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
10
To calculate the predictive value of a positive test, we need to know the prevalence of the disease in the population and the accuracy of the test. In this case, the prevalence of the disease among clinic attendees is 10%. The sensitivity and specificity of the new test are given as 60% and 70%, respectively.
1. Calculate the predictive value of a positive test:
The predictive value of a positive test is the percentage of people who test positive and actually have the disease.
To calculate this, we can use the formula:
Predictive Value of Positive Test = (Sensitivity x Prevalence) / ((Sensitivity x Prevalence) + ((1 - Specificity) x (1 - Prevalence)))
Plugging in the given values:
Predictive Value of Positive Test = (0.60 x 0.10) / ((0.60 x 0.10) + ((1 - 0.70) x (1 - 0.10)))
Predictive Value of Positive Test = 0.06 / (0.06 + 0.27)
Predictive Value of Positive Test ≈ 0.18 or 18%
Therefore, the predictive value of a positive test is approximately 18%.
2. Calculate the number of false positives:
False positives are the cases where the test indicates a positive result even though the person does not have the disease.
To calculate the number of false positives, we need to know the total number of people who tested positive and do not have the disease, and the total number of people screened.
The formula to calculate the false positives is:
False Positives = (1 - Specificity) x (1 - Prevalence) x Number of People Screened
Plugging in the given values:
False Positives = (1 - 0.70) x (1 - 0.10) x 400
False Positives = 0.30 x 0.90 x 400
False Positives ≈ 108
Therefore, the number of false positives is approximately 108.