Question

Suppose that a certain HIV test has both a sensitivity and specificity of 99.9%. This test is applied to a population of 1,000,000 people. Suppose that 6% of the population is actually infected with HIV. (a) Calculate the PPV. Suggestion: First make a table as seen below. (Round your answer to one decimal place.) Has disease Does not have disease Totals Test positive Test negative Totals (b) Calculate the NPV. (Round your answer to three decimal places.) % (C) How many people will test positive who are, in fact, disease-free?

Answer 1

Total popwation - N= 10000 oo HIV Test given that nas 6% a sensitivity and specificity of 99.9%. of the population is actually infected Now Make Taku Does not have disease Total Test positive Test Negative Total has biease TP FN TN TP = EP = EN = IN = True positive False positive False negative True negative Now Total Number of people has disease = 1000000 (6 100 a have Total sensitivity People who does not = TP TP+EN = 60000 disease = 10000oo- 60000 940000 specificity - TN. INTEP NOW sensitivity = 99.9%. TP - 0.999 = TP- 59940 6 0000

disease Test Positive Test+ Negative Total tas disease 59940 60 60000 does not have 940 939060 3400oo Total 60880 939120 10ooooo Now TP = 59940 & IN= 60000 - 599 40 Now specificity - TN TNT FP TN - 0.999 940ooo TN = 939060 FP = - g 40000 - 939060 940 TP PNV - x 100 TP + FP 59 940 x 100 60880 DVV E 98.5% (Round off to I decimal place

A NPV = TN. INTEN x 100 939 060 x 100 939 120 = 9390560 100 NPV - 99,994 %) NPV 99 994 ) C. FP Number of people Positive who are will test disease Free + [ 940 940