Survival Trees and Forest for Breast Cancer Prognostication

• Activity Number: 445
• Type: Invited
• Date/Time: Wednesday, August 5, 2009 : 10:30 AM to 12:20 PM
• Sponsor: International Indian Statistical Association
• Author(s): Mousumi Banerjee*+ and David Miller
• Companies: University of Michigan and University of Michigan
• Keywords: survival tree ; random forest ; tree distance metric ; concordance error rate ; out of bag error

Abstract

Breast cancer is the most common cancer and the second leading cause of cancer mortality among women in the US. Although breast cancer mortality rates have declined since the early nineties, there is still great heterogeneity in patient survival. This talk will examine tree-based methods for prognostication in breast cancer. We develop survival trees based on various splitting rules that focus on within-node error and between-node separation. To gain accuracy in prediction and improve the stability of the prognostic groups, we grow an ensemble of trees (forest). We propose a methodology for selecting the most representative trees in the forest based on tree distance metrics. For any two trees, the metrics are chosen to (1) measure similarity of the covariates used to split the trees; (2) reflect similar clustering of patients in the terminal nodes; and (3) measure similarity in predictions. The most representative trees in the forest are chosen based on the cumulative distance between a tree and all other trees in the forest. Out of bag estimate of error rate is computed using a neighborhood of similar trees. The methods are illustrated using data from a cohort study of breast cancer.