Assessing the Optimal Cutpoint for Tumor Size in Patients with Lung Cancer Based on Linear Rank Statistics in a Competing Risks Framework

Abstract

Purpose: In clinical studies, patients may experience several types of events during follow up under the competing risks (CR) framework. Patients are often classified into low-and high-risk groups based on prognostic factors. We propose a method to determine an optimal cutpoint value for prognostic factors on censored outcomes in the presence of CR. Materials and Methods: We applied our method to data collected in a study of lung cancer patients. From September 1, 1991 to December 31, 2005, 758 lung cancer patients received tumor removal surgery at Samsung Medical Center in Korea. The proposed statistic converges in distribution to that of the supremum of a standardized Brownian bridge. To overcome the conservativeness of the test based on an approximation of the asymptotic distribution, we also propose a permutation test based on permuted samples. Results: Most cases considered in our simulation studies showed that the permutation-based test satisfied a significance level of 0.05, while the approximation-based test was very conservative: the powers of the former were larger than those of the latter. The optimal cutpoint value for tumor size (unit: cm) prior to surgery for classifying patients into two groups (low and high risks for relapse) was found to be 1.8, with decent significance reflected as p values less than 0.001. Conclusion: The cutpoint estimator based on the maximally selected linear rank statistic was reasonable in terms of bias and standard deviation in the CR framework. The permutation-based test well satisfied type I error probability and provided higher power than the approximation-based test.