Multi-treatment optimal response-adaptive designs for phase III 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 treatments indexed by with subjects assigned to the th treatment arm under a non-randomised set up. The variable, measuring the response of the th treatment, is indicated by , and we assume that and . Let be a measure of treatment effectiveness of the th treatment, where , , is a function of and such that is decreasing in for fixed values of other s. 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 for an subject trial is naturally , where and we write . To evaluate the performance of the proposed procedures we exclusively use binary and normal response models. Then the derived allocation proportions, say, and the response model satisfy the regularity conditions of Hu and Zhang (2004) and hence we have that as ,
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.
References (31)
- et al.
An adaptive allocation for continuous response using Wilcoxon–Mann–Whitney score
Journal of Statistical Planning and Inference
(2004) - et al.
Response adaptive designs for continuous outcomes
Journal of the Statistical Planning and Inference
(2006) - et al.
Implementing optimal allocation in sequential continuous response experiments
Journal of Statistical Planning and Inference
(2009) - et al.
Bayesian adaptive biased-coin designs for clinical trials with normal responses
Biometrics
(2005) - et al.
Adaptive designs for normal responses with prognostic factors
Biometrika
(2001) - et al.
Extracorporeal circulation in neonatal respiratory failure: a prospective randomized trial
Pediatrics
(1985) - et al.
Nonlinear programming: theory and algorithms
(1993) - et al.
Optimal response-adaptive designs for normal responses
Biometrical Journal
(2009) - et al.
Optimal response-adaptive designs for continuous responses in phase III trials
Biometrical Journal
(2007)