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 the number of false positives
To calculate the predictive value of a positive test result, you need the following information:
1. Prevalence of the disease in the population: 10%
2. Sensitivity of the test: 60%
3. Specificity of the test: 70%
The predictive value of a positive test result is the proportion of true positives among all positive test results. It can be calculated using the following formula:
Predictive Value of a Positive Test Result = (Sensitivity x Prevalence) / [(Sensitivity x Prevalence) + (1 - Specificity) x (1 - Prevalence)]
In this case, the prevalence is 10%, sensitivity is 60%, and specificity is 70%. Plugging these values into the formula:
Predictive Value of a Positive Test Result = (0.60 x 0.10) / [(0.60 x 0.10) + (1 - 0.70) x (1 - 0.10)]
Predictive Value of a Positive Test Result = 0.06 / (0.06 + 0.30 x 0.90)
Predictive Value of a Positive Test Result = 0.06 / (0.06 + 0.27)
Predictive Value of a Positive Test Result = 0.06 / 0.33
Predictive Value of a Positive Test Result ≈ 0.182 (or 18.2%)
The number of false positives can be calculated by subtracting the true positives from the total number of positive test results.
Number of False Positives = Total Number of Positive Test Results - True Positives
In this case, the total number of positive test results is not provided. Therefore, we cannot calculate the exact number of false positives.
To calculate the values mentioned, we'll start with the predictive value and then move on to the number of false positives.
1. Predictive Value:
Predictive value is the probability that a person actually has the disease given a positive test result. There are two types of predictive values: positive predictive value (PPV) and negative predictive value (NPV). In this case, we are asked to calculate the PPV.
PPV = (True Positives) / (True Positives + False Positives)
To find the true positives and false positives, let's break down the information given:
- Sensitivity of the test = 60% = 0.6
- Specificity of the test = 70% = 0.7
- Prevalence of the disease = 10% = 0.1
- Total screened individuals = 400
True Positives: These are the individuals who actually have the disease and test positive for it.
False Positives: These are the individuals who do not have the disease but test positive for it.
We can calculate the number of true positives and false positives using the given information and formulas.
True Positives = (Prevalence) * (Sensitivity) * (Total screened individuals)
False Positives = (1 - Prevalence) * (1 - Specificity) * (Total screened individuals)
True Positives = (0.1) * (0.6) * (400) = 24
False Positives = (1 - 0.1) * (1 - 0.7) * (400) = 108
PPV = True Positives / (True Positives + False Positives)
PPV = 24 / (24 + 108) = 0.182 or 18.2%
Therefore, the predictive value (PPV) is 18.2%.
2. Number of False Positives:
From the calculations above, we found that the number of false positives is 108.
Hence, the number of false positives is 108.