Serial correlation in the design and analysis of crossover trials

Bayesian crossover designs for generalized linear models

This article discusses D-optimal Bayesian crossover designs for generalized linear models. Crossover trials with t treatments and p periods, for $t <= p$, are considered. The designs proposed in this paper minimize the log determinant of the variance of the estimated treatment effects over all possible allocation of the n subjects to the treatment sequences. It is assumed that the p observations from each subject are mutually correlated while the observations from different subjects are uncorrelated. Since main interest is in estimating the treatment effects, the subject effect is assumed to be nuisance, and generalized estimating equations are used to estimate the marginal means. To address the issue of parameter dependence a Bayesian approach is employed. Prior distributions are assumed on the model parameters which are then incorporated into the D-optimal design criterion by integrating it over the prior distribution. Three case studies, one with binary outcomes in a 4$\times$4 crossover trial, second one based on count data for a 2$\times$2 trial and a third one with Gamma responses in a 3$times$2 crossover trial are used to illustrate the proposed method. The effect of the choice of prior distributions on the designs is also studied.

Bayesian Crossover Designs for Generalized Linear Models

In the clinical trial randomized play-the-winner rule is used with a goal to allocate more patients to the better treatment in course of sampling. Here we provide an application of this sampling scheme in repeated measurement design. We concentrate on the simplest set up, i.e., on two treatments and two periods. We study, both numerically and theoretically, several exact and limiting properties of this design. We consider some related inferential problems. Finally we use a real data set to illustrate the applicability of our proposed design.

http://www.stat.tugraz.at/AJS/ausg093/093Bandyopadhyay.pdf

Randomized Play-the-Winner Rule in Two-Period Two-Treatment Repeated Measurement Design

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.

Multiple-objective response-adaptive repeated measurement designs in clinical trials for binary responses

Adaptive designs are sometimes used in a phase III clinical trial with the goal of allocating a larger number of patients to the better treatment. In the present paper we use some adaptive designs in a two-treatment two-period crossover trial in the presence of possible carry-over effects, where the treatment responses are binary. We use some simple designs to choose between the possible treatment combinations AA, AB, BA or BB. The goal is to use the better treatment a larger proportion of times. We calculate the allocation proportions to the possible treatment combinations and their standard deviations. We also investigate related inferential problems, for which related asymptotics are derived. The proposed procedure is compared with a possible competitor. Finally we use real data sets to illustrate the applicability of our proposed design.

Adaptive two-treatment two-period crossover design for binary treatment responses incorporating carry-over effects

Adaptive designs are sometimes used in a phase III clinical trial with the aim, of allocating a larger number of patients to the better treatment. In the present paper, we use some adaptive designs in a two-treatment two-period crossover design where the treatment responses are binary. We use some simple designs to choose between the possible treatment combinations AA, AB, BA or BB. The goal is to use the better treatment a larger proportion of times. We calculate the allocation proportions to the possible treatment combinations and their standard deviations. We also study related inferential problems. Related asymptotics are derived. The proposed procedure is compared with some possible competitors. Finally, we use real data to illustrate the applicability of our proposed design.

Adaptive two‐treatment two‐period crossover design for binary treatment responses

In the present study, we are concerned with the problem of testing the equivalence of two.treatments by using inverse sampling designs in matching pairs of experimental units. We find that the proposed tests, as in a matched pairs design based on fixed sample size, satisfy some desirable properties. We also examine various performance characteristics of the tests. Further, we compare one of the proposed tests with the corresponding test that donot retain match.

Comparison of Two Treatments in Matching Pairs Inverse Sampling Design

In the present work , we frame an adaptive allocation rule in matching pairs of experimental units. The proposed rule is a bivariate version of the randomized play the winner (RPvV) rule. We study various properties of the rule through asymptotics and simulations. Related inferential problem is also considered.

http://csa.sagepub.com/content/57/3-4/161.full.pdf

Shirsendu Mukherjee

Papers

Adaptive two-treatment two-period crossover design for binary treatment responses incorporating carry-over effects

Adaptive two‐treatment two‐period crossover design for binary treatment responses

Comparison of Two Treatments in Matching Pairs Inverse Sampling Design

Adaptive Allocation Design for Matching Pairs