Stability and coherence of health experts' upper and lower subjective probabilities about dose—response functions

Abstract

As part of a method for assessing health risks associated with primary National Ambient Air Quality Standards, T. B. Feagans and W. F. Biller (Research Triangle Park, North Carolina. EPA Office of Air Quality Planning and Standards, May 1981) developed a technique for encoding experts' subjective probabilities regarding dose—response functions. The encoding technique is based on B. O. Koopman's (Bulletin of the American Mathematical Society, 1940, 46, 763–764; Annals of Mathematics, 1940, 41, 269–292) probability theory, which does not require probabilities to be sharp, but rather allows lower and upper probabilities to be associated with an event. Uncertainty about a dose—response function can be expressed either in terms of the response rate expected at a given concentration or, conversely, in terms of the concentration expected to support a given response rate. Feagans and Biller (1981, cited above) derive the relation between the two conditional probabilities, which is easily extended to upper and lower conditional probabilities. These relations were treated as coherence requirements in an experiment utilizing four ozone and four lead experts as subjects, each providing judgments on two separate occasions. Four subjects strongly satisfied the coherence requirements in both conditions, and three more did so in the second session only. The eighth subject also improved in Session 2. Encoded probabilities were highly correlated between the two sessions, but changed from the first to the second in a manner that improved coherence and reflected greater attention to certain parameters of the dose—response function.