Question

Suppose next that we have even less knowledge of our patient, and we are only given the accuracy of the blood test and prevalence of the disease in our population. We are told that the blood test is 96 percent reliable, this means that the test will yield an accurate positive result in 96% of the cases where the disease is actually present. Gestational diabetes affects 7 percent of the population in our patient’s age group, and that our test has a false positive rate of 10 percent. Use your knowledge of Bayes’ Theorem and Conditional Probabilities to compute the following quantities based on the information given only in part 2: a) If 100,000 people take the blood test, how many people would you expect to test positive and actually have gestational diabetes? b)What is the probability of having the disease given that you test positive? c)If 100,000 people take the blood test, how many people would you expect to test negative despite actually having gestational diabetes? d)What is the probability of having the disease given that you tested negative? Comment on what you observe in the above computations. How does the prevalence of the disease affect whether the test can be trusted?

Answer 1

Solution: Given that accurate positive result in 96% Gestational diabetes affects 79% of population our test has false affected positive rate 10% . from given data, the following Table is calculated Total thve gestational Do not have gestational diabetes diabetes 0.8998 Pest positive 096X0,93 = 0.8928 0.07X0.10 -0.007 0.1002 Test negative 0.93-0.8928 = 0.0372 0.07-0.007 0.063 Total 1.00 1-0.07 -0.93 0.07 and have gestational Number of people Test positive diabetes = 100,000 X 0.8928 - 189289 189280 people would you expect and actually have gestational to test positive diabetes.

(2) > p (Hawe gestational diabetes / Test positive] - P (Have gestational diabetes Awd Test positive) P Test positive) 0.8928 0.8998 0.9922 Piave gestentional diabetes / Test positive) = 10.9922 AND Have gestational alumber of people Test negative diabetes = 100,000 X 00g|2 3720 :: (3720 people would you expect to test negative despite actually do p (Have gestational diabetes / Test negative ) - p flave gestational diabetes Anb Dost negative prest negative) 0.0372 0.1002

a 0.371257 ~0.3713] P (Have gestational diabetes l Test negative) = 10.3713] Have gestational | Donot have gestational Total diabetes diabetes | Test a=0.8928 b=0.007 0.8998 Positive 0.1002 frest d-0.063 c=0.0372 negative 0.07 0.93 hotell Sensitive = atc 0.8928 0.8928 +0.0372 0.8928 093 - 0.96 Since sensitivity, ie, the ability to correctly identify the propostion of patients with the diseak =96% is high, we can conclude that the test can be trusted