Covariate-Adjusted Adaptive Designs for Continuous Responses in a Phase III Clinical Trial: Recommendation for Practice

ABSTRACT

One adaptive design is proposed and studied by Bandyopadhyay and Biswas (2001) for comparing two treatments having continuous responses with covariates at hand in a phase III clinical trial. On the other hand, a drop-the-loser urn design is recently proposed by Ivanova (2003), which is known to have the least variability among urn-based adaptive designs for binary responses. The drop-the-loser rule for continuous data was recently introduced by Ivanova et al. (2006). But neither of the works considered covariates for the allocation design. The present paper provides a version of the newly proposed adaptive design, drop-the-loser rule, but for continuous responses and by incorporating the covariate information in the allocation procedure. Several exact and limiting properties of the design, and also of a simpler version of it, are studied. We compare the design of Bandyopadhyay and Biswas (2001) with the covariate-adjusted drop-the-loser-type rule for continuous responses and conclude that, although the drop-the-loser rule is better for binary responses, the design of Bandyopadhyay and Biswas (2001) performs better than the drop-the-loser-type rule for continuous responses with covariates. We recommend the existing design of Bandyopadhyay and Biswas (2001) for practical purposes.

Keywords:

• Immigration ball
• Limiting proportion of allocation
• Probit link
• Proportion of allocation
• Randomisation
• Response-driven adaptive design
• Treatment difference
• Urn model

ACKNOWLEDGMENTS

The authors wish to thank two anonymous referees for their constructive suggestions, which led to some improvement of the paper. The work was carried out when the first author was visiting the Department of Management Sciences and Decision Making, Tamkang University, Tamsui, Taiwan. The first author thanks the department for excellent hospitality during the visit.

Notes

Designs in the above tables: (a) CCDL (σ_Φ = 1,c = 0), (b) CCDL (σ_Φ = 1,c = (μ _A  + μ _B )/2), (c) CCDL (σ_Φ = 10,c = 0), (d) Randomized 50:50, (e) BB (σ_Φ = 1), (f) BB (σ_Φ = 3), (g) BB (σ_Φ = 10).

Designs in the above tables: (a) CCDL (σ_Φ = 1,c = 0), (b) CCDL (σ_Φ = 1,c = (μ _A  + μ _B )/2), (c) CCDL (σ_Φ = 10,c = 0), (d) Randomized 50:50, (e) BB (σ_Φ = 1), (f) BB (σ_Φ = 3), (g) BB (σ_Φ = 10).

Designs in the above tables: (a) CCDL (σ_Φ = 1,c = 0), (b) CCDL (σ_Φ = 1,c = (μ _A  + μ _B )/2), (c) CCDL (σ_Φ = 10,c = 0), (d) Randomized 50:50, (e) BB (σ_Φ = 1), (f) BB (σ_Φ = 3), (g) BB (σ_Φ = 10).