New Tests for Assessing Non-Inferiority and Equivalence from Survival Data

We propose a new nonparametric method for assessing non-inferiority of an experimental therapy compared to a standard of care. The ratio mu sub(E)/ mu sub(R) of true median survival times is the parameter of interest. This is of considerable interest in clinical trials of generic drugs. We think of the ratio m sub(E)/m sub(R) of the sample medians as a point estimate of the ratio mu sub(E)/ mu sub(R). We use the Fieller-Hinkley distribution of the ratio of two normally distributed random variables to derive an unbiased level- alpha test of inferiority null hypothesis, which is stated in terms of the ratio mu sub(E)/ mu sub(R) and a pre-specified fixed non-inferiority margin delta . We also explain how to assess equivalence and non-inferiority using bootstrap equivalent confidence intervals on the ratio mu sub(E)/ mu sub(R). The proposed new test does not require the censoring distributions for the two arms to be equal and it does not require the hazard rates to be proportional. If the proportional hazards assumption holds good, the proposed new test is more attractive. We also discuss sample size determination. We claim that our test procedure is simple and attains adequate power for moderate sample sizes. We extend the proposed test procedure to stratified analysis. We propose a "two one-sided tests" approach for assessing equivalence.