A response-adaptive design in crossover trial
01 Oct 2012-Statistics (Taylor & Francis)-Vol. 46, Iss: 5, pp 645-661
TL;DR: In this article, an adaptive allocation rule for a two-treatment two-period crossover design in the presence of possible carryover effects was proposed, which is a combination of the play-the-winner and randomized playthewinner rules.
Abstract: In the present work, whenever the response variables are binary, we frame an adaptive allocation rule for a two-treatment two-period crossover design in the presence of possible carry-over effects. The proposed rule is a combination of the play-the-winner and randomized play-the-winner rules. We study various properties of the proposed rule through asymptotics and simulations. Some related inferential problems are also considered. The proposed procedure is compared with some possible competitor.
TL;DR: This work extends the allocation strategy developed for continuous responses to constructing response-adaptive repeated measurement designs for binary responses and finds that it can successfully allocate more patients to better treatment sequences without sacrificing much estimation precision.
Abstract: A multiple-objective allocation strategy was recently proposed for constructing response-adaptive repeated measurement designs for continuous responses. We extend the allocation strategy to constructing response-adaptive repeated measurement designs for binary responses. The approach with binary responses is quite different from the continuous case, as the information matrix is a function of responses, and it involves nonlinear modeling. To deal with these problems, we first build the design on the basis of success probabilities. Then we illustrate how various models can accommodate carryover effects on the basis of logits of response profiles as well as any correlation structure. Through computer simulations, we find that the allocation strategy developed for continuous responses also works well for binary responses. As expected, design efficiency in terms of mean squared error drops sharply, as more emphasis is placed on increasing treatment benefit than estimation precision. However, we find that it can successfully allocate more patients to better treatment sequences without sacrificing much estimation precision. Copyright © 2013 John Wiley & Sons, Ltd.
01 Jan 1970
TL;DR: Binary response variables special logistical analyses some complications some related approaches more complex responses.
Abstract: The first edition of this book (1970) set out a systematic basis for the analysis of binary data and in particular for the study of how the probability of 'success' depends on explanatory variables. The first edition has been widely used and the general level and style have been preserved in the second edition, which contains a substantial amount of new material. This amplifies matters dealt with only cryptically in the first edition and includes many more recent developments. In addition the whole material has been reorganized, in particular to put more emphasis on m.aximum likelihood methods.There are nearly 60 further results and exercises. The main points are illustrated by practical examples, many of them not in the first edition, and some general essential background material is set out in new Appendices.
01 Jun 1988
TL;DR: In this paper, a set of multinomial parameters are derived about distributions subject to shape restrictions, and a conditional expectation given a sigma-lattice is given in a more general setting.
Abstract: Isotonic Regression. Tests of Ordered Hypotheses: The Normal Means Case. Tests of Ordered Hypotheses: Generalizations of the Likelihood Ratio Tests and Other Procedures. Inferences about a Set of Multinomial Parameters. Duality. Inferences Regarding Distributions Subject to Shape Restrictions. Conditional Expectation Given a sigma-lattice: Projections in a More General Setting. Complements. Tables. Bibliography and Related References. Index. Symbols and Acronyms.
... for various ordered restricted testing problems....
01 Jan 1967
TL;DR: In this article, the authors present an elementary theory of rank tests and a set of properties of rank estimators, including asymptotic optimality and efficiency, as well as non-null distributions.
Abstract: Introduction and Coverage. Preliminaries. Elementary Theory of Rank Tests. Selected Rank Tests. Computation of Null Exact Distributions. Limiting Null Distributions. Limiting Non-Null Distributions. Asymptotic Optimality and Efficiency. Rank Estimates and Asymptotic Linearity.