Superiority trials hypothesis testing

While the practical details of the statistical approaches employed in equivalence, noninferiority, and bioequivalence trials are different from those employed in superiority trials, all of the approaches employ hypothesis testing. The differences lie in the nature of the hypotheses that are created and then tested. 

In the case of equivalence, noninferiority, and bioequivalence trials, the null hypotheses established are different from the null hypothesis established in superiority trials. In addition, the null hypothesis in each case is unique, and hence they all differ from each other. However, they share a basic similarity. The null hypothesis for each of these designs states, in effect, that the test drug and the comparator drug do not have similar efficacy. As in all hypothesis testing, the statistical methodologies used look for compelling evidence to reject the respective null hypothesis in each case. 

It is noteworthy that, while the null hypothesis in each of the trial designs discussed (superiority, equivalence, noninferiority, and equivalence) is different, the hypothesis testing approach in each case is fundamentally similar to that in every other case. In each instance it is hoped that the null hypothesis will be rejected in favor of the research hypothesis. 

The research question in equivalence trials is structured differently from the research question in superiority trials. The hypothesis testing approach that works so well in superiority trials is of little value in an equivalence trial. As Matthews (2006) commented, Failing to establish that one treatment is superior to the other is not the same as establishing their equivalence. ... 

Having seen why the hypothesis testing used in superiority trials is inappropriate for equivalence trials, the appropriate approach in this context is now discussed. The first step in this approach is to establish the equivalence margin for the trial. 

For a superiority trial the null hypothesis is that the treatment effect is zero. Sponsors of drug trials would like to generate sufficient evidence, in the form of the test statistic, to reject the null hypothesis in favor of the alternate hypothesis, thereby providing compelling evidence that the treatment effect is not zero. The null hypothesis may be rejected if the treatment effect favors the test drug, and also if it favors the placebo (as discussed, we have to acknowledge this possibility). 

Consider the simple case of a superiority trial of an investigational drug (the test treatment) being compared with placebo with respect to a continuous outcome (for example, change from baseline SBP). The null hypothesis typically tested in such a trial and its complementary alternate hypothesis are ... 

Given that the research questions in these trials are different from those used in superiority trials, the formats of the null and alternate hypotheses are also different. The research question associated with an equivalence trial is Does the test drug demonstrate equivalent efficacy compared with the comparator drug The null hypothesis,... 

The hypothesis that intravenous fluid that contains sodium bicarbonate might decrease the incidence of CIN compared with NaCl was recently tested in some randomized trials [113-116]. The hypothesis for a potential benefit of bicarbonate is based on the concept that alkalinizing tubular fluid reduces the generation of injurious hydroxyl radicals. Within a retrospective Cohort Study of 7977 Patients at Mayo Clinic N-ace-tylcysteine alone and in combination with sodium bicarbonate was not associated with any significant difference in the incidence of contrast nephropathy. The use of intravenous sodium bicarbonate was associated with increased incidence of contrast nephropathy [117]. As with any retrospective study confounding by indication is always exists since patients at preceived high risk often receive the treatment that is suspected of being superior even when unproven. 

Another difficult aspect in the design of open-label studies is how one assesses those patients who withdraw from the study. The reasons for withdrawal can be at least as varied as in double-blind studies (intolerability, administrative difficulties, coincidental emergent disease or concomitant therapies, etc.). However, in addition, in an open-label design, patients may develop an opinion on the superiority of one or other treatment for reasons that may or may not be explicit. If completion of a course of therapy is one end point of the study, then all withdrawals can be accounted treatment failures, and the statistical handling is fairly straightforward. However, if there is another end point, and if withdrawals are imbalanced between the treatment groups and unrelated to product intolerability, then the situation becomes a lot more clouded. Under these latter conditions, the entire trial may have to be abandoned when it becomes apparent that the trial design cannot answer the hypothesis under test one way or the other. 

The results of the Antihypertensive and Lipid-Lowering Treatment to Prevent Heart Attack Trial (ALLHAT) was the deciding evidence that the JNC7 used to justify thiazide diuretics as first-line therapy." It was designed to test the hypothesis that newer antihypertensive agents (an a-blocker, ACE inhibitor, and dihydropyridine CCB) would be superior to thiazide diuretic therapy. The primary objective was to compare the combined end point of fatal coronary heart disease and nonfatal myocardial infarction. Other hypertension-related complications (e.g., heart failure and stroke) were evaluated as secondary end points. This was the largest hypertension trial ever conducted and included 42,418 patients aged 55 years and older with hypertension and one additional cardiovascular risk factor. This prospective, double-blind trial randomized patients to chlorthalidone (a thiazide diuretic), amlodipine (dihydropyridine CCB), doxazosin (a-blocker), or lisinopril (ACE inhibitor) for a mean follow-up of 4.9 years. 

To test the hypothesis that elevated endogenous opiate levels contribute to autism and/or to self-injurious behavior, 33 adult subjects with autism and/or self-injurious behavior were treated for 4 weeks with 50 or 150 mg/day naltrexone in a double-blind, placebo-controlled crossover trial. Naltrexone was not superior to placebo with respect to either frequency of self-injurious behavior or CGI and ABC measures of autistic symptoms (Zingarelli et al., 1992). 

There is no reason why, from the point of view of controlling the type one error rate, one cannot test for noninferiority and superiority in the same trial without having to adjust the individual significance levels. This is because the null hypotheses in question form a nested set. For example, the null hypothesis that the new drug is inferior in terms of effect on mean diastolic blood pressure by at least 2 mmHg logically implies... 

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