https://file.aiquickdraw.com/mathbot/file/1728052419346n98aga5c.jpg

Let's work through the problem based on the information and chart provided.

The data is:

|                        | Positive | Negative | Total |
|------------------------|----------|----------|-------|
| **Infected**            | 4        | 6        | 10    |
| **Not Infected**        | 10       | 280      | 290   |
| **Total**               | 14       | 286      | 300   |

1. **What percentage of patients tested have the disease?**

   The total number of infected people is 10 (sum of 4 positive + 6 negative tests in the infected row). Out of 300 total patients:
   
   \[
   \text{Percentage} = \left(\frac{10}{300}\right) \times 100 = 3.33\%
   \]

2. **What is the specificity of the screening test?**

   Specificity is the probability that a patient tests negative given they are not infected. To calculate this:
   
   \[
   \text{Specificity} = \frac{\text{True Negatives}}{\text{Total Not Infected}} = \frac{280}{290} \approx 0.9655 \text{ or } 96.55\%
   \]

3. **What is the Positive Predictive Value (PPV) of the test?**

   PPV is the probability that a patient who tests positive is actually infected. To calculate this:
   
   \[
   \text{PPV} = \frac{\text{True Positives}}{\text{Total Positives}} = \frac{4}{14} \approx 0.2857 \text{ or } 28.57\%
   \]

4. **If a patient is infected with the disease, what are their chances of getting a positive test result?**

   This is the sensitivity of the test, which is the probability of a positive test given that the patient is infected:
   
   \[
   \text{Sensitivity} = \frac{\text{True Positives}}{\text{Total Infected}} = \frac{4}{10} = 0.4 \text{ or } 40\%
   \]

5. **What is the Negative Predictive Value (NPV) of the test?**

   NPV is the probability that a patient who tests negative is not infected. To calculate this:
   
   \[
   \text{NPV} = \frac{\text{True Negatives}}{\text{Total Negatives}} = \frac{280}{286} \approx 0.979 \text{ or } 97.9\%
   \]

6. **If a patient gets a positive test result, what are their chances of actually being infected with the disease?**

   This is essentially the same as the PPV, which was calculated as 28.57%.

Would you like any further details or explanations?

Here are five related questions to expand your understanding:

1. How would the results change if the population size doubled but the proportions remained the same?
2. What impact does increasing specificity have on PPV?
3. How would the calculations change if the number of false negatives increased?
4. Can a test with 100% sensitivity still have a low PPV? Why?
5. What other factors could influence the reliability of a screening test in real-world scenarios?

**Tip:** Always remember the difference between sensitivity and specificity. Sensitivity relates to identifying those with the disease, while specificity relates to excluding those without it.

Suppose a screening test is done for a disease in a population of 300. Using the given table, calculate various statistics like disease percentage, specificity, PPV, sensitivity, NPV, and chances of being infected after a positive test.

Analyze the screening test results for a population of 300 to determine disease percentage, specificity, PPV, NPV, and sensitivity. Learn key statistical concepts used in medical screening tests.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation