Question

false positive rate - the probability a patient tests positive given they are not infected
fill in the blank 6 points
suppose a screening test is done for a disease in a population of 300. use the following chart to determine the answers to the questions below.

	positive	negative	total
not infected	10	280	290
total	14	286	300

what percentage of patients tested have the disease? choose your answer.
what is the specificity of the screening test? choose your answer.
what is the ppv of the test? choose your answer.
if a patient is infected with the disease, what are their chances of getting a positive test result? choose your answer.
what is the npv of the test? choose your answer.
if a patient gets a positive test result, what are their chances of actually being infected with the disease? choose your answer.

Explanation:

Step1: Calculate percentage of patients with disease

The number of infected patients is 10 and the total number of patients tested is 300. The percentage is $\frac{10}{300}\times100=\frac{1000}{300}\approx 3.33\%$.

Step2: Calculate specificity

Specificity = $\frac{\text{True Negative}}{\text{True Negative}+\text{False Positive}}$. True - negative is 280 and false - positive is 10. So specificity = $\frac{280}{280 + 10}=\frac{280}{290}\approx0.9655$ or 96.55%.

Step3: Calculate Positive Predictive Value (PPV)

PPV=$\frac{\text{True Positive}}{\text{True Positive}+\text{False Positive}}$. True - positive is 4 and false - positive is 10. So PPV = $\frac{4}{4 + 10}=\frac{4}{14}\approx0.2857$ or 28.57%.

Step4: Calculate probability of positive test if infected

The number of infected patients is 10 and the number of infected patients with positive test is 4. The probability is $\frac{4}{10}=0.4$ or 40%.

Step5: Calculate Negative Predictive Value (NPV)

NPV = $\frac{\text{True Negative}}{\text{True Negative}+\text{False Negative}}$. True - negative is 280 and false - negative is 6. So NPV=$\frac{280}{280+6}=\frac{280}{286}\approx0.9790$ or 97.90%.

Step6: Calculate probability of being infected given positive result

This is the same as PPV. Using the formula $\frac{\text{True Positive}}{\text{True Positive}+\text{False Positive}}$, we get $\frac{4}{4 + 10}=\frac{4}{14}\approx0.2857$ or 28.57%.

Answer:

1. Approximately 3.33%
2. Approximately 96.55%
3. Approximately 28.57%
4. 40%
5. Approximately 97.90%
6. Approximately 28.57%