Bayesian Analysis

Thomas Bayes, an English Clergyman (1702-1761) authored a method of predicting events based on known probability of occurrence. The method, Essay Toward Solving a Problem in the Doctrine of Chance (PDF), was published posthumously in 1763, and may be illustrated as follows.

Suppose that, on a certain island,

• Q fever (Q), and
• ornithosis (O)

are the only diseases known to cause

• cough (C)
• hepatomegaly (H), and
• rash (R)

Let us define:

PCQ, PHQ and PRQ The respective incidences of these symptoms in Q fever.

PCO, PHO and PRO The corresponding figures for ornithosis.

The respective annual incidences of the two diseases are IQ and IO.

Bayesian analysis tells us that the probability of a patient having Q fever - given cough, fever, and hepatomegaly is:

PCQ * PHQ * PRQ * IQ

(PCQ * PHQ * PRQ * IQ) + (PCO * PHO * PRO * IO) + etc

The "etc" in our denominator indicates that data for each additional endemic disease (d) having these symptoms would be added on to this string [e.g., (PCd * PHd * PRd * Id)].

The above example consists of two diseases and three symptoms. GIDEON can access disease rates for over 200 countries, and compute the individual likelihood of over 300 diseases given hundreds of clinical findings !

In addition to statistical data for disease and symptom occurrence, GIDEON incorporates the absence of symptoms into its formulae. Thus, if a rash is expected in 95% of patients with measles, and the user indicates that rash is not present, the resulting Bayesian formulae will incorporate "1 - .95" or 5% for the percentage of measles patients presenting with "non-rash." Since this feature virtually doubles the discriminative capacity of the program, the user is encouraged to indicate all firm negative findings when entering symptoms and signs. Similar analysis is applied to the identification of bacteria in the Microbiology module.