Determination of the hyperparameters of a prior probability model in survival analysis

This paper outlines the mathematical theory required for eliciting the hyperparameters of a subjective conjugate distribution for the exponential survival model with censoring. The technique involves the quantification of expert knowledge based on determination by the expert of expected fractiles of a survival distribution in a particular clinical trial setting. Once the prior predictive distribution is determined and the fractiles elicited one can proceed, using iterative techniques, to solve for the hyperparameters. The restrictions and constraints of the hyperparameters as well as the fractiles are studied. The theory is then applied in a clinical trial setting.