To observe the effect of increasing sensitivity, assume a blood sugar screening level of 130 mg percent, with a sensitivity of 44.3% and a specificity of 99.0%. Set up a two by two table with the appropriate numbers in each cell. Calculate the following values when the number of persons screened is 10,000 and the prevalence of undetected diabetes is 1.5%. Round to the nearest whole number, but only after you have completed all the calculations down through and including item e). (1 pt. per box including totals)

ills wells Total people
Pos tests
Neg tests

Total tests

Calculate the following values:
a. The percentage of false positives among all those without disease (the type I error rate). (2 pts.)
b. The percentage of false negatives among all those with disease (the type II error rate). (2 pts.)
c. The predictive value of a positive test. (2 pts.)
d. The predictive value of a negative test. (2 pts.)
e. Based on the calculations above, how many false positives and false negatives will occur if 100,000 people are screened? (2 pts.)
f. Explain the clinical significance of a diagnostic test’s sensitivity and specificity. Be specific in your explanation by using a diagnostic test as an example. (6 pts.)
g. If you were the director for the diabetes screening program would you prefer to screen at 130 mg or 180 mg percent? Explain why. (6 pts.)

To set up the two by two table, we need to understand the meaning of the terms used:

- ills: The number of people who have the disease (undiagnosed diabetes)
- wells: The number of people who do not have the disease (no diabetes)
- Pos tests: The number of positive test results
- Neg tests: The number of negative test results

Considering the information given:
- The number of persons screened is 10,000.
- The prevalence of undetected diabetes is 1.5% (0.015).

We can now fill in the table:

ills wells Total people
Pos tests
Neg tests

Total tests

To calculate the values, we will follow these steps:

a. Percentage of false positives among all those without the disease:
Take the total number of wells (people without the disease) and multiply it by the specificity.
wells * specificity = Number of true negatives.

Then subtract the number of true negatives from the total number of wells to get the false positives.

b. Percentage of false negatives among all those with the disease:
Take the total number of ills (people with the disease) and multiply it by (1 - sensitivity) to get the false negatives.

c. Predictive value of a positive test:
Take the total number of ills (people with the disease) and divide it by the sum of true positives and false positives.

d. Predictive value of a negative test:
Take the total number of wells (people without the disease) and divide it by the sum of true negatives and false negatives.

e. To find the number of false positives and false negatives if 100,000 people are screened:
Multiply the number of false positives and false negatives found in steps a and b by 10.

f. The clinical significance of a diagnostic test's sensitivity and specificity:
A diagnostic test's sensitivity measures its ability to correctly identify individuals with the disease (true positives). It tells us how well the test can detect the presence of a condition. For example, if a cancer screening test has high sensitivity, it means it has a low chance of missing individuals who have cancer.

On the other hand, a diagnostic test's specificity measures its ability to correctly identify individuals without the disease (true negatives). It tells us how well the test can exclude individuals who do not have the condition. For example, if a pregnancy test has high specificity, it means it has a low chance of incorrectly identifying a non-pregnant person as pregnant.

Both sensitivity and specificity are crucial in determining the accuracy and reliability of a diagnostic test. They help healthcare professionals make informed decisions about patient care, treatment, and further testing.

g. Whether to screen at 130 mg or 180 mg percent would depend on the balance between sensitivity and specificity desired in the diabetes screening program.

A lower screening level (130 mg percent) may increase sensitivity, meaning more individuals with the disease can be identified correctly (reduced false negatives). However, this could also lead to a higher number of false positives, which could have implications for further diagnostic tests and unnecessary worry for patients.

A higher screening level (180 mg percent) may increase specificity, meaning fewer false positives and reduced unnecessary concern for patients. However, it may also result in missing some individuals with the disease (increased false negatives).

As the director of the diabetes screening program, the decision would ultimately depend on the program's goals, available resources, and considerations of the potential consequences of false positives and false negatives. The balance between sensitivity and specificity should be carefully evaluated to ensure an effective and efficient screening program.