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 98 percent reliable, this means that the test will yield an accurate positive result in 98% of the cases where the disease is actually present. Gestational diabetes affects 9 percent of the population in our patient’s age group, and that our test has a false positive rate of 12 percent. Use your knowledge of Bayes’ Theorem and Conditional Probabilities to compute the following quantities.

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

Ans: A het A-disease present, B-Test result is posative P/A) = 0.09 PIB/A) = 0.98 P/B/A) - 0.02 PIB/A) = 0.12, B1A) - 0.88 6 P(A/B) = P (B/A).P(A) P(BIA). PCA) + A/B/57) (P (A) 0.98×0.09 = 10,44681) (0.98×0,09+ (6. 12*0.91 a) E/A/B) = 100000 x 10.44681 = (44681) P (B/A) (PCA) + P (DIA) P(A) 0.02%0.09 Fo.002243) (0.0200.09)+ (0.88×0,97) c) n(A1B) = 10000ox 0.002243=(224 Here p (A) = 1-0,12 -0.88]