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Title: Higher order approximations in the Cox proportional hazards model Authors:  Aneta Andrasikova - Palacky University Olomouc (Czech Republic) [presenting]
Eva Fiserova - Palacky University (Czech Republic)
Abstract: Time-to-event analysis can be applied in a wide range of sectors, such as medicine, economy and others. Its main idea comes from the evaluating of the time until the occurrence of an event of interest. The effect of some particular covariates on survival time can be described by the Cox proportional hazards model. The statistical significance of the effect of the considered covariates is verified by the likelihood ratio test, the Wald test, or the score test. These tests represent the first-order approximations which are asymptotically equivalent. They can lead to the numerically different results in applications according to available data. In addition to the standard test, higher-order asymptotics based on Barndorff-Nielsen and Lugannani-Rice formulas is applied for more accurate approximations. Comparison of the size, power, and adjusted power of these tests for small samples is performed on simulated datasets in dependence on the distributions of baseline hazard functions, various proportion of right censored data and the number and the distribution of the covariates.