Updated: 7/22/2021

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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