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Stefania Gubbiotti - One of the best experts on this subject based on the ideXlab platform.
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Bayesian sample Size Determination and re-estimation using mixtures of prior distributions
2020Co-Authors: Pierpaolo Brutti, Stefania Gubbiotti, Fulvio De SantisAbstract:In this paper we propose a predictive Bayesian approach to sample Size Determination and reestimation in clinical trials, in the presence of multiple sources of prior information. The method we suggest is based on the use of mixtures of prior distributions for the unknown quantity of interest, typically an unknown effect or an unknown effects-difference. Methodologies are developed using normal models with mixtures of conjugate priors. In particular we extend the sample Size Determination analysis of [1] and the sample Size re-estimation technique of [2].
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A decision‐theoretic approach to sample Size Determination under several priors
Applied Stochastic Models in Business and Industry, 2016Co-Authors: Fulvio De Santis, Stefania GubbiottiAbstract:In this article, we consider sample Size Determination for experiments in which estimation and design are performed by multiple parties. This problem has relevant applications in contexts involving adversarial decision makers, such as control theory, marketing, and drug testing. Specifically, we adopt a decision-theoretic perspective, and we assume that a decision on an unknown parameter of a statistical model involves two actors, Ee and Eo, who share the same data and loss function but not the same prior beliefs on the parameter. We also suppose that Ee has to use Eo's optimal action, and we finally assume that the experiment is planned by a third party, Pd. In this framework, we aim at determining an appropriate sample Size so that the posterior expected loss incurred by Ee in taking the optimal action of Eo is sufficiently small. We develop general results for the one-parameter exponential family under quadratic loss and analyze the interactive impact of the prior beliefs of the three different parties on the resulting sample Sizes. Relationships with other sample Size Determination criteria are explored. Copyright © 2016 John Wiley & Sons, Ltd.
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robust bayesian sample Size Determination in clinical trials
Statistics in Medicine, 2008Co-Authors: Pierpaolo Brutti, Fulvio De Santis, Stefania GubbiottiAbstract:This article deals with Determination of a sample Size that guarantees the success of a trial. We follow a Bayesian approach and we say an experiment is successful if it yields a large posterior probability that an unknown parameter of interest (an unknown treatment effect or an effects-difference) is greater than a chosen threshold. In this context, a straightforward sample Size criterion is to select the minimal number of observations so that the predictive probability of a successful trial is sufficiently large. In the paper we address the most typical criticism to Bayesian methods—their sensitivity to prior assumptions—by proposing a robust version of this sample Size criterion. Specifically, instead of a single distribution, we consider a class of plausible priors for the parameter of interest. Robust sample Sizes are then selected by looking at the predictive distribution of the lower bound of the posterior probability that the unknown parameter is greater than a chosen threshold. For their flexibility and mathematical tractability, we consider classes of e-contamination priors. As specific applications we consider sample Size Determination for a Phase III trial. Copyright © 2008 John Wiley & Sons, Ltd.
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Robust Bayesian sample Size Determination for Bernoulli trials
2007Co-Authors: Fulvio De Santis, Stefania GubbiottiAbstract:In a Bayesian framework a robust approach is proposed for sample Size Determination (SSD) in a Bernoulli trial. The intent is to evaluate the impact of prior information, to define robust methods for choosing the sample Size and to guarantee stable inferential conclusions. In this work we focus on the probability of success of a given treatment. First, the standard Bayesian method is presented. Historical information or experts’ beliefs are taken into account and formalized by an analysis prior distribution. Here we choose a Beta distribution, so that the derived posterior still belongs to the same family. A posterior quantity of interest is considered, such as the posterior expected value of the probability of success. Since, before performing the experiment, the expectation is random we need to define a predictive criterion for determining the optimal sample Size. In this case the criterion is based on the predictive expected value, which is calculated with respect to the marginal distribution of the data. In order to avoid the sensitivity of the standard method to the prior specification, it is possible to introduce a robust approach, considering a class of priors instead of a single prior. Therefore, the focus is on the bounds of the posterior quantity of interest. Here, we choose the epsilon-contamination class, that guarantees both computational advantages and a straightforward interpretation. Two graphical tools are proposed to compare the standard SSD method with the robust one. The first consists in plotting the robust criterion with respect to the different levels of contamination, in correspondence to the standard optimal sample Size. Alternatevely, both standard and robust criteria can be represented for increasing values of n, for a fixed level of contamination. An example is provided to show how the proposed robust approach brings to a more cautious choice, namely requires more individuals to be enrolled in the trial. The proposed approach may help the experimenter showing that standard methods are not always trustworthy and they should be used with caution. Sometimes if prior information and uncertainty on the parameter of interest are not properly accounted for, one may indeed choose inadequate sample Sizes. References Berger, J. O. (1984). The Robust Bayesian Viewpoint (with discussion), in Robustness of Bayesian Analysis, ed. J. Kadane, Amsterdam: North-Holland,pp. 63–134. De Santis F. (2006). Sample Size Determination for robust Bayesian analysis, Journal of the American Statistical Association, Vol. 101, N. 473, 278-291. Greenhouse J.B., Wasserman L. (1995). Robust Bayesian methods for monitoring clinical trials, Statistics in Medicine, Vol. 14, 1379-1391. Sivaganesan S., Berger J.O. (1989). Ranges of posterior measures for priors with unimodal contaminations, The Annals of Statistics, Vol.17, N. 2, 868-889. Spiegelhalter D.J., Abrams K.R., Miles J.P. (2004). Bayesian Approaches to Clinical Trials and Health-Care Evaluation, Statistics in Practice, Wiley. Wang F., Gelfand A.E. (2002). A simulation-based approach to Bayesian sample Size Determination for performance under a given model and for separating models, Statistical Science, Vol 17, N. 2, 193-208.
Fulvio De Santis - One of the best experts on this subject based on the ideXlab platform.
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Bayesian sample Size Determination and re-estimation using mixtures of prior distributions
2020Co-Authors: Pierpaolo Brutti, Stefania Gubbiotti, Fulvio De SantisAbstract:In this paper we propose a predictive Bayesian approach to sample Size Determination and reestimation in clinical trials, in the presence of multiple sources of prior information. The method we suggest is based on the use of mixtures of prior distributions for the unknown quantity of interest, typically an unknown effect or an unknown effects-difference. Methodologies are developed using normal models with mixtures of conjugate priors. In particular we extend the sample Size Determination analysis of [1] and the sample Size re-estimation technique of [2].
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A decision‐theoretic approach to sample Size Determination under several priors
Applied Stochastic Models in Business and Industry, 2016Co-Authors: Fulvio De Santis, Stefania GubbiottiAbstract:In this article, we consider sample Size Determination for experiments in which estimation and design are performed by multiple parties. This problem has relevant applications in contexts involving adversarial decision makers, such as control theory, marketing, and drug testing. Specifically, we adopt a decision-theoretic perspective, and we assume that a decision on an unknown parameter of a statistical model involves two actors, Ee and Eo, who share the same data and loss function but not the same prior beliefs on the parameter. We also suppose that Ee has to use Eo's optimal action, and we finally assume that the experiment is planned by a third party, Pd. In this framework, we aim at determining an appropriate sample Size so that the posterior expected loss incurred by Ee in taking the optimal action of Eo is sufficiently small. We develop general results for the one-parameter exponential family under quadratic loss and analyze the interactive impact of the prior beliefs of the three different parties on the resulting sample Sizes. Relationships with other sample Size Determination criteria are explored. Copyright © 2016 John Wiley & Sons, Ltd.
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robust bayesian sample Size Determination in clinical trials
Statistics in Medicine, 2008Co-Authors: Pierpaolo Brutti, Fulvio De Santis, Stefania GubbiottiAbstract:This article deals with Determination of a sample Size that guarantees the success of a trial. We follow a Bayesian approach and we say an experiment is successful if it yields a large posterior probability that an unknown parameter of interest (an unknown treatment effect or an effects-difference) is greater than a chosen threshold. In this context, a straightforward sample Size criterion is to select the minimal number of observations so that the predictive probability of a successful trial is sufficiently large. In the paper we address the most typical criticism to Bayesian methods—their sensitivity to prior assumptions—by proposing a robust version of this sample Size criterion. Specifically, instead of a single distribution, we consider a class of plausible priors for the parameter of interest. Robust sample Sizes are then selected by looking at the predictive distribution of the lower bound of the posterior probability that the unknown parameter is greater than a chosen threshold. For their flexibility and mathematical tractability, we consider classes of e-contamination priors. As specific applications we consider sample Size Determination for a Phase III trial. Copyright © 2008 John Wiley & Sons, Ltd.
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Robust Bayesian sample Size Determination for Bernoulli trials
2007Co-Authors: Fulvio De Santis, Stefania GubbiottiAbstract:In a Bayesian framework a robust approach is proposed for sample Size Determination (SSD) in a Bernoulli trial. The intent is to evaluate the impact of prior information, to define robust methods for choosing the sample Size and to guarantee stable inferential conclusions. In this work we focus on the probability of success of a given treatment. First, the standard Bayesian method is presented. Historical information or experts’ beliefs are taken into account and formalized by an analysis prior distribution. Here we choose a Beta distribution, so that the derived posterior still belongs to the same family. A posterior quantity of interest is considered, such as the posterior expected value of the probability of success. Since, before performing the experiment, the expectation is random we need to define a predictive criterion for determining the optimal sample Size. In this case the criterion is based on the predictive expected value, which is calculated with respect to the marginal distribution of the data. In order to avoid the sensitivity of the standard method to the prior specification, it is possible to introduce a robust approach, considering a class of priors instead of a single prior. Therefore, the focus is on the bounds of the posterior quantity of interest. Here, we choose the epsilon-contamination class, that guarantees both computational advantages and a straightforward interpretation. Two graphical tools are proposed to compare the standard SSD method with the robust one. The first consists in plotting the robust criterion with respect to the different levels of contamination, in correspondence to the standard optimal sample Size. Alternatevely, both standard and robust criteria can be represented for increasing values of n, for a fixed level of contamination. An example is provided to show how the proposed robust approach brings to a more cautious choice, namely requires more individuals to be enrolled in the trial. The proposed approach may help the experimenter showing that standard methods are not always trustworthy and they should be used with caution. Sometimes if prior information and uncertainty on the parameter of interest are not properly accounted for, one may indeed choose inadequate sample Sizes. References Berger, J. O. (1984). The Robust Bayesian Viewpoint (with discussion), in Robustness of Bayesian Analysis, ed. J. Kadane, Amsterdam: North-Holland,pp. 63–134. De Santis F. (2006). Sample Size Determination for robust Bayesian analysis, Journal of the American Statistical Association, Vol. 101, N. 473, 278-291. Greenhouse J.B., Wasserman L. (1995). Robust Bayesian methods for monitoring clinical trials, Statistics in Medicine, Vol. 14, 1379-1391. Sivaganesan S., Berger J.O. (1989). Ranges of posterior measures for priors with unimodal contaminations, The Annals of Statistics, Vol.17, N. 2, 868-889. Spiegelhalter D.J., Abrams K.R., Miles J.P. (2004). Bayesian Approaches to Clinical Trials and Health-Care Evaluation, Statistics in Practice, Wiley. Wang F., Gelfand A.E. (2002). A simulation-based approach to Bayesian sample Size Determination for performance under a given model and for separating models, Statistical Science, Vol 17, N. 2, 193-208.
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Sample Size Determination for Robust Bayesian Analysis
Journal of the American Statistical Association, 2006Co-Authors: Fulvio De SantisAbstract:This article considers a robust Bayesian approach to the sample Size Determination problem. We focus on global Bayesian robustness that studies lower bound (Ln), upper bound (Un), and range (Rn) of posterior quantities of interest, obtained as the prior varies in a class of distributions. Specifically, we are interested in the selection of an appropriate sample Size that gives guarantees to the researcher of observing a small value of the range and, depending on the problems, either a sufficiently large lower bound or a sufficiently small upper bound. Toward this end, we approach the problem as a design issue and provide new sample Size Determination criteria based on summaries of the predictive distributions of Ln, Un, and Rn, such as expectations and tail probabilities. Relationships and comparison to standard classical and (nonrobust) Bayesian methods are discussed. The proposed methods are studied for the normal model with conjugate priors and used for choosing the Size of a clinical trial.
James D. Stamey - One of the best experts on this subject based on the ideXlab platform.
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Bayesian Sample Size Determination in Two-Sample Poisson Models
Biometrics & Biostatistics International Journal, 2015Co-Authors: Ryan Sides, David Kahle, James D. StameyAbstract:Sample Size Determination is a vital part of clinical studies where cost and safety concerns lead to greater importance of not using more subjects and resources than are required. The Bayesian approach to sample Size Determination has the advantages of being able to use prior data and expert opinion to possibly reduce the total sample Size while also acknowledging all uncertainty at the design stage. We apply a Bayesian decision theoretic approach to the problem of comparing two Poisson rates and find the required sample Size to obtain a desired power while controlling the Type I error rate.
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Bayesian sample Size Determination for binary regression with a misclassified covariate and no gold standard
Computational Statistics & Data Analysis, 2012Co-Authors: Daniel P. Beavers, James D. StameyAbstract:Covariate misclassification is a common problem in epidemiology, genetics, and other biomedical areas. Because this form of misclassification is known to bias estimators, accounting for it at the design stage is of high importance. In this paper, we extend on previous work applied to response misclassification by developing a Bayesian approach to sample Size Determination for a covariate misclassification model with no gold standard. Our procedure considers both conditionally independent tests and tests in which dependence exists between classifiers. We specifically consider a Bayesian power criterion for the sample Size Determination scheme, and we demonstrate the improvement in model power for our dual classifier approach compared to a naive single classifier approach.
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Bayesian sample-Size Determination for two independent Poisson rates
Computer Methods and Programs in Biomedicine, 2010Co-Authors: Austin L. Hand, James D. Stamey, Dean M. YoungAbstract:Abstract: Because of the high cost and time constraints for clinical trials, researchers often need to determine the smallest sample Size that provides accurate inferences for a parameter of interest. Although most experimenters have employed frequentist sample-Size Determination methods, the Bayesian paradigm offers a wide variety of sample-Size Determination methodologies. Bayesian sample-Size Determination methods are becoming increasingly more popular in clinical trials because of their flexibility and easy interpretation inferences. Recently, Bayesian approaches have been used to determine the sample Size of a single Poisson rate parameter in a clinical trial setting. In this paper, we extend these results to the comparison of two Poisson rates and develop methods for sample-Size Determination for hypothesis testing in a Bayesian context. We have created functions in R to determine the parameters for the conjugate gamma prior and calculate the sample Size for the average length criterion and average power methods. We also provide two examples that implement our sample-Size Determination methods using clinical data.
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Bayesian sample-Size Determination for one and two Poisson rate parameters with applications to quality control
Journal of Applied Statistics, 2006Co-Authors: James D. Stamey, Dean M. Young, Tom L. BratcherAbstract:We formulate Bayesian approaches to the problems of determining the required sample Size for Bayesian interval estimators of a predetermined length for a single Poisson rate, for the difference between two Poisson rates, and for the ratio of two Poisson rates. We demonstrate the efficacy of our Bayesian-based sample-Size Determination method with two real-data quality-control examples and compare the results to frequentist sample-Size Determination methods.
Pierpaolo Brutti - One of the best experts on this subject based on the ideXlab platform.
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Bayesian sample Size Determination and re-estimation using mixtures of prior distributions
2020Co-Authors: Pierpaolo Brutti, Stefania Gubbiotti, Fulvio De SantisAbstract:In this paper we propose a predictive Bayesian approach to sample Size Determination and reestimation in clinical trials, in the presence of multiple sources of prior information. The method we suggest is based on the use of mixtures of prior distributions for the unknown quantity of interest, typically an unknown effect or an unknown effects-difference. Methodologies are developed using normal models with mixtures of conjugate priors. In particular we extend the sample Size Determination analysis of [1] and the sample Size re-estimation technique of [2].
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robust bayesian sample Size Determination in clinical trials
Statistics in Medicine, 2008Co-Authors: Pierpaolo Brutti, Fulvio De Santis, Stefania GubbiottiAbstract:This article deals with Determination of a sample Size that guarantees the success of a trial. We follow a Bayesian approach and we say an experiment is successful if it yields a large posterior probability that an unknown parameter of interest (an unknown treatment effect or an effects-difference) is greater than a chosen threshold. In this context, a straightforward sample Size criterion is to select the minimal number of observations so that the predictive probability of a successful trial is sufficiently large. In the paper we address the most typical criticism to Bayesian methods—their sensitivity to prior assumptions—by proposing a robust version of this sample Size criterion. Specifically, instead of a single distribution, we consider a class of plausible priors for the parameter of interest. Robust sample Sizes are then selected by looking at the predictive distribution of the lower bound of the posterior probability that the unknown parameter is greater than a chosen threshold. For their flexibility and mathematical tractability, we consider classes of e-contamination priors. As specific applications we consider sample Size Determination for a Phase III trial. Copyright © 2008 John Wiley & Sons, Ltd.
Lawrence Joseph - One of the best experts on this subject based on the ideXlab platform.
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Bayesian Sample Size Determination for Case-Control Studies When Exposure May be Misclassified
American Journal of Epidemiology, 2013Co-Authors: Lawrence Joseph, Patrick BélisleAbstract:Odds ratios are frequently used for estimating the effect of an exposure on the probability of disease in casecontrol studies. In planning such studies, methods for sample Size Determination are required to ensure sufficient accuracy in estimating odds ratios once the data are collected. Often, the exposure used in epidemiologic studies is not perfectly ascertained. This can arise from recall bias, the use of a proxy exposure measurement, uncertain work exposure history, and laboratory or other errors. The resulting misclassification can have large impacts on the accuracy and precision of estimators, and specialized estimation techniques have been developed to adjust for these biases. However, much less work has been done to account for the anticipated decrease in the precision of estimators at the design stage. Here, we develop methods for sample Size Determination for odds ratios in the presenceof exposure misclassification byusing several interval-based Bayesiancriteria. By usinga series of prototypical examples, we compare sample Size requirements after adjustment for misclassification with those required when this problem is ignored. We illustrate the methods by planning a case-control study of the effect of late introduction of peanut to the diet of children to the subsequent development of peanut allergy. Bayesian methods; case-control study; misclassification error; sample Size Determination; study design
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Bayesian Sample Size Determination for Case-Control Studies
Journal of the American Statistical Association, 2006Co-Authors: Lawrence Joseph, David B. WolfsonAbstract:Case-control studies are among the most commonly used means of assessing association between exposure and outcome. Sample Size Determination and the optimal control-to-case ratio are vital to the design of such studies. In this article we investigate Bayesian sample Size Determination and the control-to-case ratio for case-control studies, when interval estimation is the goal of the eventual statistical analysis. In certain cases we are able to derive approximate closed-form sample Size formulas. We also describe two Monte Carlo methods, each of which provides a unified approach to the sample Size problem, because they may be applied to a wide range of interval-based criteria. We compare the accuracy of the different methods. We also extend our methods to include cross-sectional designs and designs for gene–environment interaction studies.
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Some comments on Bayesian sample Size Determination
The Statistician, 1995Co-Authors: Lawrence Joseph, David B. Wolfson, Roxane Du BergerAbstract:SUMMARY Several criteria for Bayesian sample Size Determination have recently been proposed. Criteria based on highest posterior density (HPD) intervals from the exact posterior distribution in general lead to smaller sample Sizes than those based on non-HPD intervals and/or normal approximations to the exact density. The economies are variable, however, and depend both on the prior inputs and the desired posterior accuracy and coverage probability. In our reply we review several properties of sample Size methods and discuss the importance of these properties in the context of a binomial experiment. A general algorithm for Bayesian sample Size Determination that is useful for more complex sampling situations based on Monte Carlo simulations is briefly described.
