# Decision of Uncertatinty

Decision of Uncertainty
Diagnostic testing is one of the most important features of medicine. Diagnostic tests companies are multi-billion dollars companies that rely on the effectiveness of their tests which is also important for the health and well-being of those who rely on the test results. An important diagnostic test is the one for colorectal cancer, also known as the fecal occult blood test.
Analyzing the effectiveness of this test, it needs to be taken under consideration the sensitivity and specificity of the test. Sensitivity of the test is the proportion of results that correctly identify people with colorectal cancer. In symbolic terms, P(testing positive | have colorectal cancer). The specificity of the test is the proportion of tests that correctly identify those people who do not have colorectal cancer. Symbolically, it is P( testing negative | do not have colorectal cancer).
When somebody tests positive, it is interesting to know the probability of having the disease. In other words, it is interesting to know the false alarm rate, which is important from both, treatment and business perspective. For example, a test that identified everyone who took it has colorectal cancer would have perfect sensitivity, but it would have a very high false alarm rate. Similarly, a test that identifies everyone has is healthy (i.e., does not have colorectal cancer) would have perfect specificity, but it would fail to diagnose everyone who has the disease.
Let’s suppose a patient goes to the doctor for colorectal cancer screening and tests positive for the disease. What would be the probability that this person has colorectal cancer? By using Baye’s theorem, the answer of this question can be determined. Per Yaron, in Sensitivity, Specificity, and Predictive Value of Fecal Occult Blood Testing (Hemoccult II) for Colorectal Neoplasia in Symptomatic Patients: A Prospective Study with Total Colonoscopy, “The sensitivity, specificity for colorectal cancer were 69.2%,...