Bayesian sample size calculation for estimation of the difference between two binomial proportions

Pezeshk, Hamid; Nematollahi, Nader; Maroufy, Vahed; Marriott, Paul; Gittins, John

doi:10.1177/0962280211399562

Cited by 3 publications

(22 citation statements)

References 18 publications

(19 reference statements)

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“…We use the Monte Carlo method in computing ENGS and hence the optimal sample size. We present a sensitivity analysis and compare the results with those of Pezeshk et al (2011) and Pezeshk and Maroufy (2005). We also compare the results with the case where a logistic utility function is used.…”

Section: Introductionmentioning

confidence: 94%

“…M is the total number of subsequent users of the new treatment. This piecewise linear utility function models the assumption that each individual will switch to the new treatment provided that the probability of the difference between the two treatments exceeds some relatively high threshold; see Pezeshk et al (2011) for more details.…”

Section: A Fully Bayesian Approach To the Sample Size Determination Pmentioning

confidence: 99%

“…Note that in this article c is called the financial cost. Downloaded by [University of Nebraska, Lincoln] at 23:14 09 April 2015 Pezeshk et al (2011) assume that in a clinical trial X 1 and X 2 are the number of favourable outcomes for patients using the new and the existing (or placebo) treatment, respectively. They assume that there are n i , i = 1, 2, patients in each group, so with the assumption of independent observations, X i (i = 1, 2) is binomially distributed with parameters n i and p i (i = 1, 2), where p i is the probability of a favorable outcome for each individual in group i.…”

Section: Expected Value Of Sample Informationmentioning

confidence: 99%

“…In section 3 Bayesian sample size determination using Shannon information is presented with special cases discussed in section 3. In section 4 we present a sensitivity analysis and compare the sample sizes obtained by maximizing ENGS with those obtained by Pezeshk et al (Pezeshk and Maroufy, 2005;Pezeshk et al, 2011).…”

Section: Introductionmentioning

confidence: 97%

“…Coad and Rosenberger (1999) suggest using 2(p 2 (1−p 2 )+p 1 (1−p 1 )) np 2 (1−p 2 )p 1 (1−p 1 ) as an estimate of the variance of the estimator. Pezeshk et al (2011) give a fully Bayesian account of the Bernoulli sampling of two independent populations with a mixture Dirichlet prior density function for (p 1 , p 2 ). They then find the optimal sample size by maximizing the expected net benefit, which is the benefit from subsequent use of the new treatment minus the cost of conducting the trial.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

An Optimization Approach to Calculating Sample Sizes With Binary Responses

Maroufy

Marriott

Pezeshk

2014

Journal of Biopharmaceutical Statistics

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In this article, we discuss an optimization approach to the sample size question, founded on maximizing the value of information in comparison studies with binary responses. The expected value of perfect information (EVPI) is calculated and the optimal sample size is obtained by maximizing the expected net gain of sampling (ENGS), the difference between the expected value of sample information (EVSI) and the cost of conducting the trial. The data are assumed to come from two independent binomial distributions, while the parameter of interest is the difference between the two success probabilities, [Formula: see text]. To formulate our prior knowledge on the parameters, a Dirichlet prior is used. Monte Carlo integration is used in the computation and optimization of ENGS. We also compare the results of this approach with existing Bayesian methods and show how the new approach reduces the computational complexity considerably.

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Section: Introductionmentioning

confidence: 94%

Section: A Fully Bayesian Approach To the Sample Size Determination Pmentioning

confidence: 99%

Section: Expected Value Of Sample Informationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 97%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

An Optimization Approach to Calculating Sample Sizes With Binary Responses

Maroufy

Marriott

Pezeshk

2014

Journal of Biopharmaceutical Statistics

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Determination of the optimal sample size for a clinical trial accounting for the population size

Stallard

Miller

Day³

et al. 2016

Biometrical J

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The problem of choosing a sample size for a clinical trial is a very common one. In some settings, such as rare diseases or other small populations, the large sample sizes usually associated with the standard frequentist approach may be infeasible, suggesting that the sample size chosen should reflect the size of the population under consideration. Incorporation of the population size is possible in a decision‐theoretic approach either explicitly by assuming that the population size is fixed and known, or implicitly through geometric discounting of the gain from future patients reflecting the expected population size. This paper develops such approaches. Building on previous work, an asymptotic expression is derived for the sample size for single and two‐arm clinical trials in the general case of a clinical trial with a primary endpoint with a distribution of one parameter exponential family form that optimizes a utility function that quantifies the cost and gain per patient as a continuous function of this parameter. It is shown that as the size of the population, N, or expected size, N∗ in the case of geometric discounting, becomes large, the optimal trial size is O(N1/2) or O(N∗1/2). The sample size obtained from the asymptotic expression is also compared with the exact optimal sample size in examples with responses with Bernoulli and Poisson distributions, showing that the asymptotic approximations can also be reasonable in relatively small sample sizes.

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Decision-theoretic designs for small trials and pilot studies: A review

Hee

Hamborg

Day³

et al. 2015

Stat Methods Med Res

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Pilot studies and other small clinical trials are often conducted but serve a variety of purposes and there is little consensus on their design. One paradigm that has been suggested for the design of such studies is Bayesian decision theory. In this article, we review the literature with the aim of summarizing current methodological developments in this area. We find that decision-theoretic methods have been applied to the design of small clinical trials in a number of areas. We divide our discussion of published methods into those for trials conducted in a single stage, those for multi-stage trials in which decisions are made through the course of the trial at a number of interim analyses, and those that attempt to design a series of clinical trials or a drug development programme. In all three cases, a number of methods have been proposed, depending on the decision maker’s perspective being considered and the details of utility functions that are used to construct the optimal design.

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Bayesian sample size calculation for estimation of the difference between two binomial proportions

Cited by 3 publications

References 18 publications

An Optimization Approach to Calculating Sample Sizes With Binary Responses

An Optimization Approach to Calculating Sample Sizes With Binary Responses

Determination of the optimal sample size for a clinical trial accounting for the population size

Decision-theoretic designs for small trials and pilot studies: A review

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