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Updated: Dec 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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