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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

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  • Balabdaoui Fadoua

    (Université de Paris-Dauphine, CEREMADE, Frankreich)

  • Mielke Matthias

    (University of Göttingen, Institute for Mathematical Stochastics, Göttingen, Deutschland)

  • Munk Axel

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.

Suggested Citation

  • Balabdaoui Fadoua & Mielke Matthias & Munk Axel, 2009. "The likelihood ratio test for non-standard hypotheses near the boundary of the null – with application to the assessment of non-inferiority," Statistics & Risk Modeling, De Gruyter, vol. 27(1), pages 75-92, November.
    • Handle: RePEc:bpj:strimo:v:27:y:2009:i:1:p:75-92:n:5
    DOI: 10.1524/stnd.2009.1022
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    References listed on IDEAS

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    1. Skipka, G. & Munk, A. & Freitag, G., 2004. "Unconditional exact tests for the difference of binomial probabilities--contrasted and compared," Computational Statistics & Data Analysis, Elsevier, vol. 47(4), pages 757-773, November.
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