II. Indications
 Determine whether a test offers value in a patient's evaluation for a particular condition
 Likelihood combines Test Sensitivity and Test Specificity to apply a test's value to an individual patient
 Test Sensitivity and Test Specificity each in isolation apply only to a patient with a known diagnosis
 Tests are only used in patients with an unknown diagnosis
 Likelihood Ratio puts Test Sensitivity in the context of Test Specificity (in a single value)
III. Definition

General
 Numerator
 Test Sensitivity (or its reciprocal when calculating negative likelihood)
 Denominator
 Test Specificity (or its reciprocal when calculating positive likelihood)
 Numerator
 Positive Likelihood Ratio (LR+): RuleIn Condition
 Extent to which a positive test increases the likelihood that a patient has that disease
 Calculation 1: LR+ = (true positive probability) / (false positive probability)
 Calculation 2: LR+ = P (test positive  disease) / P (test positive  no disease)
 P (test positive  disease)
 Probability that a person with the condition has a positive test (true positive, Test Sensitivity)
 P (test positive  No disease)
 Probablity that a person without the condition has a positive test (false positive, 1Test Specificity)
 P (test positive  disease)
 Calculation 3: LR+ = (Test Sensitivity) / (1  Test Specificity)
 Negative Likelihood Ratio (LR): RuleOut Condition
 Extent to which a negative test decreases the likelihood that a patient has that disease
 Calculation 1: LR = (false negative probability) / (true negative probability)
 Calculation 1: LR = (pFalseNeg / pTrueNeg)= P (test negative  disease) / P (test negative  no disease)
 P (test negative  disease)
 Probability that a person with the condition has a negative test (false negative, 1Test Sensitivity)
 P (test negative  no disease)
 Probablity that a person without the condition has a negative test (true negative, Test Specificity)
 P (test negative  disease)
 Calculation 2: LR = (1  Test Sensitivity) / (Test Specificity)
IV. Interpretation: Positive Likelihood Ratio (LR+)
 LR+ over 5  10: Significantly increases likelihood of the disease
 LR+ between 0.2 to 5 (esp if close to 1): Does not modify the likelihood of the disease
 LR+ below 0.1  0.2: Significantly decreases the likelihood of the disease
V. Interpretation: Application
 Once Likelihood Ratio is known, this can be applied to an individual patient
 Start with a patient's pretest probability of a given condition
 Method 1: Using a Likelihood Ratio nomogram, calculate the PostTest Probability
 Method 2: Rough estimation of PostTest Probability
 Indication: Pretest probability between 10 and 90%
 Do not use this estimate when the pretest probability <10% or >90%
 Positive Likelihood Ratio (LR+)
 LR+ 2: Posttest Prob. = Pretest Prob + 15%
 LR+ 5: Posttest Prob. = Pretest Prob + 30%
 LR+ 10: Posttest Prob. = Pretest Prob + 45%
 Negative Likelihood Ratio (LR, significant values are the inverse of 2, 5 and 10)
 LR+ 0.5: Posttest Prob. = Pretest Prob  15%
 LR+ 0.2: Posttest Prob. = Pretest Prob  30%
 LR+ 0.1: Posttest Prob. = Pretest Prob  45%
 References
 Krise in Herbert (2017) EM:Rap 17(2): 78
 McGee (2002) J Gen Intern Med 17(8): 6469 [PubMed]
 Indication: Pretest probability between 10 and 90%
VI. Example: Mammogram Likelihood Ratios
 Given
 Mammogram Test Sensitivity: 7795%
 Mammogram Test Specificity: 9497%
 (2009) Ann Intern Med 151: 71626 [PubMed]
 Best case analysis (using 95% sensitivity and 97% Specificity)
 LR Positive (LR+) = (0.95)/(10.97) = 31
 A positive Mammogram is highly suggestive of Breast Cancer
 LR Negative (LR) = (10.95)/(0.97) = 0.05
 A negative Mammogram is very reassuring
 LR Positive (LR+) = (0.95)/(10.97) = 31
 Worst case analysis (using 77% sensitivity and 94% Specificity)
 LR Positive (LR+) = (0.77)/(10.94) =12
 A positive Mammogram is still suggestive of Breast Cancer
 LR Negative (LR) = (10.77)/(0.94) = 0.24
 A negative Mammogram does not exclude Breast Cancer with adequate Likelihood Ratio
 LR Positive (LR+) = (0.77)/(10.94) =12
VII. Example: Prostate Specific Antigen likelihood
 Given
 PSA Test Sensitivity: 80%
 PSA Test Specificity: 30%
 Analysis
 LR Positive (LR+) = (0.8)/(10.3) = 1.1
 A positive PSA does not increase the likelihood of Prostate Cancer
 LR Negative (LR) = (10.8)/(0.3) = 0.7
 A negative PSA does not decrease the likelihood of Prostate Cancer
 LR Positive (LR+) = (0.8)/(10.3) = 1.1
VIII. Resources
IX. References
 Desai (2014) Clinical Decision Making, AMIA’s CIBRC Online Course
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Concepts  Quantitative Concept (T081) 
English  likelihood ratios, likelihood ratio 