Multivariate exponential survival trees and their application to tooth prognosis

Juanjuan Fan, Martha E. Nunn, Xiaogang Su

Research output: Contribution to journalArticlepeer-review

18 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)1110-1121
Number of pages12
JournalComputational Statistics and Data Analysis
Issue number4
StatePublished - Feb 15 2009
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Computational Mathematics
  • Computational Theory and Mathematics
  • Applied Mathematics


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