Bayesian approaches for design of psychometric studies with underreporting and misclassification.
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Measurement error problems in binary regression are of considerable interest among researchers, especially in epidemiological studies. Misclassification can be considered a special case of measurement error specifically for the situation when measurement is the categorical classification of items. Bayesian methods offer practical advantages for the analysis of epidemiological data including the possibility of incorporating relevant prior scientific information and the ability to make inferences that do not rely on large sample assumptions. 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 methods, the Bayesian paradigm offers a wide variety of methodologies and are becoming increasingly more popular in clinical trials because of their flexibility and their ease of interpretation. We will simultaneously estimate efficacy and safety where the safety variable is subject to underreporting. We propose a Bayesian sample size determination method to account for the underreporting and appropriately power the study. We will allow efficacy and safety to be independent, as well as dependent using a regression model. For both models, we will allow the safety variable to be underreported.