A new screening test for a disease is developed for use in the general population. The sensitivity and specificity of the new test are 60% and 70%, respectively. Four hundred (400) people are screened at a clinic during the first year the new test is implemented. (Assume the true prevalence of the disease among clinic attendees is 10%.)Calculate the following values:

The predictive value of a positive test and The number of false positives is

To calculate the predictive value of a positive test, we need to understand what it represents. The predictive value of a positive test is the probability that a person actually has a disease given that they have tested positive.

The formula to calculate the predictive value of a positive test is:

(P × Se) / ((P × Se) + (1 - P) × (1 - Sp))

Where:
P = Prevalence of the disease
Se = Sensitivity of the test
Sp = Specificity of the test

In this case, the prevalence of the disease is given as 10%, which means P = 0.1. The sensitivity of the test is 60%, so Se = 0.6. The specificity of the test is 70%, so Sp = 0.7.

Now we can calculate the predictive value of a positive test:

(0.1 × 0.6) / ((0.1 × 0.6) + (1 - 0.1) × (1 - 0.7))
= 0.06 / (0.06 + 0.27)
= 0.06 / 0.33
≈ 0.182

Therefore, the predictive value of a positive test is approximately 0.182 or 18.2%.

To calculate the number of false positives, we need to know the total number of positive test results, as well as the prevalence and specificity of the test. The formula to calculate false positives is:

(False Positive Rate) = ((1 – Specificity) × (1 – Prevalence))

In this case, the specificity is given as 70% or 0.7 and the prevalence as 10% or 0.1.

(False Positive Rate) = ((1 – 0.7) × (1 – 0.1))
= (0.3 × 0.9)
= 0.27

Therefore, the number of false positives would be 0.27 multiplied by the total number of people screened, which is 400:

Number of false positives = 0.27 × 400
= 108

So, there would be approximately 108 false positive test results.