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

Balabdaoui Fadoua, Mielke Matthias and Munk Axel
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Balabdaoui Fadoua: Université de Paris-Dauphine, CEREMADE, Frankreich
Mielke Matthias: University of Göttingen, Institute for Mathematical Stochastics, Göttingen, Deutschland

Statistics & Risk Modeling, 2009, vol. 27, issue 1, 75-92

Abstract: We consider a class of testing problems where the null space is the union of k-1 subgraphs of the form hj(θj)≤θk, with j=1,…,k-1, (θ1,…,θk) the unknown parameter, and hj given increasing functions. The data consist of k independent samples, assumed to be drawn from a distribution with parameter θj, 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.

Keywords: likelihood ratio test; optimal allocation of samples; local asymptotic; non-inferiority trials; cone hypotheses (search for similar items in EconPapers)
Date: 2009
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DOI: 10.1524/stnd.2009.1022

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