Overview
- Diagnostic testing performance is measured in a variety of ways
- Sensitivity and specificity describe the frequency of test results by disease status
- Positive and negative predictive value describe the frequency of disease status by test result
- Precision and accuracy describe different types of variation in test results
Sensitivity, Specificity, Positive Predictive Value, and Negative Predictive Value
- These 4 measures describe how well diagnostic tests capture the true presence or absence of disease
- Predictive value changes with disease prevalence, sensitivity and specificity do not
- A 2×2 contingency table can help with calculations
- sensitivity (SN)
- highly sensitive tests are good at ruling out disease (rule out SnOut)
- tests with high sensitivity are good for screening purposes
- e.g., COVID-19 testing would benefit from high sensitivity so all potential cases can be isolated quickly, even if that means briefly isolating those who do not have the disease until follow-up test results return
- false negative rate = 1-sensitivity
- specificity (SP)
- % without disease who test negative
- = d/(b+d) = TN/(FP+TN)
- highly specific tests are good at ruling in disease (rule in SpIn)
- tests with high specificity are good confirmatory tests
- e.g., after a patient screens positive for HIV on a rapid test, the confirmatory test should be highly specific to ensure that the person is not given a false positive diagnosis of a serious illness
- sensitivity (SN)
- Cut-off point for positivity may be adjusted to optimize sensitivity and specificity for different purposes, which are inversely related (cut-off point with decreased sensitivity is associated with increased specificity and vice-versa)
- Receiver operating characteristic (ROC) curves are a graphical depiction of a test’s overall diagnostic performance
- Y axis
- sensitivity
- X axis
- 1-specificity
- the closer the curve fills out the top left corner, the better the test is
- performance is quantified by the area under the curve (AUC)
- an AUC of 0.5 states that the test performs no better than chance (bad test!)
- Y axis
- an AUC of 0.9 suggests a better-performing test
Likelihood Ratios (LRs)
- Also used to assess diagnostic test performance in isolation or in sequence
- Does not change with disease prevalence
- Represents the probability of a patient with a disease having a positive or negative test result in comparison to the probability of a patient without the disease having a positive or negative test result
- Positive LR
- “How many times more likely is a positive test result observed in cases versus non-cases?”
- suggests how well disease is ruled in
- = probability of positive test in cases/probability of positive test in non-cases
- = true positive/false positive
- = sensitivity/1-specificity
- = [a/(a+c)]/[1-(d/(b+d))] or [a/(a+c)]/[b/(b+d)]
- positive LR > 1 suggests that patients with the disease are more likely to have a positive result compared to those without the disease
- “How many times more likely is a positive test result observed in cases versus non-cases?”
- Negative LR
- “How many times more likely is a negative test result observed in cases versus non-cases?”
- suggests how well disease is ruled out
- = probability of negative test in cases/probability of negative test in non-cases
- = false negative/true negative
- = 1-sensitivity/specificity
- = [1-a/(a+c)]/[d/(b+d)] or [c/(a+c)]/[d/(b+d)]
- “How many times more likely is a negative test result observed in cases versus non-cases?”
- negative LR < 1 suggests that patients with the disease are less likely to have a negative result compared to those without the disease
Precision and Accuracy