Optimal Response‐Adaptive Designs for Normal Responses

Abstract

Most of the available response-adaptive designs in phase III clinical trial set up are not from any optimal consideration. An optimal design for binary responses is given by Rosenberger et al. (2001) and an optimal design for continuous responses is provided by Biswas and Mandal (2004). Recently, Zhang and Rosenberger (2006) [ZR] provided another design for normal responses. Biswas, Bhattacharya and Zhang (2007) pointed out that the design of ZR is not suitable for normally distributed responses, or any distribution having the possibility of negative mean, in general. But they only indicated the problem and bypassed the original problem and set up. In the present paper, we first start with the drawback of ZR. We then provide the appropriate optimal response-adaptive design for normal or continuous distributions which provides the necessary correction for the ZR problem. The proposed methods are illustrated using some real data.

A response‐adaptive randomization procedure for multi‐armed clinical trials with normally distributed outcomes

“…Next, we will report simulations that compare the FLGI for a normally distributed endpoint against the following existing randomization procedures: Equal Randomization (ER) , where each patient is randomly allocated to one of the arms with equal probability, . ER is predominant in practice (implemented, eg, by a permuted‐block randomization), thus it will be used as a reference to compare all designs. Modified Zhang and Rosenberger (MZR) , introduced by Zhang and Rosenberger () and later modified by Biswas and Bhattacharya () to allow for negative mean responses. The rule aims at minimizing the total of inverse mean responses, that is, .…”

“…Modified Zhang and Rosenberger (MZR) , introduced by Zhang and Rosenberger () and later modified by Biswas and Bhattacharya () to allow for negative mean responses. The rule aims at minimizing the total of inverse mean responses, that is, .…”

Multi-treatment optimal response-adaptive designs for phase III clinical trials

“…Biswas, Bhattacharya, and Zhang (2007) [BBZ] pointed out this drawback of ZR rule and suggested considering truncated normal responses, truncated in some subset of the positive part of the real line, in order to avoid negative responses in a normal set up. Moreover, the proportion π 1,ZR no longer remains optimal for the problem when at least one of µ i becomes negative and hence for the actual optimal solution we refer to Biswas and Bhattacharya (2009). Note that any of the optimal targets discussed so far, can be identified as a solution to the general optimisation problem: min n 1 /n 2…”

A new response-adaptive design for continuous treatment responses for phase III clinical trials

“…Thus a reasonable adaptive allocation design should take into account both the locations and variabilities of the response distributions. Allocation designs taking into account both means and variances of the continuous response distributions can be found in recently developed optimal response-adaptive designs of Biswas and Mandal (2004), Zhang and Rosenberger (2006), Biswas et al (2007) and Biswas and Bhattacharya (2009). Such allocations are observed, on an average, to combine the views of both clinician and statistician, but requires existence of variances of the response distributions.…”