The prevalence of previously undetected diabetes in a population to be screened is approximately 1.5% and it is assumed that 10,000 persons will be screened. The screening test will measure blood serum sugar content. A value of 180 mg percent or higher is considered positive. The sensitivity and the specificity associated with this screening are 22.9% and 99.8% respectively.
a. Set up a two by two table with the appropriate numbers in each cell of the table. Round to the nearest whole number, but only after you have completed all the calculations down through and including item f). (1 pt. per box including totals)
+ - Total
Total
Prevalence = 1.5%
Population = 10,000
Sensitivity = 22.9%
Specificity = 99.8%
Calculate the following values: (2 pts. each)
b. The percentage of false positives among all those without disease (the type I error rate).
c. The percentage of false negatives among all those with disease (the type II error rate).
d. The predictive value of a positive test.
e. The predictive value of a negative test.
f. Based on the calculations above, how many false positives and negatives will occur if 100,000 people are screened?
To set up a two by two table for this scenario, we can consider the test results and disease status:
+ (Positive) - (Negative) Total
D (Disease) TP FN D = TP + FN
ND (No Disease) FP TN ND = FP + TN
Total P = TP + FP N = FN + TN P + N = TP + FN + FP + TN
Now let's calculate the values one by one:
a. Prevalence = 1.5%
Population = 10,000
So, the number of people with the disease (D) = 1.5% * 10,000 = 150
Let's assume:
Sensitivity = 22.9% (Sensitivity measures the proportion of actual positives correctly identified)
Specificity = 99.8% (Specificity measures the proportion of actual negatives correctly identified)
b. The percentage of false positives among all those without the disease (ND) is calculated as:
False positives = (1 - Specificity) * ND
False positives = (1 - 99.8%) * (10,000 - 150) ≈ 20
c. The percentage of false negatives among all those with the disease (D) is calculated as:
False negatives = (1 - Sensitivity) * D
False negatives = (1 - 22.9%) * 150 ≈ 116
d. The predictive value of a positive test is calculated as:
Positive predictive value = TP / P
Positive predictive value = TP / (TP + FP)
e. The predictive value of a negative test is calculated as:
Negative predictive value = TN / N
Negative predictive value = TN / (FN + TN)
f. If 100,000 people are screened, we can use the same ratios as in the earlier steps but scale them up by 10:
False positives = 20 * 10 = 200
False negatives = 116 * 10 = 1,160
Now let's fill in the two by two table:
+ (Positive) - (Negative) Total
D (Disease) 35 115 150
ND (No Disease) 200 9,650 9,850
Total 235 9,765 10,000
So, the completed two by two table would look like this:
+ (Positive) - (Negative) Total
D (Disease) 35 115 150
ND (No Disease) 200 9,650 9,850
Total 235 9,765 10,000