Subjective Elicitation of Dirichlet Hyperparameters Using Past Data: A Study of Ovarian Cancer Patients

Abstract

Elicitation of prior plays a very important role in Bayesian paradigm especially when dealing with rare disease problems in medical field. The reason being that we do not get enough data to draw valid inferences always. Since the subject of study is human population, one cannot do experiments with their health. The prior distribution supports the final results by some additional information gained from the experts. In any case if an appropriate expert is not available, we can use past data to get information about the prior and its hyperparameters. The present paper provides a technique of elicitation of prior hyperparameters based on a well known multinomial-Dirichlet model. Since the main focus is on medical data problems, the inferences on odds ratios and interaction parameters are also provided. Numerical illustration is based on a real dataset from Israel on patients having ovarian cancer. Although the details have been given in the context of ovarian cancer patients, the development in the paper is equally well applicable for any such disease.