Diagnostic process is a method scientific, en el diagnóstico tenemos unos síntomas que nos determinan una enfermedad. Bayes´s theorem is a very useful tool to be used in medicine and health management it allows the profesional to make decisions on rational bases.

The entire scientific method began with Descartes, philosopher, mathematician and scientist (1596-1650) defined «the rules of the method.»

INDUCTIVE THINKING: from the particular to the general

DEDUCTIVE THINKING: from the general to the particular

Fisher a British statistician and geneticist (1890-1962) says that there is only one error: rejecting a null hypothesis when it is true.

In 1763 Thomas Bayes a English clergyman who set out his theory of probability: P(wi/x) is the conditional probability of wi given x (i=1,2), that is the probability of wi if x has occurred.

Bayer´s theorem allows us to write the a posteriori probabilities of w1 and w2 as a function of the a priori probabilities (P(w1) and (Pw2)) and the class-conditional probability functions (p(x/w1) and p(x/w2)), giving

      P(wi/x)= P (wi) x p (x/wi)p(x)i=1,2

Where p(x) is the probability density function of x. (Barbini, 2013)

In medical applications the area under the ROC curve (AUC) is the most commonly used global index of discrimination capacity to evaluate classification and prediction models for decision support, diagnosis, and prognosis. (Lasko, 2005)

Establishes a patient’s illness from a series of symptoms.

wi = symptoms and syndromes associated with diseases (cough, fever, etc …)

x = diseases (cancer, bronchitis, etc …)

P (wi / x) = is the conditional probability, probability of a disease to have these symptoms.

Diseases are exclusive and all are compatible with the symptom.

Bibliography

Emanuela Barbini, Pietro Manzi and Paolo Barbini (May 15th 2013). «Bayesian Approach in Medicine and Health Management, Current Topics in Public Health, Alfonso J. Rodriguez-Morales», IntechOpen, DOI: 10.5772/52402. Available from: https://www.intechopen.com/books/current-topics-in-public-health/bayesian-approach-in-medicine-and-health-management

Thomas A Lasko, Jui G Bhagwat, Kelly H Zou, Lucila Ohno-Machado. «The use of receiver operating characteristic curves in biomedical informatics». Review J Biomed Inform, 2005 Oct;38(5):404-15:doi:10.1016/j.jbi.2005.02.008. Epub 2005 Apr 2

PMID: 16198999 DOI: 10.1016/j.jbi.2005.02.008

https://pubmed.ncbi.nlm.nih.gov/16198999/