Bayesian Procedure

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Maria M Ciarleglio - One of the best experts on this subject based on the ideXlab platform.

  • sample size re estimation in a superiority clinical trial using a hybrid classical and Bayesian Procedure
    Statistical Methods in Medical Research, 2019
    Co-Authors: Maria M Ciarleglio, Christopher D Arendt
    Abstract:

    When designing studies involving a continuous endpoint, the hypothesized difference in means (θA) and the assumed variability of the endpoint (σ2) play an important role in sample size and power ca...

  • sample size determination for a binary response in a superiority clinical trial using a hybrid classical and Bayesian Procedure
    Trials, 2017
    Co-Authors: Maria M Ciarleglio, Christopher D Arendt
    Abstract:

    When designing studies that have a binary outcome as the primary endpoint, the hypothesized proportion of patients in each population experiencing the endpoint of interest (i.e., π 1,π 2) plays an important role in sample size and power calculations. Point estimates for π 1 and π 2 are often calculated using historical data. However, the uncertainty in these estimates is rarely addressed. This paper presents a hybrid classical and Bayesian Procedure that formally integrates prior information on the distributions of π 1 and π 2 into the study’s power calculation. Conditional expected power (CEP), which averages the traditional power curve using the prior distributions of π 1 and π 2 as the averaging weight conditional on the presence of a positive treatment effect (i.e., π 2>π 1), is used, and the sample size is found that equates the pre-specified frequentist power (1−β) and the conditional expected power of the trial. Notional scenarios are evaluated to compare the probability of achieving a target value of power with a trial design based on traditional power and a design based on CEP. We show that if there is uncertainty in the study parameters and a distribution of plausible values for π 1 and π 2, the performance of the CEP design is more consistent and robust than traditional designs based on point estimates for the study parameters. Traditional sample size calculations based on point estimates for the hypothesized study parameters tend to underestimate the required sample size needed to account for the uncertainty in the parameters. The greatest marginal benefit of the proposed method is achieved when the uncertainty in the parameters is not large. Through this Procedure, we are able to formally integrate prior information on the uncertainty and variability of the study parameters into the design of the study while maintaining a frequentist framework for the final analysis. Solving for the sample size that is necessary to achieve a high level of CEP given the available prior information helps protect against misspecification of hypothesized treatment effect and provides a substantiated estimate that forms the basis for discussion about the study’s feasibility during the design phase.

  • selection of the effect size for sample size determination for a continuous response in a superiority clinical trial using a hybrid classical and Bayesian Procedure
    Clinical Trials, 2016
    Co-Authors: Maria M Ciarleglio, Christopher D Arendt, Peter Peduzzi
    Abstract:

    Background:When designing studies that have a continuous outcome as the primary endpoint, the hypothesized effect size (ΔA), that is, the hypothesized difference in means (θA) relative to the assumed variability of the endpoint (σA), plays an important role in sample size and power calculations. Point estimates for θ and σ are often calculated using historical data. However, the uncertainty in these estimates is rarely addressed.Methods:This article presents a hybrid classical and Bayesian Procedure that formally integrates prior information on the distributions of θ and σ into the study’s power calculation. Conditional expected power, which averages the traditional power curve using the prior distributions of θ and σ as the averaging weight, is used, and the value of ΔA is found that equates the prespecified frequentist power (1−β) and the conditional expected power of the trial. This hypothesized effect size is then used in traditional sample size calculations when determining sample size for the study....

  • selection of the treatment effect for sample size determination in a superiority clinical trial using a hybrid classical and Bayesian Procedure
    Contemporary Clinical Trials, 2015
    Co-Authors: Maria M Ciarleglio, Christopher D Arendt, Robert W Makuch, Peter Peduzzi
    Abstract:

    Specification of the treatment effect that a clinical trial is designed to detect (θA) plays a critical role in sample size and power calculations. However, no formal method exists for using prior information to guide the choice of θA. This paper presents a hybrid classical and Bayesian Procedure for choosing an estimate of the treatment effect to be detected in a clinical trial that formally integrates prior information into this aspect of trial design. The value of θA is found that equates the pre-specified frequentist power and the conditional expected power of the trial. The conditional expected power averages the traditional frequentist power curve using the conditional prior distribution of the true unknown treatment effect θ as the averaging weight. The Bayesian prior distribution summarizes current knowledge of both the magnitude of the treatment effect and the strength of the prior information through the assumed spread of the distribution. By using a hybrid classical and Bayesian approach, we are able to formally integrate prior information on the uncertainty and variability of the treatment effect into the design of the study, mitigating the risk that the power calculation will be overly optimistic while maintaining a frequentist framework for the final analysis. The value of θA found using this method may be written as a function of the prior mean μ0 and standard deviation τ0, with a unique relationship for a given ratio of μ0/τ0. Results are presented for Normal, Uniform, and Gamma priors for θ.

Christopher D Arendt - One of the best experts on this subject based on the ideXlab platform.

  • sample size re estimation in a superiority clinical trial using a hybrid classical and Bayesian Procedure
    Statistical Methods in Medical Research, 2019
    Co-Authors: Maria M Ciarleglio, Christopher D Arendt
    Abstract:

    When designing studies involving a continuous endpoint, the hypothesized difference in means (θA) and the assumed variability of the endpoint (σ2) play an important role in sample size and power ca...

  • sample size determination for a binary response in a superiority clinical trial using a hybrid classical and Bayesian Procedure
    Trials, 2017
    Co-Authors: Maria M Ciarleglio, Christopher D Arendt
    Abstract:

    When designing studies that have a binary outcome as the primary endpoint, the hypothesized proportion of patients in each population experiencing the endpoint of interest (i.e., π 1,π 2) plays an important role in sample size and power calculations. Point estimates for π 1 and π 2 are often calculated using historical data. However, the uncertainty in these estimates is rarely addressed. This paper presents a hybrid classical and Bayesian Procedure that formally integrates prior information on the distributions of π 1 and π 2 into the study’s power calculation. Conditional expected power (CEP), which averages the traditional power curve using the prior distributions of π 1 and π 2 as the averaging weight conditional on the presence of a positive treatment effect (i.e., π 2>π 1), is used, and the sample size is found that equates the pre-specified frequentist power (1−β) and the conditional expected power of the trial. Notional scenarios are evaluated to compare the probability of achieving a target value of power with a trial design based on traditional power and a design based on CEP. We show that if there is uncertainty in the study parameters and a distribution of plausible values for π 1 and π 2, the performance of the CEP design is more consistent and robust than traditional designs based on point estimates for the study parameters. Traditional sample size calculations based on point estimates for the hypothesized study parameters tend to underestimate the required sample size needed to account for the uncertainty in the parameters. The greatest marginal benefit of the proposed method is achieved when the uncertainty in the parameters is not large. Through this Procedure, we are able to formally integrate prior information on the uncertainty and variability of the study parameters into the design of the study while maintaining a frequentist framework for the final analysis. Solving for the sample size that is necessary to achieve a high level of CEP given the available prior information helps protect against misspecification of hypothesized treatment effect and provides a substantiated estimate that forms the basis for discussion about the study’s feasibility during the design phase.

  • selection of the effect size for sample size determination for a continuous response in a superiority clinical trial using a hybrid classical and Bayesian Procedure
    Clinical Trials, 2016
    Co-Authors: Maria M Ciarleglio, Christopher D Arendt, Peter Peduzzi
    Abstract:

    Background:When designing studies that have a continuous outcome as the primary endpoint, the hypothesized effect size (ΔA), that is, the hypothesized difference in means (θA) relative to the assumed variability of the endpoint (σA), plays an important role in sample size and power calculations. Point estimates for θ and σ are often calculated using historical data. However, the uncertainty in these estimates is rarely addressed.Methods:This article presents a hybrid classical and Bayesian Procedure that formally integrates prior information on the distributions of θ and σ into the study’s power calculation. Conditional expected power, which averages the traditional power curve using the prior distributions of θ and σ as the averaging weight, is used, and the value of ΔA is found that equates the prespecified frequentist power (1−β) and the conditional expected power of the trial. This hypothesized effect size is then used in traditional sample size calculations when determining sample size for the study....

  • selection of the treatment effect for sample size determination in a superiority clinical trial using a hybrid classical and Bayesian Procedure
    Contemporary Clinical Trials, 2015
    Co-Authors: Maria M Ciarleglio, Christopher D Arendt, Robert W Makuch, Peter Peduzzi
    Abstract:

    Specification of the treatment effect that a clinical trial is designed to detect (θA) plays a critical role in sample size and power calculations. However, no formal method exists for using prior information to guide the choice of θA. This paper presents a hybrid classical and Bayesian Procedure for choosing an estimate of the treatment effect to be detected in a clinical trial that formally integrates prior information into this aspect of trial design. The value of θA is found that equates the pre-specified frequentist power and the conditional expected power of the trial. The conditional expected power averages the traditional frequentist power curve using the conditional prior distribution of the true unknown treatment effect θ as the averaging weight. The Bayesian prior distribution summarizes current knowledge of both the magnitude of the treatment effect and the strength of the prior information through the assumed spread of the distribution. By using a hybrid classical and Bayesian approach, we are able to formally integrate prior information on the uncertainty and variability of the treatment effect into the design of the study, mitigating the risk that the power calculation will be overly optimistic while maintaining a frequentist framework for the final analysis. The value of θA found using this method may be written as a function of the prior mean μ0 and standard deviation τ0, with a unique relationship for a given ratio of μ0/τ0. Results are presented for Normal, Uniform, and Gamma priors for θ.

Peter Peduzzi - One of the best experts on this subject based on the ideXlab platform.

  • selection of the effect size for sample size determination for a continuous response in a superiority clinical trial using a hybrid classical and Bayesian Procedure
    Clinical Trials, 2016
    Co-Authors: Maria M Ciarleglio, Christopher D Arendt, Peter Peduzzi
    Abstract:

    Background:When designing studies that have a continuous outcome as the primary endpoint, the hypothesized effect size (ΔA), that is, the hypothesized difference in means (θA) relative to the assumed variability of the endpoint (σA), plays an important role in sample size and power calculations. Point estimates for θ and σ are often calculated using historical data. However, the uncertainty in these estimates is rarely addressed.Methods:This article presents a hybrid classical and Bayesian Procedure that formally integrates prior information on the distributions of θ and σ into the study’s power calculation. Conditional expected power, which averages the traditional power curve using the prior distributions of θ and σ as the averaging weight, is used, and the value of ΔA is found that equates the prespecified frequentist power (1−β) and the conditional expected power of the trial. This hypothesized effect size is then used in traditional sample size calculations when determining sample size for the study....

  • selection of the treatment effect for sample size determination in a superiority clinical trial using a hybrid classical and Bayesian Procedure
    Contemporary Clinical Trials, 2015
    Co-Authors: Maria M Ciarleglio, Christopher D Arendt, Robert W Makuch, Peter Peduzzi
    Abstract:

    Specification of the treatment effect that a clinical trial is designed to detect (θA) plays a critical role in sample size and power calculations. However, no formal method exists for using prior information to guide the choice of θA. This paper presents a hybrid classical and Bayesian Procedure for choosing an estimate of the treatment effect to be detected in a clinical trial that formally integrates prior information into this aspect of trial design. The value of θA is found that equates the pre-specified frequentist power and the conditional expected power of the trial. The conditional expected power averages the traditional frequentist power curve using the conditional prior distribution of the true unknown treatment effect θ as the averaging weight. The Bayesian prior distribution summarizes current knowledge of both the magnitude of the treatment effect and the strength of the prior information through the assumed spread of the distribution. By using a hybrid classical and Bayesian approach, we are able to formally integrate prior information on the uncertainty and variability of the treatment effect into the design of the study, mitigating the risk that the power calculation will be overly optimistic while maintaining a frequentist framework for the final analysis. The value of θA found using this method may be written as a function of the prior mean μ0 and standard deviation τ0, with a unique relationship for a given ratio of μ0/τ0. Results are presented for Normal, Uniform, and Gamma priors for θ.

Kevin Mccabe - One of the best experts on this subject based on the ideXlab platform.

  • behavior in a dynamic decision problem an analysis of experimental evidence using a Bayesian type classification algorithm
    Econometrica, 2004
    Co-Authors: Daniel Houser, Michael Keane, Kevin Mccabe
    Abstract:

    Different people may use different strategies, or decision rules, when solving complex decision problems. We provide a new Bayesian Procedure for drawing inferences about the nature and number of decision rules present in a population, and use it to analyze the behaviors of laboratory subjects confronted with a difficult dynamic stochastic decision problem. Subjects practiced before playing for money. Based on money round decisions, our Procedure classifies subjects into three types, which we label “Near Rational,”“Fatalist,” and “Confused.” There is clear evidence of continuity in subjects' behaviors between the practice and money rounds: types who performed best in practice also tended to perform best when playing for money. However, the agreement between practice and money play is far from perfect. The divergences appear to be well explained by a combination of type switching (due to learning and/or increased effort in money play) and errors in our probabilistic type assignments.

  • behavior in a dynamic decision problem an analysis of experimental evidence using a Bayesian type classification algorithm
    Econometrica, 2004
    Co-Authors: Daniel Houser, Michael P Keane, Kevin Mccabe
    Abstract:

    Different people may use different strategies, or decision rules, when solving complex decision problems. We provide a new Bayesian Procedure for drawing inferences about the nature and number of decision rules present in a population, and use it to analyze the behaviors of laboratory subjects confronted with a difficult dynamic stochastic decision problem. Subjects practiced before playing for money. Based on money round decisions, our Procedure classifies subjects into three types, which we label "Near Rational,""Fatalist," and "Confused." There is clear evidence of continuity in subjects' behaviors between the practice and money rounds: types who performed best in practice also tended to perform best when playing for money. However, the agreement between practice and money play is far from perfect. The divergences appear to be well explained by a combination of type switching (due to learning and/or increased effort in money play) and errors in our probabilistic type assignments. Copyright The Econometric Society 2004.

  • behavior in a dynamic decision problem an analysis of experimental evidence using a Bayesian type classification algorithm
    Experimental, 2002
    Co-Authors: Daniel Houser, Michael Keane, Kevin Mccabe
    Abstract:

    It has been long recognized that different people may use different strategies, or decision rules, when playing games or dealing with other complex decision problems. We provide a new Bayesian Procedure for drawing inferences about the nature and number of decision rules that are present in a population of agents. We show that the algorithm performs well in both a Monte Carlo study and in an empirical application. We apply our Procedure to analyze the actual behavior of subjects who are confronted with a difficult dynamic stochastic decision problem in a laboratory setting. The Procedure does an excellent job of grouping the subjects into easily interpretable types. Given the difficultly of the decision problem, we were surprised to find that nearly a third of subjects were a “Near Rational” type that played a good approximation to the optimal decision rule. More than 40% of subjects followed a rule that we describe as “fatalistic,” since they play as if they don’t appreciate the extent to which payoffs are a controlled stochastic process. And about a quarter of the subjects are classified as “Confused,” since they play the game quite poorly. Interestingly, we find that those subjects who practiced most before playing the game for money were the most likely to play poorly. Thus, lack of effort does not seem to account for poor performance. It is our hope that, in future work, our type classification algorithm will facilitate the positive analysis of peoples’ behavior in many types of complex decision problems.

Daniel Houser - One of the best experts on this subject based on the ideXlab platform.

  • behavior in a dynamic decision problem an analysis of experimental evidence using a Bayesian type classification algorithm
    Econometrica, 2004
    Co-Authors: Daniel Houser, Michael Keane, Kevin Mccabe
    Abstract:

    Different people may use different strategies, or decision rules, when solving complex decision problems. We provide a new Bayesian Procedure for drawing inferences about the nature and number of decision rules present in a population, and use it to analyze the behaviors of laboratory subjects confronted with a difficult dynamic stochastic decision problem. Subjects practiced before playing for money. Based on money round decisions, our Procedure classifies subjects into three types, which we label “Near Rational,”“Fatalist,” and “Confused.” There is clear evidence of continuity in subjects' behaviors between the practice and money rounds: types who performed best in practice also tended to perform best when playing for money. However, the agreement between practice and money play is far from perfect. The divergences appear to be well explained by a combination of type switching (due to learning and/or increased effort in money play) and errors in our probabilistic type assignments.

  • behavior in a dynamic decision problem an analysis of experimental evidence using a Bayesian type classification algorithm
    Econometrica, 2004
    Co-Authors: Daniel Houser, Michael P Keane, Kevin Mccabe
    Abstract:

    Different people may use different strategies, or decision rules, when solving complex decision problems. We provide a new Bayesian Procedure for drawing inferences about the nature and number of decision rules present in a population, and use it to analyze the behaviors of laboratory subjects confronted with a difficult dynamic stochastic decision problem. Subjects practiced before playing for money. Based on money round decisions, our Procedure classifies subjects into three types, which we label "Near Rational,""Fatalist," and "Confused." There is clear evidence of continuity in subjects' behaviors between the practice and money rounds: types who performed best in practice also tended to perform best when playing for money. However, the agreement between practice and money play is far from perfect. The divergences appear to be well explained by a combination of type switching (due to learning and/or increased effort in money play) and errors in our probabilistic type assignments. Copyright The Econometric Society 2004.

  • behavior in a dynamic decision problem an analysis of experimental evidence using a Bayesian type classification algorithm
    Experimental, 2002
    Co-Authors: Daniel Houser, Michael Keane, Kevin Mccabe
    Abstract:

    It has been long recognized that different people may use different strategies, or decision rules, when playing games or dealing with other complex decision problems. We provide a new Bayesian Procedure for drawing inferences about the nature and number of decision rules that are present in a population of agents. We show that the algorithm performs well in both a Monte Carlo study and in an empirical application. We apply our Procedure to analyze the actual behavior of subjects who are confronted with a difficult dynamic stochastic decision problem in a laboratory setting. The Procedure does an excellent job of grouping the subjects into easily interpretable types. Given the difficultly of the decision problem, we were surprised to find that nearly a third of subjects were a “Near Rational” type that played a good approximation to the optimal decision rule. More than 40% of subjects followed a rule that we describe as “fatalistic,” since they play as if they don’t appreciate the extent to which payoffs are a controlled stochastic process. And about a quarter of the subjects are classified as “Confused,” since they play the game quite poorly. Interestingly, we find that those subjects who practiced most before playing the game for money were the most likely to play poorly. Thus, lack of effort does not seem to account for poor performance. It is our hope that, in future work, our type classification algorithm will facilitate the positive analysis of peoples’ behavior in many types of complex decision problems.