Bayesian sample‐size determination for inference on two binomial populations with no gold standard classifier

We develop a Bayesian simulation based approach for determining the sample size required for estimating a binomial probability and the difference between two binomial probabilities where we allow for dependence between two fallible diagnostic procedures. Examples include estimating the prevalence of disease in a single population based on results from two imperfect diagnostic tests applied to sampled individuals, or surveys designed to compare the prevalences of two populations using diagnostic outcomes that are subject to misclassification. We propose a two stage procedure in which the tests are initially assumed to be independent conditional on true disease status (i.e. conditionally independent). An interval based sample size determination scheme is performed under this assumption and data are collected and used to test the conditional independence assumption. If the data reveal the diagnostic tests to be conditionally dependent, structure is added to the model to account for dependence and the sample size routine is repeated in order to properly satisfy the criterion under the correct model. We also examine the impact on required sample size when adding an extra heterogeneous population to a study.

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“…This prior structure is identical to Johnson, Gastwirth and Pearson (2001), Dendukuri et al (2004), Stamey et al (2005) and others.…”

Section: Introductionmentioning

confidence: 77%

A General Approach to Sample Size Determination for Prevalence Surveys that Use Dual Test Protocols

2007

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“…A similar question is studied for the regular one-sample binomial model with misclassification by Rahme et al (2000) and for the two-sample binomial model with misclassification by Stamey et al (2005). We study the impact of sample size via the average length criterion (ALC) for sample size determination originally used by Joseph et al (1995).…”

Section: Impact Of Fallible Sample Sizementioning

confidence: 99%

Bayesian Estimation of Intervention Effect with Pre- and Post-Misclassified Binomial Data

Stamey

Seaman

Young

2007

Journal of Biopharmaceutical Statistics

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We consider studies in which an enrolled subject tests positive on a fallible test. After an intervention, disease status is re-diagnosed with the same fallible instrument. Potential misclassification in the diagnostic test causes regression to the mean that biases inferences about the true intervention effect. The existing likelihood approach suffers in situations where either sensitivity or specificity is near 1. In such cases, common in many diagnostic tests, confidence interval coverage can often be below nominal for the likelihood approach. Another potential drawback of the maximum likelihood estimator (MLE) method is that it requires validation data to eliminate identification problems. We propose a Bayesian approach that offers improved performance in general, but substantially better performance than the MLE method in the realistic case of a highly accurate diagnostic test. We obtain this superior performance using no more information than that employed in the likelihood method. Our approach is also more flexible, doing without validation data if necessary, but accommodating multiple sources of information, if available, thereby systematically eliminating identification problems. We show via a simulation study that our Bayesian approach outperforms the MLE method, especially when the diagnostic test has high sensitivity, specificity, or both. We also consider a real data example for which the diagnostic test specificity is close to 1 (false positive probability close to 0).

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“…Prior for p i (i = 1, 2) may be any distribution with its support lying in interval (0,1). For simplicity, we here consider the conjugate priors for p 1 and p 2 , that is, p i ∼ Beta(α i , β i ) for i = 1 and 2 (see, e.g., [9]). …”

Section: Bayes Decision Function and The Most Powerful Testmentioning

confidence: 99%

“…For example, Joseph, Berger and Bélisle [6] , and Pham-Gia and Turkkan [7] proposed a Bayesian sample size calculation procedure for the Bayesian analysis of the difference of two proportions; Katsis and Toman [8] developed a Bayesian method for calculating sample size in testing the difference of two binomial proportions; Stamey, Seaman and Young [9] considered the impact of test properties on the required sample size for the Bayesian design problem in comparing two proportions with error-prone data; Rahme and Joseph [10] discussed the exact sample size determination for binomial experiments from a Bayesian point of view; Katsis [11] established a Bayesian methodology for obtaining the optimal sample size with prior information expressed through a Dirichlet distribution when a hypothesis test between two binomial populations is performed; De Santis [12] studied the sample size determination on the basis of robust Bayesian analysis. Although the above mentioned Bayesian methods are very useful, their computational burden is very large.…”

Section: Introductionmentioning

confidence: 99%

Sample-size determination for two independent binomial experiments

Zhao

Tang

2011

J Syst Sci Complex

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Sample size determination is commonly encountered in modern medical studies for two independent binomial experiments. A new approach for calculating sample size is developed by combining Bayesian and frequentist idea when a hypothesis test between two binomial proportions is conducted. Sample size is calculated according to Bayesian posterior decision function and power of the most powerful test under 0-1 loss function. Sample sizes are investigated for two cases that two proportions are equal to some fixed value or a random value. A simulation study and a real example are used to illustrate the proposed methodologies.

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Bayesian sample‐size determination for inference on two binomial populations with no gold standard classifier

Cited by 15 publications

References 31 publications

A General Approach to Sample Size Determination for Prevalence Surveys that Use Dual Test Protocols

A General Approach to Sample Size Determination for Prevalence Surveys that Use Dual Test Protocols

Bayesian Estimation of Intervention Effect with Pre- and Post-Misclassified Binomial Data

Sample-size determination for two independent binomial experiments

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