We consider the problem of testing whether an identified treatment is better than each of K treatments. Suppose there are univariate test statistics Si that contrast the identified treatment with treatment i for i = 1, 2,...., K. The min test is defined to be the alpha-level procedure that rejects the null hypothesis that the identified treatment is not best when, for all i, Si rejects the one-sided hypothesis, at the alpha-level, that the identified treatment is not better than the ith treatment. In the normal case where Si are t statistics the min test is the likelihood ratio test. For distributions satisfying mild regularity conditions, if attention is restricted to test statistics that are monotone nondecreasing functions of Si, then regardless of their covariance structure the min test is an optimal alpha-level test. Tables of the sample size needed to achieve power .5, .8, .90, and .95 are given for the min test when the Si are Student's t and Wilcoxon.
Nonparametric generalized maximum likelihood product limit point estimators and confidence intervals are given for a cure model with random censorship. One-, two-, and K-sample likelihood ratio tests for inference on the cure rates are developed. In the two-sample case its power is compared to the power of several alternatives, including the log-rank and Gray and Tsiatis (1989, Biometrics 45, 899-904) tests. Implications for the use of the likelihood ratio test in a clinical trial designed to compare cure rates are discussed.
Current statistical designs for studying whether two or more agents in combination act synergistically nearly always require the study of several doses of many dose ratios. The analysis is usually based on an assumed parametric model of the dose-response surface. In this paper, for both quantal and quantitative response variables, sufficient conditions are given for establishing synergy at a dose of the combination without the need to specify the model. This enables the use of simple designs with few doses even when there is sparse knowledge of the dose-response curves of the individual agents. The Min test, used for testing whether an identified treatment is best, may be used for testing synergy. Power issues are discussed.
SUMMARYMethods for statistical inference for cost-effectiveness (C/E) ratios for individual treatments and for incremental cost-effectiveness (∆C/∆E) ratios when two treatments are compared are presented. In a lemma, we relate the relative magnitude of two C/E ratios to the ∆C/∆E ratio. We describe a statistical procedure to test for dominance, or admissibility, that can be used to eliminate an inferior treatment. The one-sided Bonferroni's confidence interval procedure is generalized to the two-sided case. The method requires only that two confidence intervals be available, one for cost and one for effectiveness. We describe Fieller-based confidence intervals and show them to be shorter than Bonferroni intervals. When distribution assumptions hold and variance and covariance estimates are available, Fieller intervals are preferable. However, Bonferroni intervals can be applied in more diverse situations and are easier to calculate. A simple Bonferroni based technique, and a likelihood ratio statistic given by Siegel, Laska and Meisner, for testing the null hypothesis that the C/E ratios of two treatments are equal is presented. The approaches are applied to the data from a phase II clinical trial of a new treatment for sepsis considered previously by others.
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