Question

A patient underwent a diagnostic test for hypothyroidism. The diagnostic test correctly identifies patients who in fact have the disease in 93% of the cases and correctly labels healthy patients as healthy in 81% of the cases. Assume that about 4% of all patients have the disease and the test for this particular patient comes back positive (i.e., the test indicates that the patient has the disease). Without any calculations, how likely is it in your opinion that the patient in fact has the disease?

1. What percentage of patients is correctly identified as having/not having a disease?

Answer 1

The likelihood that a patient has a disease given a positive diagnostic test result can be estimated to be between the sensitivity and specificity rates.

Step-by-step explanation:

The question asks about the likelihood that a patient actually has a disease given a positive diagnostic test result. This is related to the concept of conditional probability. In this case, we are given that the diagnostic test correctly identifies patients who have the disease 93% of the time (true positive rate or sensitivity) and correctly labels healthy patients as healthy 81% of the time (true negative rate or specificity).

Without any further calculations, we can say that the likelihood of the patient actually having the disease given a positive test result can be estimated to be higher than the sensitivity rate of 93% but lower than the specificity rate of 81%. However, to obtain a more precise estimate, we would need to use the prevalence of the disease and the positive predictive value of the test, which also takes into account the false positive rate.

In summary, without any calculations, we cannot determine the exact likelihood, but we can infer that it is somewhere between the sensitivity and specificity rates.