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

Author

Listed:
  • Hua Jin

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

  • Ying Lu

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

  • Kaite Stone

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

  • Dennis M. Black

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

Abstract

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.

Suggested Citation

  • Hua Jin & Ying Lu & Kaite Stone & Dennis M. Black, 2004. "Alternative Tree-Structured Survival Analysis Based on Variance of Survival Time," Medical Decision Making, , vol. 24(6), pages 670-680, November.
    • Handle: RePEc:sae:medema:v:24:y:2004:i:6:p:670-680
    DOI: 10.1177/0272989X04271048
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    References listed on IDEAS

    as
    1. Gordon, Louis & Olshen, Richard A., 1984. "Almost surely consistent nonparametric regression from recursive partitioning schemes," Journal of Multivariate Analysis, Elsevier, vol. 15(2), pages 147-163, October.
    2. Ciampi, Antonio & Thiffault, Johanne & Nakache, Jean-Pierre & Asselain, Bernard, 1986. "Stratification by stepwise regression, correspondence analysis and recursive partition: a comparison of three methods of analysis for survival data with covariates," Computational Statistics & Data Analysis, Elsevier, vol. 4(3), pages 185-204, October.
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