Uttam Bandyopadhyay

An adaptive allocation for continuous response using Wilcoxon-Mann-Whitney score

Abstract In clinical trials, adaptive designs are sometimes used to force imbalance in allocation between two or more competitive treatments. Existing works are mostly based on dichotomous or polychotomous responses. In the present work, assuming that the responses are continuous variables, we investigate a two-treatment allocation scheme based on Wilcoxon–Mann–Whitney scores. The proposed scheme is used to provide two nonparametric test procedures for identity of two univariate continuous populations against location alternatives. Again, we give an exactly distribution free solution for generalized Behrens–Fisher problem.

Nonparametric Partial Sequential Test for Location Shift at an Unknown Time Point

Abstract In the present work, we introduce a partial sequential sampling scheme to develop a sequential rank-based nonparametric test for the identity of two unknown univariate continuous distribution functions against one-sided shift in location occurring at an unknown time point. Our work is motivated by Wolfe (1977) as well as Orban and Wolfe (1980). We provide detailed discussion on asymptotic studies related to the proposed test. We compare the proposed test with a usual rank-based test. Some simulation studies are also presented.

Delayed Response in Randomized Play-The-Winner Rule; A Decision Theoretic Outlook

In the context of comparing two treatments in clinical trials, randomized play-the-winner rule is used with a goal to treat more patients by the better treatment. On its basis some decision rules are proposed taking delayed response into account. Some exact and asymptotic results of the decision rules are studied. Minimax decison rule is also obtained.

A Bayesian adaptive design for two-stage clinical trials with survival data.

A randomized two-stage adaptive Bayesian design is proposed and studied for allocation and comparison in a phase III clinical trial with survival time as treatment response. Several exact and limiting properties of the design and the follow-up inference are studied, both numerically and theoretically, and are compared with a single-stage randomized procedure. The applicability of the proposed methodology is illustrated by using some real data.

Inverse Sampling Based on General Scores for Non-Parametric Two-Sample Problems

The problem considered in this paper is that of testing the identity of two univariate distribution functions F1(x) and F9(x) when there is a sample of fixed size from F1 (x) and the observations (Y) from F2(x) are drawn sequentially. Two score functions 4> 1(u), 0 < u < 1, l= I, 2, which reflect departures from the null hypothesis in specific ways are taken. Writing F~. (x) for a certain uniformly consistent estimate of F1 (x) based on the first sample, sums of the type S,. 01 = £ 4> 1 (Ft. (Y;)) are calculated for successive observations ;-1 on Y. Observation is stopped as soon as S,. ( 11 reaches a pre-fixed upper bound. The hypothesis is rejected or accepted on the basis of the terminal value of Sn <•>. Different large sample procedures based on this approach are formulated and examined.

Nonparametric Partial Sequential Tests for Patterned Alternatives in Multisample Problems

Abstract In the present work we develop partial sequential nonparametric tests for multiple comparison. We provide tests for the identity of several unknown univariate continuous distribution functions against patterned alternatives. Our tests are based on Wilcoxon score. We conduct some Monte Carlo studies related to the proposed tests. We carry out a detailed comparison between the proposed procedures and the corresponding nonsequential procedures. We register significant gain in sample size through the proposed procedure, maintaining almost the same level and power for both the tests. We perform an analysis of life data arising out of a geological survey related to arsenic contamination. We also present some asymptotics in this context.

Controlling Type-I Error Rate in Monitoring Structural Changes Using Partially Sequential Procedures

In the present article, we develop some asymptotically power on partially sequential nonparametric tests for monitoring structural changes. Our test procedures are based on Wilcoxon score. We use the idea of curved stopping boundaries. We derive some exact results and perform simulation studies to provide various properties of the tests. We see that one of the proposed procedures significantly controls the Type I error rate. This procedure may be very effective for fluctuation monitoring. We illustrate the procedures by using real life data from the stock market.

Adaptive Allocation and Failure Saving in Randomised Clinical Trials

In the present work, we develop a randomized two-treatment single period response adaptive design by combining two contrasting aspects (i.e., ethics and optimality), where optimality is defined in a meaningful way. We compare this rule with some of the existing rules by computing various performance measures of the rules.

Sequential comparison of two treatments in clinical trials:a decision theoretic approach based on randomized play-the-winner rule

In the context of comparing two treatments in clinical trials randomized play-the-winner rule is used with the goal of treating more patients by the better treatment On its basis we give two decision rules by introducing stopping rule Some performance characteristics of one of the decision rules are discussed and examined .A minimax rule is suggested Finally some exact and asymptotic properties of the decision rule is derived

Some Sequential Tests in Clinical Trials Based on Randomized-Play-The-Winner Rule

The present paper provides a nonpararnetric test procedure for comparing two treatments in clinical trials by using a sampling design which allocates more patients to the better treatment in course of decision making. Some exact and asymptotic results related to the performance characteristics and the properties of the proposed test are discussed and examined. Finally, the performance characteristics of the test are compared numerically with its possible competitors.