Multi-treatment optimal response-adaptive designs for phase III clinical trials

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Abstract

Response-adaptive designs are used in phase III clinical trials to allocate a larger number of patients to the better treatment. Optimal response-adaptive designs have become popular in recent days for this purpose, where the design is derived from some optimal viewpoints, mostly by optimizing some objective function subject to some constraint(s). However, most of the optimal designs are derived with two treatments and only a few works are available for several treatments. The present paper provides a generalized framework to derive multi-treatment optimal response-adaptive designs. A detailed performance study is provided for three treatment trials minimising failures. The applicability is also judged by redesigning some real clinical trials.

Section snippets

Background and introduction

Response-adaptive designs are used in phase III clinical trials to achieve some ethical goal by assigning a larger number of patients to the better treatment arm. Several such adaptive designs are available for binary treatment responses, e.g., the play-the-winner (PW) rule (Zelen, 1969), the randomized play-the-winner (RPW) rule (Wei & Durham, 1978), the generalized Pòlya urn design (GPU) (Wei, 1979), the success driven design (Durham, Flournoy, & Li, 1998), the birth and death design (

The optimal proportion

Consider a clinical trial with k treatments indexed by 1,2,,k with nj subjects assigned to the jth treatment arm under a non-randomised set up. The variable, measuring the response of the jth treatment, is indicated by Xj, and we assume that E(Xj)=μj and Var(Xj)=σj2(<). Let Ψj be a measure of treatment effectiveness of the jth treatment, where Ψj(>0), j=1,,k, is a function of μ1,,μk and σ1,,σk such that Ψj is decreasing in μj for fixed values of other μjs. Then in any case our objective is

Evaluating the performance: exact and asymptotic

With the notations introduced in the previous section, the observed allocation proportion to treatment j for an n subject trial is naturally Njnn, where Njn=i=1nδji,j=1,2,,k and we write Nn=(N1n,N2n,,Nkn)T. To evaluate the performance of the proposed procedures we exclusively use binary and normal response models. Then the derived allocation proportions, say, ρ(θ) and the response model satisfy the regularity conditions of Hu and Zhang (2004) and hence we have that as n,(a)Nnnρ(θ)

Erosive esophagitis trial: a binary response trial

A multicentre, randomized, double-blind, eight week comparative efficacy and safety study of H 199/18 20 mg(H20), H 199/18 40 mg(H40) and Omeprazole 20 mg(O20) for subjects with erosive esophagitis (see http://www.astrazenecaclinicaltrials.com/Article/511963.aspx). It was a phase III trial, conducted by AstraZeneca (1999) between September 1997 and May 1998. Primary objective was to assess the healing efficacy of H40 compared to O20 and H20 by week 8 for treatment of patients with erosive

Concluding remarks

The present paper provides a reasonable formulation to get multi-treatment optimal targets both for continuous and discrete responses. Actually, we have considered minimisation of a general objective function subject to a number of reasonable constraints based on the asymptotic variances of some relevant estimated elementary treatment contrasts.Some important issues like the presence of covariates in the design are not discussed. In fact, the level of complexity of the problem will increase

Acknowledgements

The authors wish to thank the Editor, the Associate Editor and the anonymous reviewers for helpful comments and suggestions which led to an improvement over an earlier version of the manuscript. The research of S. Mandal is supported by the Natural Sciences and Engineering Research Council (NSERC) of Canada.

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