. The data structure is taken both as right censored and interval censored. Cox regression model and parametric survival models are applied and the results are discussed. Keywords: Interval censoring, Cox regression model, accelerated failure time model, proportional hazards, right censoring.