Bayes theorem

What is Bayes theorem? How does it relate to the diagnosis of peptide-secreting tumors? 

Bayes theorem links the prevalence of the diagnosis to the positive predictive value of a diagnostic test. The positive predictive value of a test depends on the likelihood of the condition in the population to be tested, not only on the accuracy of the test. For example, peptide-secreting tumors are rare causes of chronic diarrhea with prevalences ranging from 1 per 5000 to 1 per 500,000 patients with chronic diarrhea, depending on tumor type. Bayes theorem can be expressed in the following simplified formula:

Posttest odds of diagnosis = Pretest odds X Likelihood ratio

where the likelihood ratio = probability of true-positive result/probability of true-negative result. 

Because the pretest odds of a peptide-secreting tumor are so long and the false-positive rate of serum peptide assays for that diagnosis is so high (approximately 45%), the positive predictive value for serum peptide assays is substantially less than 1%.

An abnormal test result would be misleading more than 99% of the time.

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