2. Create a contingency table on the bottom of the page using a hypothetical sam
ID: 3052709 • Letter: 2
Question
2. Create a contingency table on the bottom of the page using a hypothetical sample of 100,000 people given that the baseline rate of a disease is 4 out of 1000, the sensitivity of the test is 90% and the specificity is 92%. Use the table to answer these questions a) What is the false negative rate? (percent form) b) What is the false positive rate? (percent form) gpewten forhelPobbe for omecone who has the diseave d) What is the probability that someone who does not have the disease will test negative? (percent form)Explanation / Answer
Disease (D)
No Disease (C )
Total
Total Positive (P)
TP
FP
P = TP + FP
Total Negative (N)
FN
TN
N = FN + TN
Total
D = TP + FN
C = FP + TN
n = TP +FP + FN + TN
Given:
Sample Size = n = 100,000 = TP +FP + FN + TN --------------------------------------------------------(i)
Baseline Rate = 4/1000 = D / n = (TP + FN) / (TP +FP + FN + TN)-----------------------------------(ii)
Sensitivity = 0.90 = TP / (TP + FN)--------------------------------------------------------------------------(iii)
Specificity = 0.92 = TN / (FP + TN)-------------------------------------------------------------------------(iv)
Solving above four equations:
From equation (i) & (ii)
TP + FN = 0.004 X 100000 = 400 ----------------------------------------------------------------------------(v)
FP + TN = 100000 – 400 = 99,600………………………………………………………………………………………..(vi)
From equation (iii) & (V)
TP = 0.9 X 400 = 360
FN = 40
From equation (vi) & (iv)
TN = 0.92 X 99600 = 91632
FP = 99600 – 91632 = 7968
Disease (D)
No Disease (C )
Total
Total Positive (P)
TP = 360
FP = 7968
P = 8328
Total Negative (N)
FN = 40
TN = 91632
N = 91672
Total
D = 400
C = 99600
n = 100000
Disease (D)
No Disease (C )
Total
Total Positive (P)
TP
FP
P = TP + FP
Total Negative (N)
FN
TN
N = FN + TN
Total
D = TP + FN
C = FP + TN
n = TP +FP + FN + TN
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