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## versão impressa ISSN 0120-1751

### Rev.Colomb.Estad. v.34 n.2 Bogotá jun. 2011

Skeptical and Optimistic Robust Priors for Clinical Trials

Ensayos clínicos bajo un enfoque bayesiano robusto con previas escépticas y optimistas

JOHN COOK1, JAIRO FÚQUENE2, LUIS PERICCHI3

1University of Texas, M.D. Anderson Cancer Center, Division of Quantitative Sciences, Houston. Professor. Email: jdcook@mdanderson.org
2University of Puerto Rico, School of Business Administration, Institute of Statistics, San Juan, Puerto Rico. Instructor. Email: jairo.a.fuquene@uprrp.edu
3University of Puerto Rico, Department of Mathematics, San Juan, Puerto Rico. Professor. Email: luarpr@gmail.com

Abstract

A useful technique from the subjective Bayesian viewpoint, is to ask the subject matter researchers and other parties involved, such as pharmaceutical companies and regulatory bodies, for reasonable optimistic and pessimistic priors regarding the effectiveness of a new treatment. Up to now, the proposed skeptical and optimistic priors have been limited to conjugate priors, though there is no need for this limitation. The same reasonably adversarial points of view can take with robust priors. Robust priors permit a much faster and efficient resolution of the disagreement between the conclusions based on skeptical and optimistic priors. As a consequence, robust Bayesian clinical trials tend to be shorter. Our proposal in this paper is to use Cauchy and intrinsic robust priors for both skeptical and optimistic priors leading to results more closely related with the sampling data when prior and data are in conflict. In other words, the use of robust priors removes the dogmatism implicit in conjugate priors. Dogmatism here has very precise meaning: Conjugate priors affect the posterior conclusions by a fixed rate, regardless if there is a conflict between prior and data. Robust priors are automatically discounted by Bayes Theorem in the presence of conflict.

Key words: Clinical trials, Bayesian robustness, Prior distribution.

Resumen

Palabras clave: distribución a priori, ensayos clínicos, robustez bayesiana.

Texto completo disponible en PDF

References

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3. Cook, J. D. (2010), Asymptotic results for normal-cauchy model´, . UT MD Anderson Cancer Center Department of Biostatistics Working Paper Series. Working Paper 61. *http://www.bepress.com/mdandersonbiostat/paper61, \text{Web 2 March 2011}         [ Links ]

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[Recibido en septiembre de 2010. Aceptado en febrero de 2011]

Este artículo se puede citar en LaTeX utilizando la siguiente referencia bibliográfica de BibTeX:

@ARTICLE{RCEv34n2a06,     AUTHOR  = {Cook, John and Fúquene, Jairo and Pericchi, Luis},     TITLE   = {{Skeptical and Optimistic Robust Priors for Clinical Trials}},     JOURNAL = {Revista Colombiana de Estadística},     YEAR    = {2011},     volume  = {34},     number  = {2},     pages   = {333-345} }`