Generalized Beta Regression to Elicit Conditional Distributions of Medical Variables

Abstract

Univariate conditional models are of core importance in supporting medical reasoning, as they allow to decompose a joint probability distribution using the chain rule. Although several methods are available for the elicitation of the joint prior distribution of parameters when the response is a medical categorical variable, the case of a medical continuous response is typically difficult to address, because its sample space is often bounded to an interval and its relationship with explanatory variables may be not linear. In these situations, the elicitation of an informative prior distribution on parameters of a univariate conditional model is challenging, because some level of statistical training is required to a medical expert for interpreting parameters and for retrieving appropriate quantitative information about them. The task can be eased and made efficient by recognizing that physicians typically distinguish among values involving medically normal and pathological patient conditions on the grounds of their personal clinical experience. In this paper, we propose a Generalized Beta regression where parameter elicitation is performed by establishing a correspondence among measured values expressed as relative positions within intervals with a clinical interpretation, regardless the original scales of variables. Software implementing the elicitation procedure is freely available.