Cumulative Incidence in Competing Risks Data and Competing Risks Regression Analysis

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Abstract
Competing risks occur commonly in medical research. For example, both treatment-related mortality and disease recurrence are important outcomes of interest and well-known competing risks in cancer research. In the analysis of competing risks data, methods of standard survival analysis such as the Kaplan-Meier method for estimation of cumulative incidence, the log-rank test for comparison of cumulative incidence curves, and the standard Cox model for the assessment of covariates lead to incorrect and biased results. In this article, we discuss competing risks data analysis which includes methods to calculate the cumulative incidence of an event of interest in the presence of competing risks, to compare cumulative incidence curves in the presence of competing risks, and to perform competing risks regression analysis. A hypothetical numeric example and real data are used to compare those three methods in the competing risks data analysis to their respective counterparts in the standard survival analysis. The source and magnitude of bias from the Kaplan-Meier estimate is also detailed.