Bayesian crossover designs for generalized linear models

Singh, Satya Prakash; Mukhopadhyay, Susanta

doi:10.1016/j.csda.2016.06.002

Cited by 13 publications

(4 citation statements)

References 43 publications

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“…where W j = Cov(Y j ). As mentioned by Singh and Mukhopadhyay (2016) in the paper (Zeger et al, 1988, equation (3.2)) it has also been shown that if the true correlation structure varies from "working correlation" structure, then Var(θ) is given by the sandwich formula…”

Section: Generalized Estimating Equationsmentioning

confidence: 96%

Optimal Crossover Designs for Generalized Linear Models

Jankar

Mandal

Yang

2020

J Stat Theory Pract

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We identify locally D-optimal crossover designs for generalized linear models. We use generalized estimating equations to estimate the model parameters along with their variances. To capture the dependency among the observations coming from the same subject, we propose six different correlation structures. We identify the optimal allocations of units for different sequences of treatments. For two-treatment crossover designs, we show via simulations that the optimal allocations are reasonably robust to different choices of the correlation structures. We discuss a real example of multiple treatment crossover experiments using Latin square designs. Using a simulation study, we show that a two-stage design with our locally D-optimal design at the second stage is more efficient than the uniform design, especially when the responses from the same subject are correlated.for crossover experiments with responses under univariate GLMs, including binary, binomial, Poisson, Gamma, Inverse Gaussian responses, etc.Among different types of experiments that are available for treatment comparisons with multiple periods, the crossover designs are among the most important ones. In these experiments, every subject is exposed to a sequence of treatments over different time periods, i.e., subjects crossover from one treatment to another. One of the most important aspects of crossover designs is that we can get the same number of observations as other designs but with less number of subjects. This is an important consideration since human participants are often scarce in clinical trials. The order in which treatments are applied to subjects is known as a sequence and the time at which these sequences are applied is known as a period. In most of the cases, the main aim of such experiments is to compare t treatments over p periods. In each period, each subject receives a treatment, and the corresponding response is recorded. In different periods, a subject may receive different treatments, but treatment may also be repeated on the same subject. Naturally, crossover designs also provide within-subject information about treatment differences.Most of the research in the crossover design literature dealt with continuous response variables (see, for example, Kershner and Federer (1981), Laska and Meisner (1985), Matthews (1987), Carriere and Huang (2000), and the references therein). The problem of determining optimal crossover designs for continuous responses has been studied extensively (see, for example, Bose and Dey (2009), for a review of results). For examples of practical cases where the responses are discrete in nature, such as binary responses, one may refer to Jones and Kenward (2014) and Senn (2003). Among many fixed effects models proposed in the literature, the following linear model is used extensively to formulate crossover designs.where Y ij is the observation from the jth subject in the ith time period, with i = 1, . . . , p and j = 1, . . . , n. Here d(i, j) stands for the treatment assignment to the jth subject at time peri...

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Section: Generalized Estimating Equationsmentioning

confidence: 96%

Optimal Crossover Designs for Generalized Linear Models

Jankar

Mandal

Yang

2020

J Stat Theory Pract

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“…A pseudo‐Bayesian approach was adopted by Woods and Van de Ven (2011) in the context of block designs for nonnormal responses, Singh and Mukhopadhyay (2016a) for cluster designs, Singh and Mukhopadhyay (2016b) for crossover designs, Singh and Davidov (2020) for multiple comparison problems, and Singh et al. (2021) for binary cluster designs.…”

Section: Bayesian Designmentioning

confidence: 99%

Bayesian optimal stepped wedge design

Singh

2023

Biometrical J

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Recently, there has been a growing interest in designing cluster trials using stepped wedge design (SWD). An SWD is a type of cluster–crossover design in which clusters of individuals are randomized unidirectional from a control to an intervention at certain time points. The intraclass correlation coefficient (ICC) that measures the dependency of subject within a cluster plays an important role in design and analysis of stepped wedge trials. In this paper, we discuss a Bayesian approach to address the dependency of SWD on the ICC and robust Bayesian SWDs are proposed. Bayesian design is shown to be more robust against the misspecification of the parameter values compared to the locally optimal design. Designs are obtained for the various choices of priors assigned to the ICC. A detailed sensitivity analysis is performed to assess the robustness of proposed optimal designs. The power superiority of Bayesian design against the commonly used balanced design is demonstrated numerically using hypothetical as well as real scenarios.

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“…Then for the misspecified models, we regard the estimators as the single prior to select locally general optimal design

d_{o, m i s_{j}}^{L}

, or construct the prior space based on the estimators and select the Bayesian general optimal design

d_{o, m i s_{j}}^{B}, j =

4, …, 11. After obtaining these designs, similar to Singh and Mukhopadhyay (2016), we compare the

R E

s of them relative to

d_{o}^{L}

under

{\hat{boldα}}_{o}

which is selected without misspecification. The results are shown in Table 3.…”

Section: Data Illustration: Cattle Datamentioning

confidence: 99%

D‐optimal designs of mean‐covariance models for longitudinal data

Zhou

Pan

2021

Biometrical J

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Longitudinal data analysis has been very common in various fields. It is important in longitudinal studies to choose appropriate numbers of subjects and repeated measurements and allocation of time points as well. Therefore, existing studies proposed many criteria to select the optimal designs. However, most of them focused on the precision of the mean estimation based on some specific models and certain structures of the covariance matrix. In this paper, we focus on both the mean and the marginal covariance matrix. Based on the mean–covariance models, it is shown that the trick of symmetrization can generate better designs under a Bayesian D‐optimality criterion over a given prior parameter space. Then, we propose a novel criterion to select the optimal designs. The goal of the proposed criterion is to make the estimates of both the mean vector and the covariance matrix more accurate, and the total cost is as low as possible. Further, we develop an algorithm to solve the corresponding optimization problem. Based on the algorithm, the criterion is illustrated by an application to a real dataset and some simulation studies. We show the superiority of the symmetric optimal design and the symmetrized optimal design in terms of the relative efficiency and parameter estimation. Moreover, we also demonstrate that the proposed criterion is more effective than the previous criteria, and it is suitable for both maximum likelihood estimation and restricted maximum likelihood estimation procedures.

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Bayesian crossover designs for generalized linear models

Cited by 13 publications

References 43 publications

Optimal Crossover Designs for Generalized Linear Models

Optimal Crossover Designs for Generalized Linear Models

Bayesian optimal stepped wedge design

D‐optimal designs of mean‐covariance models for longitudinal data

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