Question

Suppose that the prevalence of breast cancer in a certain population of women is 0.30. Assume that the sensitivity of a mammogram to detect breast cancer is 0.83, and the specificity of a mammogram is 0.90. What is the predictive value positive for this test, in this population?

Answer 1

given

prevalence =0.30

sensitivity =0.83

specificity =0.90

useful formulas

prevalence = a+c a+b+c+d

sensitivity = a+c

specificity = b + d

positive predictive value = a + b

sensitivity * prevalence positive predictive value=; (sensitivity * prevalence) + (1 - specificity) (1 - prevalence)

using the above formula

positive predictive value = 0.83 0.3 (0.83 *0.3) + (1 -0.9)(1 – 0.3) 0.249 0.249 + 0.1 * 0.7 0.249 0.319 = 0.7805