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survival analysis; likelihood ratio test; wald test; score test; statistical power; adjusted power; higher-order approximation; confidence band
Survival analysis is applied in a wide range of sectors (medicine, economy, etc.), and its main idea is based on evaluating the time until the occurrence of an event of interest. The effect of some particular covariates on survival time is usually described by the Cox proportional hazards model and the statistical significance of the impact of covariates is verified by the likelihood ratio test, the Wald test, or the score test. In addition to standard tests, appropriate higher-order approximations based on Barndorff-Nielsen and Lugannani-Rice formulas are used for more accurate approximations. In this paper, comparison of these tests' size and power for small sample sizes is performed on simulated datasets with various proportions of right-censored data, distributions of baseline hazard functions and different types of covariate---continuous or discrete.
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