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%, 73.2%, respectively” (Yaron, 1995, pag 1974-1977), and the overall incidence of colorectal cancer is 1 in 1834 or 0.0005. (Wrong diagnosis, 2009) Baye’s Theorem is a helpful tool that can be used to determine the probability that a patient has colorectal cancer. Let’s define event A as having colorectal cancer and + as testing positive for colorectal cancer. Then the calculations can be written out as follows: P(A | +) = P(+ | A) * P(A) / (P(+ | A) * P(A) + P(+ | not A) * P(not A)) = 0.692 * 0.005 / (0.692 * 0.005 + (1 - 0.732) * 0.995) = 0.0128 Per the above results can be inferred that a positive test result indicates only a very small probability of actually having the disease. This result might lead to ask what use the test is. A similar calculation answers the question. What is the probability that a patient doesn’t have colorectal cancer, given that he/she test negative. The calculation is similar: P(not A | not +) = P(not + | not A) * P(not A) / (P(not + | not A) * P(not A) + P(not + | A)*P(A)) = 0.732 * 0.995 / (0.732 * 0.995 + (1 - 0.692) * 0.005) = 0.9979 The screening test shows that a negative test results in veritable certainty that a patient doesn’t have the disease. This is the value and importance of this test. If it is the case that the test is fairly inexpensive to give, then it makes good sense to perform this test regularly on a mass scale. Even though it gives a fairly high level of false positives, it does quite a good job of eliminating those people who do not, in fact have colorectal cancer. Those who pass screening with this test can be very confident that they do not currently have the disease. Those who do not pass also do not likely have colorectal cancer, but only these patients should be subjected to more costly and more invasive tests such as colonoscopy. In short, using Baye’s theorem to analyze these probabilities will allow to greatly reduce the number of costly an exploratory procedures preformed to screen for colorectal cancer. This can reduce the costs for a hospital, insurance company, and patient. It can also reduce the number and complexity of treatments that patients who are exhibiting no symptoms must undergo as a part of their preventative health care. References Niv, Y., & Ad, S. (Noviembre, 1995). Sensitivity, Specificity, and Predictive Value of Fecal Occult Blood Testing (Hemoccult II) for Colorectal Neoplasia in Symptomatic Patients: A Prospective Study with Total Colonoscopy. American journal of Gastroenterology, 90(11), 1974-1977. Prevalence and Incidence of Colorectal Cancer. (January 12th, 2009). Retrieved September 25th, 2009, from Wrong Diagnosis Web site: http://www.wrongdiagnosis.com/c/colorectal/prevalence.htm