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Multivariate exponential survival trees and their application to tooth prognosis

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  • Fan, Juanjuan
  • Nunn, Martha E.
  • Su, Xiaogang

Abstract

This paper is concerned with developing rules for assignment of tooth prognosis based on actual tooth loss in the VA Dental Longitudinal Study. It is also of interest to rank the relative importance of various clinical factors for tooth loss. A multivariate survival tree procedure is proposed. The procedure is built on a parametric exponential frailty model, which leads to greater computational efficiency. We adopted the goodness-of-split pruning algorithm of [LeBlanc, M., Crowley, J., 1993. Survival trees by goodness of split. Journal of the American Statistical Association 88, 457-467] to determine the best tree size. In addition, the variable importance method is extended to trees grown by goodness-of-fit using an algorithm similar to the random forest procedure in [Breiman, L., 2001. Random forests. Machine Learning 45, 5-32]. Simulation studies for assessing the proposed tree and variable importance methods are presented. To limit the final number of meaningful prognostic groups, an amalgamation algorithm is employed to merge terminal nodes that are homogeneous in tooth survival. The resulting prognosis rules and variable importance rankings seem to offer simple yet clear and insightful interpretations.

Suggested Citation

  • Fan, Juanjuan & Nunn, Martha E. & Su, Xiaogang, 2009. "Multivariate exponential survival trees and their application to tooth prognosis," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 1110-1121, February.
    • Handle: RePEc:eee:csdana:v:53:y:2009:i:4:p:1110-1121
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    References listed on IDEAS

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    1. Gao, Feng & Manatunga, Amita K. & Chen, Shande, 2004. "Identification of prognostic factors with multivariate survival data," Computational Statistics & Data Analysis, Elsevier, vol. 45(4), pages 813-824, May.
    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.
    3. Xiaogang Su & Juanjuan Fan, 2004. "Multivariate Survival Trees: A Maximum Likelihood Approach Based on Frailty Models," Biometrics, The International Biometric Society, vol. 60(1), pages 93-99, March.
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    Cited by:

    1. Olivier Lopez & Xavier Milhaud & Pierre-Emmanuel Thérond, 2015. "Tree-based censored regression with applications to insurance," Working Papers hal-01141228, HAL.
    2. Olivier Lopez & Xavier Milhaud & Pierre-Emmanuel Thérond, 2016. "Tree-based censored regression with applications in insurance," Post-Print hal-01141228, HAL.
    3. Rancoita, Paola M.V. & Zaffalon, Marco & Zucca, Emanuele & Bertoni, Francesco & de Campos, Cassio P., 2016. "Bayesian network data imputation with application to survival tree analysis," Computational Statistics & Data Analysis, Elsevier, vol. 93(C), pages 373-387.

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