Making sense of equivalence and non-inferiority trials - Australian ...

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VOLUME 36 : NUMBER 5 : OCTOBER 2013ARTICLE‘good’ end of the 95% confidence interval goes, justas long as the ‘bad’ end is within an acceptable limit.For this reason most trials will use a non-inferiorityanalysis, and although it sounds weaker it is just asgood as an equivalence analysis.In an equivalence trial the statisticians look at bothends of the boundary. Is the new drug no better or noworse? (see Fig. 2).Setting the equivalence boundaryThe two main methods for setting the equivalenceboundary are clinical and statistical. The statisticalmethod is more widely used.Fig. 1 Effect of trial size on the 95% confidence intervalTrial 1Trial 2Trial 3Clinical methodA group of clinicians give their opinion on the ‘minimumclinically important difference’ which is the smallestdifference that they or their patients would think wasimportant. This might be a change of 5 mmHg of bloodpressure or 10 mm on a pain scale. The basis for thesearbitrary judgements is rarely explained, such as why itis 10 mm rather than 8 mm or 13 mm. Small differenceslike this might make all the difference in statisticaltesting. There is also the problem that although5 mmHg is a small change in blood pressure it stillmakes a difference to stroke risk, and 10 mm on a painscale still affects the patient’s comfort.Statistical methodThe statistical method relies on examining thedifference between the standard treatment andplacebo. This is derived from the original placebocontrolledstudies of efficacy. The equivalenceboundary could be set to prove that the newtreatment is no worse than the outcome for placeboin the original trials, although sometimes it is set to be50% better than placebo.As the minimum clinically important differencebetween active treatments is usually smaller than thetreatment benefit found in placebo-controlled trials,the sample size required for non-inferiority trials isgenerally bigger than for superiority trials.Relative riskConfidence intervals reduce with larger trial sizes (represented by the size of thediamonds). A narrow confidence interval increases the chance that the observed resultis close to the true value.Fig. 2 Spectrum of outcomes included in non-inferiority trialsABCD0.1 0.5 0.9 1.0 1.2 2.0 10Favours new treatmentFavours old treatmentDifferences in analysisThe analysis of a superiority trial should be by‘intention to treat’. This means that the outcomesare measured in patients who were randomisedeven if they did not take the treatment or completethe trial. This analysis is conservative, because ifanything it biases the result towards a null effect. Ina non-inferiority trial an intention-to-treat analysiswith its bias toward a null effect could be misleading.It is good practice to also perform a ‘per protocol’analysis, in which groups are defined by who took thedrug rather than just by randomisation.Relative riskFavours new treatmentAll of A B C D are ‘non-inferior’ to old drugA + B are not statistically superior or inferiorC is statistically inferiorD is statistically superiorNon-inferiority0.1 0.5 0.9 1.0 1.2 2.0 10Favours old treatmentFull text free online at www.australianprescriber.com171
VOLUME 36 : NUMBER 5 : OCTOBER 2013ARTICLEMaking sense of equivalence, non-inferiority and active control trialsInterpretationIn assessing non-inferiority trials the issues of trialdesign, such as randomisation, blinding and followup,are considered in the same way as they are intrials looking for superiority. However, there areother considerations when assessing non-inferioritytrials. It can be difficult to judge if the statisticalequivalence boundary has been appropriately set.There is scope for pharmaceutical companies to setthe equivalence boundary too wide, making it easy toclaim equivalence when it may not exist.TrapsProving that two drugs are equivalent could meanthat they are both ineffective or even harmful. Theevidence for the old drug must be considered whenrelying on an equivalence trial to show evidence forthe efficacy of a new drug. If drug A is superior toplacebo and drug B is proved non-inferior to drug A(and becomes the drug of choice because it ischeaper and easier to administer) but later drug C isproved to be non-inferior to drug B, can we be certaindrug C is superior to placebo? This problem has beencalled ‘biocreep’ and could lead to the acceptance ofprogressively worse treatments if non-inferiority isblindly accepted. It can be avoided by selecting themost effective drug in the class as the control for noninferioritytrials, even if this is not the drug in mostcommon use.Can the data from a failed superiority trial be used todemonstrate non-inferiority (Fig. 2 – Trial A, B, C)?Can the data from a non-inferiority trial that goesparticularly well be used to demonstrate superiority(Fig. 2 – Trial D)? These are controversial questions,however there is a view that if the non-inferiorityboundary is selected a priori a failed superiority trialcan be taken as evidence of non-inferiority, althoughthe test for statistical significance should be adjustedfor multiple comparisons.Example 1The RE-LY trial set out to demonstrate non-inferiorityof dabigatran versus warfarin for preventing stroke inpatients with atrial fibrillation. 1Choice of boundaryThe non-inferiority boundary was chosen as a relativerisk of 1.46 for stroke or systemic embolism. Thisboundary was derived on statistical grounds froma meta-analysis of trials of warfarin versus placeboand chosen as 50% of the proven benefit of warfarin.Although this may have satisfied the statisticians it isclearly not acceptable to clinicians that a new drugcould allow 46% more strokes and still be regardedas non-inferior. As it turned out, dabigatran 110 mgdose reduced the relative risk to 0.91 (95% confidenceinterval 0.74–1.11). The upper boundary of an 11%increase in strokes is probably acceptable to cliniciansand patients.AnalysisAn intention-to-treat analysis was performed. As99.9% of the patients were followed up, loss tofollow-up did not introduce bias. The proportionsdiscontinuing treatment were 14.5% for the low doseand 15.5% for the high dose of dabigatran and 10.2%for warfarin, possibly biasing the relative risktowards 1.0. This could have given a spurious noninferiorityresult if the point estimate had been arelative risk greater than 1.0, but would not have hadthis effect on a point estimate less than 1.0. A perprotocol analysis was not done.The trial set out to demonstrate non-inferiority,but ended up showing superiority of the 150 mgdose over warfarin with a relative risk of 0.66 (95%confidence interval 0.53–0.82) so the intention totreat analysis is appropriate for a claim of superiority(see Fig. 3). If the trial had claimed non-inferiorityby showing the relative risk for stroke had a 95%confidence interval extending just short of theboundary (for example to 1.45), it should not havebeen accepted. To me the possibility that the newdrug could lead to a 45% increased risk of strokewould be unacceptable.Example 2A study set out to show that once-daily dosing withmesalazine granules was as good as three-times-dailydosing at inducing remission during first episodes ofulcerative colitis. The rate of non-remission at eightweeks was 24.3% in the three-times-daily group, butonly 20.9% in the once-daily group. The relative riskwas 0.86 (95% confidence interval 0.59–1.25). Thenon-inferiority boundary was set at relative risk of 1.6,and as the upper limit of the confidence interval isclear of this, non-inferiority is accepted (see Fig. 3). 2Example 3The Captopril Prevention Project compared theefficacy of the drug to older antihypertensives inthe prevention of stroke, myocardial infarction andcardiovascular death. The authors presented bothintention to treat and per protocol analyses, showingsomewhat worse outcomes for captopril. Theadjusted relative risk was 1.12 (95% confidence interval0.94–1.32). The authors claimed equivalence, but didnot pre-specify an equivalence boundary. Patientsmay not view the possible 32% increase in seriousoutcomes as equivalent (see Fig. 3). 3172Full text free online at www.australianprescriber.com
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