A comparison between two treatments in a clinical trial with an ethical allocation design

TL;DR: In this paper, the authors compared two treatments, say A and B, in the context of a clinical trial using the Mann-Whitney-Wilcoxon (MWW) statistic.

Abstract: The present article compares two treatments, say A and B, in the context of a clinical trial. Let X and Y be, respectively, the responses corresponding to A and B which have some continuous distributions. Here, the comparison is done through the parameter θ=P(X

TL;DR: A flexible method of extending a study based on conditional power, where the significance of the treatment difference at the planned end is used to determine the number of additional observations needed and the critical value necessary after accruing those additional observations.

TL;DR: In this article, the authors provided a statistical inference on comparative performances of two treatments in a clinical trial under a two-stage adaptive allocation design, where a fixed number (2m+n, say) of subjects are available for treatment by any of the two competing treatments, for a particular ailment.

Abstract: The present article provides a statistical inference on comparative performances of two treatments in a clinical trial under a two-stage adaptive allocation design Suppose a fixed number (2m+n, say) of subjects are available for treatment by any of the two competing treatments, say, A and B for a particular ailment As per the proposed allocation design, 2m incoming subjects are randomised equally between A and B at the first stage Then, at the second stage, the remaining n subjects are exclusively assigned to the treatment which has higher observed median response evaluated in the first stage Under such an ethical allocation design we decide on the better treatment through an asymptotically distribution-free test procedure The related asymptotic results are also studied

TL;DR: In this paper , a distribution-free test procedure for comparing the effectiveness of two competing treatments A and B, say, in a clinical trial, is provided, where the relative treatment effect is measured by the functional θ=P(X

Abstract: The present article provides a distribution-free test procedure for comparing the effectiveness of two competing treatments A and B, say, in a clinical trial. Here, the relative treatment effect is measured by the functional θ=P(X

TL;DR: In this article, the authors considered the problem of estimating a U-statistic of the population characteristic of a regular functional function, where the sum ∑″ is extended over all permutations (α 1, α m ) of different integers, 1 α≤ (αi≤ n, n).

Abstract: Let X 1 …, X n be n independent random vectors, X v = , and Φ(x 1 …, x m ) a function of m(≤n) vectors . A statistic of the form , where the sum ∑″ is extended over all permutations (α1 …, α m ) of different integers, 1 α≤ (αi≤ n, is called a U-statistic. If X 1, …, X n have the same (cumulative) distribution function (d.f.) F(x), U is an unbiased estimate of the population characteristic θ(F) = f … f Φ(x 1,…, x m ) dF(x 1) … dF(x m ). θ(F) is called a regular functional of the d.f. F(x). Certain optimal properties of U-statistics as unbiased estimates of regular functionals have been established by Halmos [9] (cf. Section 4)

TL;DR: In this article, the authors present an elementary theory of rank tests and a set of properties of rank estimators, including asymptotic optimality and efficiency, as well as non-null distributions.

Abstract: Introduction and Coverage. Preliminaries. Elementary Theory of Rank Tests. Selected Rank Tests. Computation of Null Exact Distributions. Limiting Null Distributions. Limiting Non-Null Distributions. Asymptotic Optimality and Efficiency. Rank Estimates and Asymptotic Linearity.

TL;DR: Weight reduction is the most effective of the strategies tested for reducing blood pressure in normotensive persons, and sodium reduction is also effective.

Abstract: Objective. —To test the short-term feasibility and efficacy of seven nonpharmacologic interventions in persons with high normal diastolic blood pressure. Design. —Randomized control multicenter trials. Setting. —Volunteers recruited from the community, treated and followed up at special clinics. Participants. —Of 16821 screenees, 2182 men and women, aged 30 through 54 years, with diastolic blood pressure from 80 through 89 mm Hg were selected. Of these, 50 did not return for follow-up blood pressure measurements. Interventions. —Three life-style change groups (weight reduction, sodium reduction, and stress management) were each compared with unmasked nonintervention controls over 18 months. Four nutritional supplement groups (calcium, magnesium, potassium, and fish oil) were each compared singly, in double-blind fashion, with placebo controls over 6 months. Main Outcome Measures. —Primary: change in diastolic blood pressure from baseline to final follow-up, measured by blinded observers. Secondary: changes in systolic blood pressure and intervention compliance measures. Results. —Weight reduction intervention produced weight loss of 3.9 kg (P .05). Conclusions. —Weight reduction is the most effective of the strategies tested for reducing blood pressure in normotensive persons. Sodium reduction is also effective. The long-term effects of weight reduction and sodium reduction, alone and in combination, require further evaluation. (JAMA. 1992;267:1213-1220)

TL;DR: In this article, a simple testing problem for one-sample problems is discussed, and a theory of permutation tests for multisample problems is presented. But this problem is not applicable to the problem of multivariate multi-sample problem.

Abstract: Preface. Notation and Abbreviations. Introduction. Discussion of a Simple Testing Problem. Theory of Permutation Tests for One-Sample Problems. Examples of Univariate Multi-Sample Problems. Theory of Permutation Tests for Multi-Sample Problems. Nonparametric Combination Methodology. Examples of Nonparametric Combination. Permutation Analysis in Factorial Designs. Permutation Testing with Missing Data. The Behrens-Fisher Permutation Problem. Permutation Testing for Repeated Measurements. Further Applications. References. Index