Cauchy.Binomial {ClinicalRobustPriors}R Documentation

The Binomial Likelihood with Beta and Cauchy Priors

Description

Compute the distributions (prior, likelihood, posterior predictive and posterior) and moments for the Beta/Binomial conjugate model and Cauchy/Binomial robust model. The plots are processed in Log-Odds and Theta Scale.

Usage

Cauchy.Binomial(n,x,a,b,m,min.value=NULL,max.value=NULL,iter=NULL)

Arguments

n sample size or number of observed patients.
x number of positive responses in n trials.
a the usual parameter of Beta prior and the number of positive responses in the prior information.
b the usual parameter of Beta prior and the number of negative responses in the prior information.
m number of additional patients for predictions
min.value minimum value in Log-Odds scale for the plots. The default min.value is 5.
max.value maximum value in Log-Odds scale for the plots. The default max.value is -5.
iter number of iterations in rejection sampling for the moments for the Cauchy/Binomial model. The default iter is 10000.

Author(s)

Jairo A. Fuquene P. <jairo.a.fuquene@uprrp.edu>

References

Fuquene, J. A., Cook, J. D. & Pericchi, L. R. (2008), A Case for Robust Bayesian priors with Applications to Binary Clinical Trials. UT MD Anderson Cancer Center Department of Biostatistics Working Paper Series. Working Paper 44. 2008. http://www.bepress.com/mdandersonbiostat/paper44.

Spiegelhalter, D. J., Abrams, K. R. & Myles, J. P. (2004), Bayesian Approaches to Clinical Trials and Health-Care Evaluation, Wiley, London.

Examples

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# Example 1: sample and prior are in conflict
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Cauchy.Binomial(20,16,3,12,40)
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# Example 2: sample and prior are consistent
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Cauchy.Binomial(20,16,12,3,50,min.value=-5,max.value=5,iter=5000)

[Package ClinicalRobustPriors version 2.1-2 Index]