Cost-benefit considerations of the biased diagnostician

In the cognitive process of establishing a diagnosis, the performance of a diagnostician can be characterized in terms of sensitivity and specificity. The aims of the present study are to analyze in quantitative terms how cognitive bias affects the performance of a diagnostician, and how a diagnostician's biased decision making is further influenced by personal cost-benefit considerations.

The test matrices of two sequential diagnostic tests are manipulated according to the rules of linear algebra, using multiplication of the second with the first test matrix to calculate their joint test characteristics. The decision tree and receiver operating characteristic (ROC) of a biased and unbiased diagnostician are used to calculate which combination of test characteristics maximizes the expected utility value.

Biased diagnosticians cannot establish a diagnosis beyond their own limited or distorted level of understanding. An unbiased and a biased diagnostician alike adjust their choice of test characteristics according to their different cost-benefit estimation of the various test outcomes. From the perspective of an unbiased diagnostician, the choices made by a biased diagnostician appear to invert reality. However, the same appearance of inverted reality is perceived by the biased diagnostician, judging the choices made by the unbiased diagnostician.

As a general principle, human testers cannot test beyond their own level of understanding. They only see what they know. As they base their judgment on preconceived notions about the utilities associated with different test outcomes, human testers also tend to only know what they want to know.