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% (240) and 70%, (280) 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%.)
To answer questions related to the screening test, we can use the concepts of sensitivity, specificity, prevalence, and positive predictive value. Let's apply these concepts to the given scenario step by step.
1. Sensitivity: Sensitivity measures the proportion of true positive results correctly identified by the test. It tells us how well the test can correctly identify individuals with the disease.
In the given scenario, the sensitivity of the new screening test is 60%. This means that out of all the people with the disease, the test correctly identifies 60% or 240 individuals.
2. Specificity: Specificity measures the proportion of true negative results correctly identified by the test. It tells us how well the test can correctly identify individuals without the disease.
In the given scenario, the specificity of the new screening test is 70%. This means that out of all the people without the disease, the test correctly identifies 70% or 280 individuals.
3. Prevalence: Prevalence refers to the proportion of individuals in a population who have the disease at a given time.
In the given scenario, the true prevalence of the disease among clinic attendees is stated to be 10%. This implies that out of the 400 people screened, 10% or 40 individuals actually have the disease.
4. Positive Predictive Value: Positive Predictive Value (PPV) is the proportion of individuals with a positive test result who actually have the disease.
To calculate the PPV, we need to use Bayes' theorem:
PPV = (Sensitivity * Prevalence) / ((Sensitivity * Prevalence) + ((1 - Specificity) * (1 - Prevalence)))
Using the given values:
PPV = (0.60 * 0.10) / ((0.60 * 0.10) + ((1 - 0.70) * (1 - 0.10)))
PPV = 0.06 / (0.06 + 0.27)
PPV = 0.06 / 0.33
PPV ≈ 0.182 (or 18.2%)
Therefore, the Positive Predictive Value (PPV) of the new screening test is approximately 18.2%. This means that among those who tested positive for the disease, approximately 18.2% actually have the disease.