Last update:
12-Feb-2001

Arch Hellen Med, 16(5), September-October 1999, 511-515

APPLIED MEDICAL RESEARCH

Application of Bayesian diagnostic inference to a non-medical problem

L. SPAROS
Laboratory of Clinical Epidemiology, Faculty of Nursing, University of Athens, Greece

The application of Bayesian reasoning in clinical practice and especially in the diagnostic domain continues to present difficulties, despite the aid of computer science. The concepts of prior (or primary) and posterior (or secondary) probabilities, the likelihood ratio and the weight of evidence, despite their clear content, have not been broadly adopted by the medical and academic communities. Bayesian inference, however, has numerous applications in everyday practice, and the following example may help in the understanding of Bayesian reasoning. One night a traffic accident took place. A witness testified that the accident was caused by a blue taxi. In that city 15% of the taxis were blue and 85% were green. The witness was subjected to a test in order to examine the validity of his testimory. He was shown 100 taxis and asked to identify their color under night time conditions. The witness identified correctly 80% of the blue and green taxis. Given these data one can deduce that (a) without the presence of the witness the prior probability (p) of a blue taxi causing the accident was 15% only (p=0.15), and (b) after the testimory of the witness, who had shown that he could identify correctly the color of 80% of the taxis (likelihood ratio, L=4) the posterior probabili ty becomes 0.41.

Posterior probability

This example is analogous to a diagnostic problem. The percentage of blue taxis (15%) corresponds to the prevalence of the underlying disease and the 80% correct testimony of the witness to the positive likelihood ratio of a particular clinical profile distinguishing the disease at issue from the alternative diseases.

Key words: Bayesian inference, Logit, Odds, Ratio of new information, Weight of evidence.