A response adaptive design for ordinal categorical responses.

doi:10.1080/10543406.2018.1439053

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A response adaptive design for ordinal categorical responses.

Journal Article•DOI•

A response adaptive design for ordinal categorical responses.

Atanu Biswas¹, Rahul Bhattacharya², Soumyadeep Das²•Institutions (2)

Indian Statistical Institute¹, University of Calcutta²

05 Mar 2018-Journal of Biopharmaceutical Statistics (Taylor & Francis)-Vol. 28, Iss: 6, pp 1169-1181

TL;DR: A two treatment response adaptive design is developed for phase III clinical trials with ordinal categorical treatment outcome using Goodman-Kruskal measure of association.

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Abstract: A two treatment response adaptive design is developed for phase III clinical trials with ordinal categorical treatment outcome using Goodman-Kruskal measure of association. Properties of the proposed design are studied both empirically and theoretically and the acceptability is further illustrated using two real data-sets; one from a clinical trial with trauma patients and the other from a trial with patients having rheumatoid arthritis.

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Journal Article•DOI•

A multi-treatment response adaptive design for ordinal categorical responses.

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Atanu Biswas¹, Rahul Bhattacharya², Soumyadeep Das³•Institutions (3)

Indian Statistical Institute¹, University of Calcutta², Government College³

01 Mar 2020-Statistical Methods in Medical Research

TL;DR: For practical implementation, the proposed response-adaptive randomization (RAR) is suggested, that is, update the allocation probabilities dynamically using the available allocation and response information to favor the treatment doing better.

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Abstract: A multi-treatment response adaptive procedure is developed considering “comparison with the best” philosophy of multiple comparison procedures for clinical trials with ordinal categorical responses...

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3 citations

Journal Article•DOI•

A response adaptive design for ordinal categorical responses weighing the cumulative odds ratios

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Atanu Biswas¹, Rahul Bhattacharya², Soumyadeep Das³•Institutions (3)

Indian Statistical Institute¹, University of Calcutta², Government College³

03 Sep 2019

TL;DR: In this paper, a two treatment response adaptive design for phase III clinical trial is proposed for ordinal categorical responses, which weighs the cumulative odds ratios suitably, and proposes a two-treatment response adaptive scheme.

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Abstract: Weighing the cumulative odds ratios suitably, a two treatment response adaptive design for phase III clinical trial is proposed for ordinal categorical responses. Properties of the proposed...

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2 citations

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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Journal Article•DOI•

An optimal response adaptive design for multi-treatment clinical trials with ordinal categorical outcomes.

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Soumyadeep Das¹, Rahul Bhattacharya², Atanu Biswas³•Institutions (3)

Government College¹, University of Calcutta², Indian Statistical Institute³

31 Aug 2021-Journal of Biopharmaceutical Statistics

TL;DR: In clinical trials, fixed randomizations in a prefixed proportion (e.g. 1:1 or 2:1 for two treatment trials) may be adopted to allocate the entering patients among the competing treatments as mentioned in this paper.

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Abstract: In clinical trials, fixed randomizations in a prefixed proportion (e.g. 1:1 or 2:1 for two treatment trials) may be adopted to allocate the entering patients among the competing treatments. However...

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1 citations

Journal Article•DOI•

Multi-arm covariate adjusted response adaptive designs for ordinal outcome clinical trials

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Soumyadeep Das, Rahul Bhattacharya, Atanu Biswas

20 Oct 2022-Statistical Methods in Medical Research

TL;DR: Covariate adjusted response adaptive designs with ordinal categorical responses for phase III clinical trial involving multiple treatments are developed in this paper , where stochastic ordering principle is used to order the treatments according to effectiveness and consequently allocation functions are developed by combining the cumulative odds ratios suitably.

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Abstract: Covariate adjusted response adaptive designs are developed with ordinal categorical responses for phase III clinical trial involving multiple treatments. Stochastic ordering principle is used to order the treatments according to effectiveness and consequently allocation functions are developed by combining the cumulative odds ratios suitably. The performance of the proposed designs is investigated through relevant exact as well as large sample measures. To investigate the performance in a real situation, a real clinical trial involving lung cancer patients is further redesigned using the proposed allocation design.

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References

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Monograph•DOI•

Categorical data analysis

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Alan Agresti

01 May 1993-Contemporary Sociology

TL;DR: In this article, the authors present a generalized linear model for categorical data, which is based on the Logit model, and use it to fit Logistic Regression models.

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Abstract: Preface. 1. Introduction: Distributions and Inference for Categorical Data. 1.1 Categorical Response Data. 1.2 Distributions for Categorical Data. 1.3 Statistical Inference for Categorical Data. 1.4 Statistical Inference for Binomial Parameters. 1.5 Statistical Inference for Multinomial Parameters. Notes. Problems. 2. Describing Contingency Tables. 2.1 Probability Structure for Contingency Tables. 2.2 Comparing Two Proportions. 2.3 Partial Association in Stratified 2 x 2 Tables. 2.4 Extensions for I x J Tables. Notes. Problems. 3. Inference for Contingency Tables. 3.1 Confidence Intervals for Association Parameters. 3.2 Testing Independence in Two Way Contingency Tables. 3.3 Following Up Chi Squared Tests. 3.4 Two Way Tables with Ordered Classifications. 3.5 Small Sample Tests of Independence. 3.6 Small Sample Confidence Intervals for 2 x 2 Tables . 3.7 Extensions for Multiway Tables and Nontabulated Responses. Notes. Problems. 4. Introduction to Generalized Linear Models. 4.1 Generalized Linear Model. 4.2 Generalized Linear Models for Binary Data. 4.3 Generalized Linear Models for Counts. 4.4 Moments and Likelihood for Generalized Linear Models . 4.5 Inference for Generalized Linear Models. 4.6 Fitting Generalized Linear Models. 4.7 Quasi likelihood and Generalized Linear Models . 4.8 Generalized Additive Models . Notes. Problems. 5. Logistic Regression. 5.1 Interpreting Parameters in Logistic Regression. 5.2 Inference for Logistic Regression. 5.3 Logit Models with Categorical Predictors. 5.4 Multiple Logistic Regression. 5.5 Fitting Logistic Regression Models. Notes. Problems. 6. Building and Applying Logistic Regression Models. 6.1 Strategies in Model Selection. 6.2 Logistic Regression Diagnostics. 6.3 Inference About Conditional Associations in 2 x 2 x K Tables. 6.4 Using Models to Improve Inferential Power. 6.5 Sample Size and Power Considerations . 6.6 Probit and Complementary Log Log Models . 6.7 Conditional Logistic Regression and Exact Distributions . Notes. Problems. 7. Logit Models for Multinomial Responses. 7.1 Nominal Responses: Baseline Category Logit Models. 7.2 Ordinal Responses: Cumulative Logit Models. 7.3 Ordinal Responses: Cumulative Link Models. 7.4 Alternative Models for Ordinal Responses . 7.5 Testing Conditional Independence in I x J x K Tables . 7.6 Discrete Choice Multinomial Logit Models . Notes. Problems. 8. Loglinear Models for Contingency Tables. 8.1 Loglinear Models for Two Way Tables. 8.2 Loglinear Models for Independence and Interaction in Three Way Tables. 8.3 Inference for Loglinear Models. 8.4 Loglinear Models for Higher Dimensions. 8.5 The Loglinear Logit Model Connection. 8.6 Loglinear Model Fitting: Likelihood Equations and Asymptotic Distributions . 8.7 Loglinear Model Fitting: Iterative Methods and their Application . Notes. Problems. 9. Building and Extending Loglinear/Logit Models. 9.1 Association Graphs and Collapsibility. 9.2 Model Selection and Comparison. 9.3 Diagnostics for Checking Models. 9.4 Modeling Ordinal Associations. 9.5 Association Models . 9.6 Association Models, Correlation Models, and Correspondence Analysis . 9.7 Poisson Regression for Rates. 9.8 Empty Cells and Sparseness in Modeling Contingency Tables. Notes. Problems. 10. Models for Matched Pairs. 10.1 Comparing Dependent Proportions. 10.2 Conditional Logistic Regression for Binary Matched Pairs. 10.3 Marginal Models for Square Contingency Tables. 10.4 Symmetry, Quasi symmetry, and Quasiindependence. 10.5 Measuring Agreement Between Observers. 10.6 Bradley Terry Model for Paired Preferences. 10.7 Marginal Models and Quasi symmetry Models for Matched Sets . Notes. Problems. 11. Analyzing Repeated Categorical Response Data. 11.1 Comparing Marginal Distributions: Multiple Responses. 11.2 Marginal Modeling: Maximum Likelihood Approach. 11.3 Marginal Modeling: Generalized Estimating Equations Approach. 11.4 Quasi likelihood and Its GEE Multivariate Extension: Details . 11.5 Markov Chains: Transitional Modeling. Notes. Problems. 12. Random Effects: Generalized Linear Mixed Models for Categorical Responses. 12.1 Random Effects Modeling of Clustered Categorical Data. 12.2 Binary Responses: Logistic Normal Model. 12.3 Examples of Random Effects Models for Binary Data. 12.4 Random Effects Models for Multinomial Data. 12.5 Multivariate Random Effects Models for Binary Data. 12.6 GLMM Fitting, Inference, and Prediction. Notes. Problems. 13. Other Mixture Models for Categorical Data . 13.1 Latent Class Models. 13.2 Nonparametric Random Effects Models. 13.3 Beta Binomial Models. 13.4 Negative Binomial Regression. 13.5 Poisson Regression with Random Effects. Notes. Problems. 14. Asymptotic Theory for Parametric Models. 14.1 Delta Method. 14.2 Asymptotic Distributions of Estimators of Model Parameters and Cell Probabilities. 14.3 Asymptotic Distributions of Residuals and Goodnessof Fit Statistics. 14.4 Asymptotic Distributions for Logit/Loglinear Models. Notes. Problems. 15. Alternative Estimation Theory for Parametric Models. 15.1 Weighted Least Squares for Categorical Data. 15.2 Bayesian Inference for Categorical Data. 15.3 Other Methods of Estimation. Notes. Problems. 16. Historical Tour of Categorical Data Analysis . 16.1 Pearson Yule Association Controversy. 16.2 R. A. Fisher s Contributions. 16.3 Logistic Regression. 16.4 Multiway Contingency Tables and Loglinear Models. 16.5 Recent and Future? Developments. Appendix A. Using Computer Software to Analyze Categorical Data. A.1 Software for Categorical Data Analysis. A.2 Examples of SAS Code by Chapter. Appendix B. Chi Squared Distribution Values. References. Examples Index. Author Index. Subject Index. Sections marked with an asterisk are less important for an overview.

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4,650 citations

Journal Article•DOI•

Regression Models for Ordinal Data

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Peter McCullagh¹•Institutions (1)

University of Chicago¹

01 Jan 1980-Journal of the royal statistical society series b-methodological

TL;DR: In this article, a general class of regression models for ordinal data is developed and discussed, which utilize the ordinal nature of the data by describing various modes of stochastic ordering and this eliminates the need for assigning scores or otherwise assuming cardinality instead of ordinality.

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Abstract: SUMMARY A general class of regression models for ordinal data is developed and discussed. These models utilize the ordinal nature of the data by describing various modes of stochastic ordering and this eliminates the need for assigning scores or otherwise assuming cardinality instead of ordinality. Two models in particular, the proportional odds and the proportional hazards models are likely to be most useful in practice because of the simplicity of their interpretation. These linear models are shown to be multivariate extensions of generalized linear models. Extensions to non-linear models are discussed and it is shown that even here the method of iteratively reweighted least squares converges to the maximum likelihood estimate, a property which greatly simplifies the necessary computation. Applications are discussed with the aid of examples.

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3,647 citations

"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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Journal Article•DOI•

Nonlinear Programming Theory and Algorithms

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Katta G Murty

01 Feb 2007-Technometrics

TL;DR: Taylor and Francis shall not be liable for any losses, actions, claims, proceedings, demands, costs, expenses, damages, and other liabilities whatsoever or howsoever caused arising directly or indirectly in connection with, in relation to or arising out of the use of the Content.

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Abstract: (2007). Nonlinear Programming Theory and Algorithms. Technometrics: Vol. 49, No. 1, pp. 105-105.

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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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Book Chapter•DOI•

Measures of Association for Cross Classifications III: Approximate Sampling Theory

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Leo A. Goodman¹, William Kruskal¹•Institutions (1)

University of Chicago¹

01 Jun 1963-Journal of the American Statistical Association

TL;DR: In this paper, the authors derived large sample normal distributions with their associated standard errors for various measures of association and various methods of sampling and explained how the large sample normality may be used to test hypotheses about the measures and about differences between them, and to construct corresponding confidence intervals.

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Abstract: The population measures of association for cross classifications, discussed in the authors' prior publications, have sample analogues that are approximately normally distributed for large samples. (Some qualifications and restrictions are necessary.) These large sample normal distributions with their associated standard errors, are derived for various measures of association and various methods of sampling. It is explained how the large sample normality may be used to test hypotheses about the measures and about differences between them, and to construct corresponding confidence intervals. Numerical results are given about the adequacy of the large sample normal approximations. In order to facilitate extension of the large sample results to other measures of association, and to other modes of sampling, than those treated here, the basic manipulative tools of large sample theory are explained and illustrated.

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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....
[...]
...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....
[...]

Book Chapter•DOI•

Ordered Families of Distributions

[...]

Erich L. Lehmann¹•Institutions (1)

University of California¹

01 Sep 1955-Annals of Mathematical Statistics

TL;DR: In this article, a comparison is made of several definitions of ordered sets of distributions, some of which were introduced earlier by the author [7], [8] and by Rubin [10], and the results are applied to obtaining tests that give a certain guaranteed power with a minimum number of observations.

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Abstract: A comparison is made of several definitions of ordered sets of distributions, some of which were introduced earlier by the author [7], [8] and by Rubin [10]. These definitions attempt to make precise the intuitive notion that large values of the parameter which labels the distributions go together with large values of the random variables themselves. Of the various definitions discussed the combination of two, (B) and (C) of Section 2, appears to be statistically most meaningful. In Section 3 it is shown that this ordering implies monotonicity for the power function of sequential probability ratio tests. In Section 4 the results are applied to obtaining tests that give a certain guaranteed power with a minimum number of observations. Finally, in Section 5, certain consequences are derived regarding the comparability of experiments in the sense of Blackwell [1].

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397 citations