On Multi-Treatment Adaptive Allocation Design for Dichotomous Response

Abstract

The use of ridit, as a probability score, is a very common practice to compare discrete random variables in discrete data analysis. In the present work we formulate ridit reliability functionals for some comparison of K independent binary random variables. We use such functionals to provide a generalized response-adaptive design (GRAD) on K(≥ +2) treatment-arms for dichotomous response variables. We exhibit some properties of the proposed design and compare it with some of the existing competitors by computing its various performance measures. We also provide a discussion towards a possible modification of the GRAD in the presence of covariates.

Keywords:

• Adaptive
• Covariate
• Ethical
• Ridit

Mathematics Subject Classification:

• Primary 62L05
• Secondary 62F35

Acknowledgment

The authors wish to thank the Editor, the Associate, and the anonymous referee for their valuable suggestions and comments which led to an improvement in this article. We also thank Professor Dipak Shankar Chakraborty, Department of English, R. K. Mission College at Narendrapur, Kolkata for his careful reading of the manuscript.

Notes

Note. Four-tupple in each cell provides the powers of proposed rule, competitor I, competitor II, and the DL rule, respectively.

Note. In each cell the first entry provides the limiting value of the allocation proportion to treatment A and the second one provides the limiting value of the overall failure proportion.