Multivariate exponential survival trees and their application to tooth prognosis

Authors:
Juanjuan Fan;Martha E. Nunn;Xiaogang Su
Affiliations:
Department of Mathematics and Statistics, San Diego State University, San Diego, CA 92182, USA;Department of Health Policy and Health Services Research, Goldman School of Dental Medicine, Boston University, Boston, MA 02118, USA;Department of Statistics and Actuarial Science, University of Central Florida, Orlando, FL 32816, USA
Venue:
Computational Statistics & Data Analysis
Year:
2009

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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.