The assessment of non‐inferiority in a gold standard design with censored, exponentially distributed endpoints

The objective of this paper is to develop statistical methodology for non‐inferiority hypotheses to censored, exponentially distributed time to event endpoints. Motivated by a recent clinical trial in depression, we consider a gold standard design where a test group is compared with an active reference and with a placebo group. The test problem is formulated in terms of a retention of effect hypothesis. Thus, the proposed Wald‐type test procedure assures that the effect of the test group is better than a pre‐specified proportion Δ of the treatment effect of the reference group compared with the placebo group. A sample size allocation rule to achieve optimal power is presented, which only depends on the pre‐specified Δ and the probabilities for the occurrence of censoring. In addition, a pretest is presented for either the reference or the test group to ensure assay sensitivity in the complete test procedure. The actual type I error and the sample size formula of the proposed tests are explored asymptotically by means of a simulation study showing good small sample characteristics. To illustrate the procedure a randomized, double blind clinical trial in depression is evaluated. An R‐package for implementation of the proposed tests and for sample size determination accompanies this paper on the author's web page. Copyright © 2008 John Wiley & Sons, Ltd.