Urn-Based Response Adaptive Procedures and Optimality
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Urn-Based Response Adaptive Procedures and Optimality
Rahul Bhattacharya Asutosh College, Kolkata, India
Key Words Urn model; Odds ratio; Optimality Correspondence Address Rahul Bhattacharya, Department of Statistics, Asutosh College, 92 S.P. Mukherjee Road, Kolkata 700 026, India (email: [email protected]).
In most of the two-treatment clinical trials, patients are randomized to either treatment in a balanced fashion, and at the end of the experiment a decision is made as to which treatment is more effective. But such a strategy of finding the effective treatment by assigning half of the subjects to the inferior treatment lacks ethical imperative. Urn-based allocation procedures are often used as better alternatives for their ability to use the accrued patient
INTRODUCTION Suppose patients enter a clinical trial sequentially and are to be randomized to one of the available treatments. Since any clinical trial involves human beings, there is an ethical imperative to provide any individual the best possible medical care, especially when the response is potentially fatal. Thus whenever the accrued data reveal the superiority of a treatment arm, the allocation should be meaningfully skewed so that a larger number of allocations to this treatment can be ensured. Allocation designs able to change the allocation strategy based upon the observed data are generally referred to as response-adaptive designs. Urn models have long been used as a valuable mathematical tool to skew the allocation to the treatment doing better by utilizing the information accrued thus far. Significant application of urn models in clinical trials with binary response starts with the play-the-winner (PW) rule of Zelen (1) subsequently modified by Wei and Durham (2) to provide a randomized version of PW, the randomized-play-the-winner (RPW). Some other urn-based allocation designs include the success-driven design of Durham et al. (3), birth-death urn-based designs of Ivanova et al. (4) and the drop-the-loser (DL) of Ivanova (5), among others. The latest addition in the list is the generalized drop-the-loser (GDL) of
outcomes to sensibly adjust the allocation of the future subjects. However, these designs leave the final goal (may be maximization of power or minimization of overall failures) unexplained to date. This unexplained ultimate goal or optimality of the useful urn designs is established considering odds ratio as the measure of effect. A comparative study of the performance based on both simulated and reallife data is provided.
Zhang et al. (6). These designs are also popular with practitioners of clinical trials and a few instances can be cited where the RPW rule has been used for a major clinical trial: the Michigan extracorporeal membrane oxygenation (ECMO) trial (7) and the trials of fluoxetine sponsored by Eli Lilly to treat outpatients with depressive disorders (8). But all these allocation strategies are developed with an aim to increase the allocation probability of a successful treatment. However, this cannot be co
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