Clinical Trials

Clinical Trials: A Practical Guide ■❚❙❘Table 1. Features of equivalence and noninferiority trials.AssumptionsLet π Nand π Sbe the rates of outcomes (eg, deaths or myocardial infarctions) with thenew and standard treatments, respectively, and let a smaller value mean better efficacyStatistical testNull hypothesisAlternative hypothesisExampleEquivalenceTwo-sided equivalence testH 0: π N– π S≤ –D or π N– π S≥ DWhere D is the magnitude of prespecifieddifference between outcome rates withthe new and standard treatments.The null hypothesis (H 0) implies thatthe new and standard treatmentshave differing outcome rates.H a: –D < π N– π S< DThe new treatment is statistically similarin outcome rates to the standardtreatment, within a predefined range(–D to D).In an equivalence trial, the standardtreatment has an event rate of 10% (π S).Medical experts in that field agree thatan absolute reduction of events within1% (D) of the standard treatment mightbe acceptable to determine the newtreatment as having an equivalentefficacy. So we have (–D, D) = (–1%, 1%).The result shows that the 95% CI forπ N– π S= (–0.5%, 0.5%). As this intervalfalls within (–D, D), equivalence betweenthe new treatment and the standard onecan be established. If the 95% CI forπ N– π S= (–2%, 2%), then equivalencebetween the new treatment andstandard one cannot be concluded.NoninferiorityOne-sided equivalence testH 0: π N– π S≥ MWhere M is the prespecified maximumallowable limit of difference inoutcome rates between the newand standard treatments.The null hypothesis (H 0) implies that the newtreatment is inferior to the standard one.H a: π N– π S< MThe new treatment is clinicallynoninferior to the standard treatmentwithin the predefined allowablerange (M) of clinical significance.Consider a trial in which we wouldprespecify that if the effectiveness ofthe new treatment is 20% (M) less thanthat of the standard treatment, thenwe would consider the new treatmentto be clinically inferior.The result shows that a new treatmentis 10% less effective than standardtreatment (π N– π S= 10%), with a one-sided95% CI for π N– π Sbeing 5–15%. As theupper limit of the 95% CI (15%) is < M(20%), the new treatment is deemed tobe noninferior to the standard treatment.If the prespecified limit (M) is 12%, thenthe new treatment fails the noninferioritytest as 15% is higher than the predefined12% threshold.a 95% confidence interval (CI) of 5–15% less. The prespecified definition ofnoninferiority (see Chapter 14) for this trial might state that the upper limit of the95% CI must be