The Bifocal Lens Model and Equation

Background. Brunswik’s Lens Model and lens model equation (LME) have been applied extensively in medical decision making. Clinicians often face the dual challenge of formulating a judgment of patient risk for some adverse outcome and making a yes or no decision regarding a particular risk-reducing treatment option. Objective. In this article, I examine the correlation between clinical risk judgments and treatment-related decisions, referring to this linkage as “cohesion”. A novel form of the LME is developed to decompose cohesion. The approach is “bifocal” in that it focuses on 2 sets of linked responses from the same individual. Methods. Data from 2 studies were analyzed to illustrate how individual differences in cohesion could be explained by differences in the parameters of the bifocal lens model equation (BiLME). Results. Cohesion varied because of differences in cognitive control, similarities in the judgment and decision policies, and a possible reliance on a subjective threshold value applied to the judgments to make decisions. The parameters of the BiLME accounted for individual differences in cohesion; however, their relative influences differed between the two studies. Conclusion. The BiLME links the results from two regression models—one linear and one logistic—based on the same set of cases. In its current form, the equation holds promise for understanding cognitive individual differences that could underlie practice variation. With minor modifications, it becomes possible to apply the equation to traditional, dual-system judgment analysis studies, where continuous judgments are compared with an ecology composed of dichotomous outcomes, or vice versa. In this regard, the BiLME is quite flexible and adds to the set of tools available to judgment analysts.