A General Multi-Treatment Adaptive Design for Multivariate Responses

ABSTRACT

A general adaptive allocation design is proposed for continuous multivariate responses where the covariance matrix of the response vectors is unknown. There are K > 2 competing treatments, possible prognostic factors are considered in the allocation procedure, potential delayed responses are allowed for, and treatment-covariate interactions are incorporated. The allocation rule for any incoming patient is dependent on all the allocation-and-response-and-prognostic factor history of the previously allocated patients as well as the prognostic factor vector of the current patient. The design is a generalization of the approach suggested by Bandyopadhyay and Biswas (2001), which was presented for a much simpler scenario. The performance characteristics of the proposed design and some follow-up inference procedures are studied analytically and also numerically illustrated. An extension of the present approach to the situation where some components of the response vectors are continuous and some binary is then considered. Some further extensions of the work are briefly indicated.

Recommended by Nitis Mukhopadhyay

Key Words:

• Allocation proportion
• Delayed response
• Mixed responses
• Multivariate normal distribution
• Probit link
• Prognostic factor
• Unknown variability

Subject Classifications:

• 62L05
• 62H12
• 62H15

ACKNOWLEDGMENTS

This work was carried out while the first author was visiting the School of Mathematical Sciences, University of Sussex, during April and May 2002, and in receipt of Visiting Fellowship Research Grant GR/R92455 from the U.K. Engineering and Physical Sciences Research Council. The first author wishes to thank the School of Mathematical Sciences for its hospitality during his visit. The authors also wish to thank the three referees for their detailed comments, which have led to a much improved paper.

Notes

Recommended by Nitis Mukhopadhyay