A family of slope tests for comparing survival curves under nonproportional hazards.

Abstract Censored data are nearly ubiquitous in survival analysis. If the proportional hazard assumption is invalid, traditional test methods, such as the log-rank tests, rapidly lose power. In this article, a new slope strategy is presented to improve the power of the test. The aim of this study is to establish effective tests that are familiar in biomedical research and medical practice for censored data. Four tests based on slope are proposed in this article, and Monte Carlo simulations with different survival curves, sample sizes, and censoring rate scenarios are performed to evaluate the test power. Four common tests, the log-rank test, Gehan–Wilcoxon test, and Fleming–Harrington with different parameters, are compared with four new slope tests. The slope tests are more effective when the censoring rate is greater than or equal to 30%, especially for scenarios involving early hazard function differences. Two clinical cases also indicate that the proposed slope methods can detect differences for real data. Slope tests may supplement computing methods of survival curve tests, and they will be more useful when considering higher censoring rates. [ABSTRACT FROM AUTHOR]