Sensitivity is the ability of a test to correctly identify individuals who have the disease (true positive rate). The question describes assessing the test's performance in a population of known infected individuals.

Specificity is the ability of a test to correctly identify individuals who do not have the disease (true negative rate). The study aims to measure the proportion of healthy individuals who are correctly identified as negative, which is the definition of specificity.

Sensitivity is calculated as True Positives / (True Positives + False Negatives). Here, True Positives (TP) = 180. The total number of infected patients is 200, so False Negatives (FN) = 200 - 180 = 20. Sensitivity = 180 / (180 + 20) = 180 / 200 = 90%.

Specificity is calculated as True Negatives / (True Negatives + False Positives). Here, True Negatives (TN) = 225. The total number of patients without the disease is 250, so False Positives (FP) = 250 - 225 = 25. Specificity = 225 / (225 + 25) = 225 / 250 = 90%.

A highly sensitive test is best for ruling out a disease. If a test has high sensitivity, it will correctly identify most individuals with the disease, meaning a negative result is very likely to be a true negative. This is often remembered by the mnemonic SN-N-OUT (Sensitive test, Negative result, rules OUT disease).

A highly specific test is best for confirming a diagnosis. If a test has high specificity, it has a low false-positive rate. A positive result from a highly specific test provides strong evidence that the disease is present. This is often remembered by the mnemonic SP-P-IN (Specific test, Positive result, rules IN disease).

The positive predictive value (PPV) is the probability that a patient with a positive test result truly has the disease. The patient's question directly corresponds to the definition of PPV.

The negative predictive value (NPV) is the probability that a patient with a negative test result is truly free of the disease. The patient's question directly corresponds to the definition of NPV.

First, construct a 2x2 table. With a prevalence of 10% in a population of 1000, 100 individuals have the disease and 900 do not. False Negatives (FN) = 100 * (1 - sensitivity) = 100 * 0.20 = 20. True Negatives (TN) = 900 * specificity = 900 * 0.90 = 810. NPV = TN / (TN + FN) = 810 / (810 + 20) = 810 / 830 ≈ 98%.

The positive predictive value (PPV) is highly dependent on the prevalence of the disease in the population being tested. As the prevalence of a disease decreases, the PPV of a test also decreases. Therefore, using the test in a low-prevalence population will result in a lower PPV.