Determining of complexity parameter for recursive partitioning trees by simulation of survival data and an application on breast cancer data

Abstract

The objective of our study is to determine the optimal complexity parameter (cp) value to show the effects of the factors on survival time in recursive partitioning (RP) and to reduce the leaves of a tree and find an optimal tree in the decision trees. We simulated the generated data by checking for RP under varying cp, sample sizes and the number of independent variables on survival data. For each situation, 1000 simulations and 10-fold cross validation were performed. Further, in a real data set application, breast cancer data set related to disease-free survival obtained from 423 diagnosed breast cancer patients was used. In the present study, we investigated the critical cp values on different sample sizes and the number of variables for survival data. We found optimal cp values in the 0.010-0.025 range according to sample size. As the sample size increased the optimal cp value decreased. As cp value increased, the standard deviation of the C-index error rate increased for each sample size (n = 100, 250, 500 and 1000). Also, we discovered that the results of the breast cancer data conformed to simulation data. Consequently, in our study we choose cp and will evaluate the data by using RP in future studies, focusing on survival time.

Keywords:

• Recursive partitioning
• Complexity parameter
• Pruning
• Disease-free survival
• Monte Carlo simulation