Assessing non-inferiority with time-to-event data via the method of non-parametric covariance

Non-parametric methods have been well recognised as useful tools for time-to-event (survival) data analysis because they provide valid statistical inference with few assumptions. Tangen and Koch have proposed the use of the method of non-parametric covariance for time-to-event data in a traditional superiority setting. In this article, we extended their method to assess non-inferiority of two treatments. To evaluate this non-parametric method versus the classical semi-parametric Cox proportional hazards regression model, simulations in terms of the Type 1 error rate and power were performed and compared. The results showed that the two methods were generally comparable regarding the Type 1 error rate when adjustment for the covariates correlated with the survival time was made. In the non-inferiority setting, the covariate-adjusted non-parametric analysis was shown to always increase power. However, this was not necessarily the case for the adjusted Cox model where results were inconsistent to those seen in the superiority setting. For illustration, an application of the proposed non-parametric method to a trial involving pemetrexed, a recently approved drug for first-line treatment of non-small cell lung cancer, is included.