ABSTRACT
In the first two chapters, we focused on the analysis of right censored data, which is the most typical censored survival data in biomedical studies. In addition to right censoring, the loss of information in a follow-up study may produce other types of incomplete data structure. We devote this chapter to the investigation of interval censored data, which may arise in many practical studies and pose a distinct challenge to data analysts. It should be noted that many aspects of interval censored data analysis, for example parametric methods, are very similar to those for right censored data. To avoid redundancy, such aspects will be briefly mentioned. Unlike some of the existing textbooks on survival analysis, this chapter aims to offer a more rigorous account of some theoretical aspects of interval censored data. The theoretical study of interval censored data can be more challenging than with right censored data, mainly because martingale techniques are no longer applicable, and advanced empirical processes techniques have to be adopted. We recognize the importance of the theoretical investigation, at the same time, we also acknowledge that it can be difficult for less theory-oriented readers. For those who are more interested in applications, you may selectively choose sections within the chapter and also refer to other textbooks, in particular Sun (2006). For those who are only interested in right censoring, it is also possible to completely skip this chapter. The notations in this chapter are mostly self-contained in order to be consistent with published papers in this area.
