Updated: 12/29/2021

Testing and Screening

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  • 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 2x2 contingency table can help with calculations
      •  sensitivity (SN) 
        • % with disease who test positive 
        • = a/(a+c) = TP/(TP+FN)
        • 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
      • 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
      • positive predictive value (PPV) 
        • % positive test results that are true positives
        • = a/(a+b) = TP/(TP+FP)
        • ↑ prevalence causes ↑ PPV
      • negative predictive value (NPV)
        • % negative test results that are true negatives
        • = d/(c+d) = TN/(FN+TN)
        • ↑ prevalence causes ↓ NPV
    • 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!)
        • 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
    • 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)]
      • 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
    • Precision
      • also known as reliability
      • consistent
      • reproducible
      • no random variation
    • Accuracy
      • reflects true value
      • no systematic variation

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