Question

The screening test for Crohn's has a sensitivity of 80% and a specificity of 90.2%, Assume that this test s applied to the group of approximately 3.3 million Americans who suffer om symptoms that are very smilar to those of Crohn's. Suppose also that all of the 0.58 million Crohn's sufferers belong to this group. Fill in the following table based on this group of 3.3 million. (Write your answers in millions and round to two decimal places.) Totals Does not have disease Has disease Test positive (millions) Test negative (millions) Totals eBook Submit Answer Save Progress

Answer 1

Does not have disease False positive (b) True negative (d) Totals Has disease Test Positive (millions) True positive (a) Test negative millions) False negative (c) Totals a+ b c+d a+ bc+d b+ d at c As the total number of patient who were tested I s3.3millions thena+b+c +d- 3.3 millions As 0.58 million Crohn's sufferers belong to this group, that is a + c- 0.58millions ..(1) Thus b +d-3.33 - 0.58 -2.72 millions....2) Sensitivity - true positive tests True positive+False negative true negative tests True negative+False positive true positive tests 80% 0.8 Total number of affected (positive) a+c Specificity true negative tests -- 90.2% 0.902 Total number of unaffected (negative) patients tested b+d 0.8(a c) or, a 0.8 × 0.58 or, a Thus a 0.464millions c = 0.2 × 0.58 0.116 millions 0.902b 0.098 - 9.20408b d 0.902(b + d) or, 0.098d 0.902b or,d -

Also as d2.72- b-9.20408b, or, b-0.26656millions 10.20408 d 2.72 0.26656millions 2.45344millions Has disease Does not have disease Totals 0.464 millions 0.116 millions 0.26656millions 0.73056millions 2.45344millions 2.56944 millions Test Positive (millions) Test negative millions) Totals 0.58millions 2.72millions 3.3 millions