Robust Bayesian decision theory applied to optimal dosage.
We give a model for constructing an utility function u(theta,d) in a dose prescription problem. theta and d denote respectively the patient state of health and the dose. The construction of u is based on the conditional probabilities of several variables. These probabilities are described by logistic models. Obviously, u is only an approximation of the true utility function and that is why we investigate the sensitivity of the final decision with respect to the utility function. We construct a class of utility functions from u and approximate the set of all Bayes actions associated to that class. Then, we measure the sensitivity as the greatest difference between the expected utilities of two Bayes actions. Finally, we apply these results to weighing up a chemotherapy treatment of lung cancer. This application emphasizes the importance of measuring robustness through the utility of decisions rather than the decisions themselves.
Abraham
Christophe
C
Unité Mixte de Recherche 'Analyse des systèmes et biométrie' Ecole Nationale Supérieure Agronomique de Montpellier, France. abraham@ensam.inra.fr
Daurès
Jean-Pierre
JP
D000970:Antineoplastic Agents / Q000008:administration & dosage; D001499:Bayes Theorem; D002945:Cisplatin / Q000008:administration & dosage; D003662:Decision Theory; D006801:Humans; D008175:Lung Neoplasms / Q000188:drug therapy; D008954:Models, Biological; D004364:Pharmaceutical Preparations / Q000008:administration & dosage*
D000970:Antineoplastic Agents; D004364:Pharmaceutical Preparations; D002945:Cisplatin