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?

Construct a conditional probability table and all relevant computation

Answer 1

a.) No. of people have diabetes = 9 x 1,00 1000 = 9600 No. of positive and diosetes y = 98, K9000 8820 sedle. dieare posesive) P diesec P (positi positive tres resel 9x98 9x98 + 91x12 = 44.68 %

gatives and diabetes = 2 X 960o = 180 d.) e ( disease ease ativ ) = negative el disease) e P (negatives) disen - 9x2 9x2 +91 88 :P (negative nodisen - - FPRT = 0.22%