Properties of Diagnostic Data Distributions

It is argued that the prevailing paradigm of diagnostic statistics, which concentrates on incidence of symptoms for given disease, is largely inappropriate and should be replaced by an emphasis on diagnostic distributions, and the generalized logistic model is seen to fit naturally into the new framework.

Abstract

In applications of statistical methods to medical diagnosis, information on patients' diseases and symptoms is collected and the resulting data-base is used to diagnose new patients. The data-structure is complicated by a number of factors, two of which are examined here: selection bias and unstable population. Under reasonable conditions, no correction for selection bias is required when assessing probabilities for diseases based on symptom information, and it is suggested that these "diagnostic distributions" should form the principal object of study. Transformation of these distributions under changing population structure is considered and shown to take on a simple form in many situations. It is argued that the prevailing paradigm of diagnostic statistics, which concentrates on incidence of symptoms for given disease, is largely inappropriate and should be replaced by an emphasis on diagnostic distributions. The generalized logistic model is seen to fit naturally into the new framework.