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Survival trees based on heterogeneity in time‐to‐event and censoring distributions using parameter instability test

Survival analysis of right‐censored data often arises in many areas of research including medical research. The effect of covariates (and their interactions) on survival distribution can be studied through existing methods that require pre‐specifying the functional form of the covariates including their interactions. Survival trees offer a relatively flexible approach when the form of covariates' effects is unknown. We have proposed the SurvCART algorithm to construct a survival tree. There are two features that distinguish the SurvCART algorithm from the rest. First, most of the currently available survival tree construction techniques are not based on a formal test of significance and, hence, prone to spurious findings. The proposed SurvCART algorithm utilizes the “conditional inference” framework that selects splitting variable via parameter instability test and subsequently finds the optimal split based on some maximally chosen statistic. We used likelihood score‐based parameter instability tests that converge to distribution with known distribution function so that the p‐value can be obtained easily without any approximation. Second, the SurvCART algorithm has the flexibility to extend the concept of heterogeneity to the censoring time distribution as well, a feature that can be useful when censoring distribution is influenced by baseline covariates. We evaluated the operating characteristics of the parameter instability test and compared the performance of the SurvCART algorithm with other survival tree algorithms via simulation. Finally, the SurvCART algorithm was applied to a real data setting. The proposed method is implemented in R package LongCART available on CRAN.