Lasso Tree for Cancer Stage Grouping

• Activity Number: 126
• Type: Contributed
• Date/Time: Monday, July 30, 2012 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistical Computing
• Author(s): Yunzhi Lin*+ and Sijian Wang and Rick Chappell
• Companies: University of Wisconsin-Madison and University of Wisconsin-Madison and University of Wisconsin-Madison
• Keywords: Lasso Tree ; Cancer staging ; Model selection ; Lasso ; Cox model

Abstract

The tumor-node-metastasis (TNM) staging system has been the lynchpin of cancer diagnosis, treatment, and prognosis for many years. For meaningful clinical use, an orderly grouping of the T and N categories into a staging system needs to be defined. This can be reframed as a model selection problem with respect to features arranged on a partially ordered two-way grid, and a L1 penalized regression method is proposed for selecting the optimal grouping. Instead of penalizing the L1-norm of the coefficients like lasso, in order for the grouping to occur, we place L1 constraints on the differences between neighboring coefficients. A partial ordering constraint is also required as both the T and N categories are ordinal. A series of optimal groupings with different numbers of groups can be obtained by varying the tuning parameter, which gives a tree-like structure offering a visual aid on how the groupings are made progressively. We hence call the proposed method the lasso tree. We illustrate the utility of our method by applying it to the staging of colorectal cancer. Simulation studies demonstrate that the lasso tree is able to give the right grouping with moderate sample size.