Nonparametric Tree-Structured Modeling for Interval-Censored Survival Data

Survival analysis has been a major research area in statistics. In survival analysis, time to some event is usually the outcome variable. The objective of a survival study is to identify the relationship between treatments, risk factors or other covariates and the time to event. However, in a real clinical trial or longitudinal study, the exact time to event for each participant is not always known. The exact time to event might be unknown because either it takes too long to follow every participant until his (her) event occurs or each participant is only evaluated periodically, that is, the time to event is only known inside an interval. When the time to event is known to occur inside an interval, we say that the survival time is interval-censored. Left censoring and right censoring are special cases of interval censoring. The idea of recursive partitioning was first proposed by Morgan and Sonquist (1963). Breiman, Friedman, Olshen and Stone (1984) advanced the development of tree-structured models. Meanwhile, the availability of their software, CART (Classification And Regression Trees), helped tree-structured methods become a popular statistical tool. Treestructured regression models were introduced into survival analysis using different splitting and pruning approaches by Gordon and Olshen (1985), Segal (1988), Davis and Anderson (1989), Ciampi (1991), LeBlanc and Crowley (1992), LeBlanc and Crowley (1993) and Ahn and Loh (1994). However, most of those methods only deal with right-censored survival data. Bacchetti and Segal (1995) extended the method in Segal (1988) to allow for left truncation and time-dependent covariates. Huang, Chen and Soong (1998) proposed a piecewise exponential survival tree with time-dependent covariates. All of the above tree-structured models are applicable to data that are right-censored or data that are both left-truncated and right-censored. In this paper, we propose to extend the tree-structured model further to accommodate interval-censored survival data in two ways. First, we extend the exponential tree model proposed by Davis and Anderson (1989) to interval-censored survival data (Yin and Anderson (2001)). We also propose a nonparametric method to construct tree models for interval-censored data. The performance of the two methods will be compared through two sets of simulation.