Trees for correlated survival data by goodness of split, with applications to tooth prognosis

In this article the regression tree method is extended to correlated survival data and applied to the problem of developing objective prognostic classification rules in periodontal research. The robust logrank statistic is used as the splitting statistic to measure the between-node difference in survival, while adjusting for correlation among failure times from the same patient. The partition-based survival function estimator is shown to converge to the true conditional survival function. Tooth loss data from 100 periodontal patients (2,509 teeth) was analyzed using the proposed method. The goal is to assign each tooth to one of the five prognosis categories (good, fair, poor, questionable, or hopeless). After the best-sized tree was identified, an amalgamation procedure was used to form five prognostic groups. The prognostic rules established here may be used by periodontists, general dentists, and insurance companies in devising appropriate treatment plans for periodontal patients.