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

67A Designed extension of studies based on conditional power

Abstract: We propose a flexible method of extending a study based on conditional power. The possibility for extension when the p value at the planned end is small but not statistically significant is built in to the design of the study. 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 for use after accruing those additional observations. It may therefore be thought of as a two-stage procedure. Even though the observed treatment difference at stage 1 is used to make decisions, the Type I error rate is protected.

A distribution-free approach for selecting better treatment through an ethical allocation

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

A Class of Statistics with Asymptotically Normal Distribution

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)

Theory of rank tests

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.

The Effects of Nonpharmacologic Interventions on Blood Pressure of Persons With High Normal Levels: Results of the Trials of Hypertension Prevention, Phase I

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)

Multivariate Permutation Tests : With Applications in Biostatistics

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