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Alternative Tree-Structured Survival Analysis Based on Variance of Survival Time

Department of Radiology, the University of California at San Francisco and the Department of Mathematics, South China Normal University, Guangzhou, China

Ying Lu, PhD

Department of Radiology and the Department of Epidemiology and Biostatistics, the University of California at San Francisco

Kaite Stone, PhD

Department of Epidemiology and Biostatistics, the University of California at San Francisco

Dennis M. Black, PhD

Department of Epidemiology and Biostatistics, the University of California at San Francisco

Tree-structured survival analysis (TSSA) is a popular alternative to the Cox proportional hazards regression in medical research of survival data. Several methods for constructing a tree of different survival profiles have been developed, including TSSA based on log-rank statistics, martingale residuals, L^p Wasserstein metrics between Kaplan-Meier survival curves, and a method based on a weighted average of the within-node impurity of the death indicator and the within-node loss function of follow-up times. Lu and others used variance of restricted mean lifetimes as an index of degree of separation (DOS) to measure the efficiency in separations of survival profiles by a classification method. Like tree-based regression analysis that uses variance as a criterion for node partition and pruning, the variance of restricted mean lifetimes between different groups can be an alternative index to log-rank test statistics in construction of survival trees. In this article, the authors explore the use of DOS in TSSA. They propose an algorithm similar to the least square regression tree for survival analysis based on the variance of the restricted mean lifetimes. They apply the proposed method to prospective cohort data from the Study of Osteoporotic Fracture that motivated the research and then compare their classification rule to those rules based on the conventional TSSA mentioned above. A limited simulation study suggests that the proposed algorithm is a competitive alternative to the log-rank or martingale residual-based TSSA approaches.

Key Words: tree-structured survival analysis • variance of restricted mean lifetimes • osteoporotic fractures

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