Properties of a Diagnostic Test
| Property | Reference standard is positive | Reference standard is negative | Total |
|---|---|---|---|
| Test is positive | a | b | a + b |
| Test is negative | c | d | c + d |
| Total | a + c | b + d | a + b + c + d |
| Terms and Calculations | |||
| a = true-positive results, b = false-positive results, c = false-negative results, d = true-negative results. | |||
| Sensitivity = a /(a + c) = true-positive rate = “positivity in disease.” Question answered: What proportion of patients with disease is correctly identified by the test? | |||
| Specificity = d/(b + d) = true-negative rate = “negativity in health.” Question answered: What proportion of patients without the disease is correctly identified by the test? | |||
| Positive predictive value = a/(a + b). Question answered: What proportion of positive tests is correct? | |||
| Negative predictive value = d/(c + d). Question answered: What proportion of negative tests is correct? | |||
| Likelihood ratio of a positive test = probability of a positive test in diseased people/probability of a positive test in non-diseased people = true-positive rate/false-positive rate = [a/(a+c)]/[b/(b+d)]. | |||
| Likelihood ratio of a negative test = probability of a negative test in diseased people/probability of a negative test in non-diseased people = false-negative rate/true-negative rate = [/(a+c)]/[d/(b+d)]. | |||