# A response adaptive design for ordinal categorical responses.

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### Cites background or methods from "A response adaptive design for ordi..."

...where p̂(0) is the ML estimate of the common value under H0 and p̂ (1) k is the ML estimate of pk under H0 ∪ H1, k = A, B (see [9] for detailed derivation)....

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...In a recent work [9], a two treatment RAR for ordinal responses is developed without assigning any set of scores to the ordinal categories....

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1 citations

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### "A response adaptive design for ordi..." refers methods in this paper

...Moreover, response of patients is often influenced by covariates and one can use proportional odds model of McCullagh (1980) for a similar development....

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1,317 citations

### Additional excerpts

...…Ps j¼1 pkj ¼ 1 for any k ¼ A;B; we get the parameter estimates under the null hypothesis as p̂ð0ÞAj ¼ p̂ð0ÞBj ¼ NAjðnÞ þ NBjðnÞ n ; j ¼ 1; 2; ; s: However, obtaining the estimates p̂k ð1Þ; k ¼ A;B is not straightforward and requires techniques of nonlinear optimization (Bazaraa et al., 1993)....

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470 citations

### "A response adaptive design for ordi..." refers background or methods in this paper

...To circumvent the problem, we propose an allocation function using the Goodman-Kruskal association measure (Goodman and Kruskal, 1954)....

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...Hu and Rosenberger (2003) investigated the issue for binary response trials and established under mild conditions that average loss in power is proportional to the variability of the design. Naturally, lower variability is desirable to control the loss in power. In a further work, Hu et al. (2006) developed the concept of asymptotically best target which attains the lower bound related to the variance of the observed allocation proportion and observed that drop-the-loser allocation (Ivanova, 2003) and efficient response adaptive design of Hu et al. (2009) are asymptotically best. However, for a brief account of the ongoing development, we refer the interested reader to the review by Sverdlov (2016). But, often the response in a clinical trial is categorical and is measured in ordinal scale. For example, in several bio-medical studies, the responses (e.g. pain and post-operative conditions) are measured in ordinal scale. But the literature of response adaptive designs with ordinal categorical responses is not rich enough and the number of available works till date is only two, namely, Categorical Randomized Play-the-Winner procedure by Bandyopadhyay and Biswas (2001) and Categorical Drop-the-loser procedure by Biswas et al. (2007). However both the designs use a representative numerical figure for each ordinal category....

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...However, for s > 2, development of a measure of treatment effectiveness is not straightforward and we start with one of the extensions of Δ, namely, Goodman-Kruskal gamma (Goodman and Kruskal, 1954)....

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...Hu and Rosenberger (2003) investigated the issue for binary response trials and established under mild conditions that average loss in power is proportional to the variability of the design....

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...Hu and Rosenberger (2003) investigated the issue for binary response trials and established under mild conditions that average loss in power is proportional to the variability of the design. Naturally, lower variability is desirable to control the loss in power. In a further work, Hu et al. (2006) developed the concept of asymptotically best target which attains the lower bound related to the variance of the observed allocation proportion and observed that drop-the-loser allocation (Ivanova, 2003) and efficient response adaptive design of Hu et al....

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397 citations

### "A response adaptive design for ordi..." refers background in this paper

...The above definition is consistent with the notion of simple stochastic ordering introduced by Lehmann (1955)....

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