Question

A screening program of 9000 persons at risk for hearing loss showed 700 persons positive on the screening test, although 40 of these were false positive results.

Later, after diagnosis was completed, it was learned that there were 760 persons who were truly positive for hearing loss.

Complete the table with all values:

	Disease		Total
	yes	no
Screen yes
Screen no
Total			9,000

Show your work and calculate as a percent to one decimal place. In other words: x/y = z.n %

Sensitivity = __/__ = __ . _ %

Specificity = __/__ = __ . _ %

Positive predictive value = __/__ = __ . _ %

Negative predictive value = __/__ = __ . _ %

Answer 1

Both the diagnostic tests(screening) and the disease diagnosis state will have a positive and negative outcome.

When the test result is positive & the patient actually has the disease it is called ad True Positive(TP)

The test result is positive but the patient does not have the disease the disease then it is False Positive (FP)

The test result is negative but the patient has the disease then it is False Negative(FN)

The test outcome is negative & the patient dosen't have the disease is True Negative (TN)

1. Sensitivity = proportion of patients with a positive test result among the patient who actually have the disease

Sn = TP/(TP+FN)

Total true Positive cases in this scenario = 760

Total False negative cases = 60

Sn= 760/(760 + 60) = 0.9268

= 0.9268 x 100 = 92.68

Sn = 92.7%

2. Specificity is the proportion of patients with a negative test result among the patient who do not have the disease

Sp = TN/(TN + FP)

Total true negatives = total population - total number of positive cases

= 9000 - 760 = 8,240

Total False positive cases = 40

Sp = 8,240/(8,240 + 40)

= 8,240/8,280 = 0.9951

= 0.9951 x 100 = 99.51

Sp = 99.5%

3. Positive Predictive Value(PPV) is the probability of the individuals tested positive during screening to actually have the disease

PPV = TP/(TP + FP) x 100

= 760/(760 + 40) x100

= 0.95 x 100 = 95

PPV = 95%

4. Negative Predictive Value(NPV) is the probability of the individuals who were tested negative during the screening to be truly not affected.

NPV = TN/(TN + FN) x 100

= 8,240/(8,240 + 60) x 100

= 0.9927 x 100 = 99.27

NPV = 99.3%