Testing noninferiority in three‐armed clinical trials based on likelihood ratio statistics

Munk, Axel; Mielke, Matthias; Skipka, Guido; Freitag, G

doi:10.1002/cjs.5550350306

Cited by 11 publications

(11 citation statements)

References 41 publications

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“…In Munk et al (2007) the power of three sample non-inferiority likelihood ratio test for binary outcomes has been investigated numerically. The question of optimal allocation of treatments, when the total number of samples is prespecified has not been addressed for this problem.…”

Section: Power Calculations -Application To the Binomial Modelmentioning

confidence: 99%

“…, h k−1 are given increasing functions. See Röhmel and Mansmann (1999), Munk et al (2007) or Skipka et al (2006) for a discussion of several choices of h j . This type of hypotheses occurs also in the context of order restricted inference, see e.g.…”

Section: Introductionmentioning

confidence: 98%

“…For a good review on the subject, see e.g. Röhmel (1998), Jones et al (1996), Pigeot et al (2003), Kieser and Friede (2007), the Special Issue on "Therapeutic EquivalenceClinical Issues and Statistical Methodology in Noninferiority Trials" (2005), D' Agostino et al (2003), Senn (1997), Skipka et al (2004) and Munk et al (2007). W.l.o.g.…”

Section: Introductionmentioning

confidence: 99%

“…, r k . The case k = 3 has been considered by Munk et al (2007) (see their hypothesis H U ) for the particular case of binomial samples. They showed that, under the null hypothesis, the log-likelihood ratio converges weakly to a random variable which is stochastically greater than (1/2) : (1/2) mixture of a Dirac at zero and a central χ 2 1 .…”

Section: Introductionmentioning

confidence: 99%

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The likelihood ratio test for non-standard hypotheses near the boundary of the null – with application to the assessment of non-inferiority

Balabdaoui

Mielke

Munk³

2009

Statistics &Amp; Decisions

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We consider a class of testing problems where the null space is the union of k − 1 subgraphs of the form h j (θ j ) ≤ θ k , with j = 1, . . . , k − 1, (θ 1 , . . . , θ k ) the unknown parameter, and h j given increasing functions. The data consist of k independent samples, assumed to be drawn from a distribution with parameter θ j , j = 1, . . . , k, respectively. An important class of examples covered by this setting is that of non-inferiority hypotheses, which have recently become important in the evaluation of drugs or therapies. When the true parameter approaches the boundary at a 1/ √ n rate, we give the explicit form of the asymptotic distribution of the log-likelihood ratio statistic. This extends previous work on the distribution of likelihood ratio statistics to local alternatives. We consider the prominent example of binomial data and illustrate the theory for k = 2 and 3 samples. We explain how this can be used for planning a non-inferiority trial. To this end we calculate the optimal sample ratios yielding the maximal power in a binomial non-inferiority trial.

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Section: Power Calculations -Application To the Binomial Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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The likelihood ratio test for non-standard hypotheses near the boundary of the null – with application to the assessment of non-inferiority

Balabdaoui

Mielke

Munk³

2009

Statistics &Amp; Decisions

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“…Noninferiority studies can also be carried out for more than two treatment arms, and appropriate statistical testing procedures have been developed for some of these situations. 41,42 Equivalence trial: In an equivalence trial, the aim is to confirm that there is no statistically significant difference in the effectiveness of the new and standard treatment/placebo (control arm). 43 Efficacy is determined by comparing the difference in the proportion of events between the new drug arm (p N ) and the control arm ( p C ) to a predetermined interval, with the choice of the interval being based on clinical relevance.…”

Section: -38mentioning

confidence: 99%

Pharmacological modeling and biostatistical analysis of a new drug

Ananthakrishnan¹,

Gona²

2010

OAJCT

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Clinical research and clinical trials of experimental drugs to treat human diseases have gained greater importance in recent years. Phase I-IV clinical trials offer patients the opportunity to gain access to a new, more efficacious and safer medication to alleviate or cure their disease. There are potential side effects of every new drug; however, such trials and studies are crucial for drug development and testing in humans. The US Food and Drug Administration (FDA) regulated process of evaluating a new drug for treating a particular disease in humans is long, rigorous, and includes the stages starting from preclinical research through the entire human clinical trials process. This review synthesizes results from the above stages and describes the entire mechanism of the clinical study of a new drug for human disease. It emphasizes the associated mathematical modeling and statistical analyses, and bridges pharmacological modeling and biostatistics in clinical research and also provides a basic theoretical overview to biomedical experimentalists. The modern trend in clinical research involves a unified approach among several biomedical subspecialties and it is hoped that even more integrated studies of new drugs will continue to be carried out, leading to novel drugs that are highly effective in curing the associated condition.

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A more powerful exact test of noninferiority from binary matched‐pairs data

Lloyd

Moldovan

2008

Statistics in Medicine

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Assessing the therapeutic noninferiority of one medical treatment compared with another is often based on the difference in response rates from a matched binary pairs design. This paper develops a new exact unconditional test for noninferiority that is more powerful than available alternatives. There are two new elements presented in this paper. First, we introduce the likelihood ratio statistic as an alternative to the previously proposed score statistic of Nam (Biometrics 1997; 53:1422-1430). Second, we eliminate the nuisance parameter by estimation followed by maximization as an alternative to the partial maximization of Berger and Boos (Am. Stat. Assoc. 1994; 89:1012-1016) or traditional full maximization. Based on an extensive numerical study, we recommend tests based on the score statistic, the nuisance parameter being controlled by estimation followed by maximization.

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Testing noninferiority in three‐armed clinical trials based on likelihood ratio statistics

Cited by 11 publications

References 41 publications

The likelihood ratio test for non-standard hypotheses near the boundary of the null – with application to the assessment of non-inferiority

The likelihood ratio test for non-standard hypotheses near the boundary of the null – with application to the assessment of non-inferiority

Pharmacological modeling and biostatistical analysis of a new drug

A more powerful exact test of noninferiority from binary matched‐pairs data

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