On non-inferiority analysis based on delta-method confidence intervals

For many indications where there is an effective standard therapy, active controlled trials are generally conducted when it is unethical to use a placebo. The efficacy objective of most such trials is the demonstration that the experimental therapy has superior efficacy to the active-control. The efficacy objective of a non-inferiority trial may be to rule out that the experimental treatment loses some prespecified fraction of the active-control effect. The size of the active-control effect may be based on previous trials comparing this active-control with a placebo--for example, through a meta-analysis. Delta-method 95% confidence interval procedures are among the testing procedures that have been proposed to test a non-inferiority hypothesis that an experimental treatment retains more than some prespecified fraction of the active-control effect. For time-to-event endpoints using hazard ratios, we will examine the type I error probability of such testing procedures under the assumption that the current active-control effect has been correctly modeled. Conditions are discussed for when such testing procedures maintain a desired approximate type I error rate and when such testing procedures will not. Two applications (one in Cardiorenalogy and one in Oncology) are given--one maintains the desired approximate type I error probability and the other does not. The delta-method 95% confidence interval procedures will also be contrasted with Fieller 95% confidence intervals. Testing based on Fieller 95% confidence intervals will maintain a desired approximate type I error rate.