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 Delta 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 Delta 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.