Epi
Likelihood Ratio
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Likelihood Ratio
, Positive Likelihood Ratio, LR+, Negative Likelihood Ratio, LR-
See Also
Screening Test
Contingency Grid
or
Cross Tab
(includes
Statistics Example
)
Bayes Theorem
(
Bayesian Statistics
)
Fagan Nomogram
Experimental Error
(
Experimental Bias
)
Lead-Time Bias
Length Bias
Selection Bias
(
Screening Bias
)
Number Needed to Screen
(
Number Needed to Treat
,
Absolute Risk Reduction
,
Relative Risk Reduction
)
Negative Predictive Value
Positive Predictive Value
Pre-Test Odds
or
Post-Test Odds
Receiver Operating Characteristic
Test Sensitivity
(
False Negative Rate
)
Test Specificity
(
False Positive Rate
)
U.S. Preventive Services Task Force Recommendations
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)
Definition
Gene
ral
Numerator
Test Sensitivity
(or its reciprocal when calculating negative likelihood)
Denominator
Test Specificity
(or its reciprocal when calculating positive likelihood)
Positive Likelihood Ratio (LR+): Rule-In 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, 1-
Test Specificity
)
Calculation 3: LR+ = (
Test Sensitivity
) / (1 -
Test Specificity
)
Negative Likelihood Ratio (LR-): Rule-Out 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, 1-
Test Sensitivity
)
P (test negative | no disease)
Probablity that a person without the condition has a negative test (true negative,
Test Specificity
)
Calculation 2: LR- = (1 -
Test Sensitivity
) / (
Test Specificity
)
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
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
Post-Test Probability
http://www.cebm.net/index.aspx?o=1043
Method 2: Rough estimation of
Post-Test 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: Post-test Prob. = Pretest Prob + 15%
LR+ 5: Post-test Prob. = Pretest Prob + 30%
LR+ 10: Post-test Prob. = Pretest Prob + 45%
Negative Likelihood Ratio (LR-, significant values are the inverse of 2, 5 and 10)
LR+ 0.5: Post-test Prob. = Pretest Prob - 15%
LR+ 0.2: Post-test Prob. = Pretest Prob - 30%
LR+ 0.1: Post-test Prob. = Pretest Prob - 45%
References
Krise in Herbert (2017) EM:Rap 17(2): 7-8
McGee (2002) J Gen Intern Med 17(8): 646-9 [PubMed]
Example
Mammogram Likelihood Ratios
Given
Mammogram
Test Sensitivity
: 77-95%
Mammogram
Test Specificity
: 94-97%
(2009) Ann Intern Med 151: 716-26 [PubMed]
Best case analysis (using 95% sensitivity and 97%
Specificity
)
LR Positive (LR+) = (0.95)/(1-0.97) = 31
A positive
Mammogram
is highly suggestive of
Breast Cancer
LR Negative (LR-) = (1-0.95)/(0.97) = 0.05
A negative
Mammogram
is very reassuring
Worst case analysis (using 77% sensitivity and 94%
Specificity
)
LR Positive (LR+) = (0.77)/(1-0.94) =12
A positive
Mammogram
is still suggestive of
Breast Cancer
LR Negative (LR-) = (1-0.77)/(0.94) = 0.24
A negative
Mammogram
does not exclude
Breast Cancer
with adequate Likelihood Ratio
Example
Prostate Specific Antigen
likelihood
Given
PSA
Test Sensitivity
: 80%
PSA
Test Specificity
: 30%
Analysis
LR Positive (LR+) = (0.8)/(1-0.3) = 1.1
A positive PSA does not increase the likelihood of
Prostate Cancer
LR Negative (LR-) = (1-0.8)/(0.3) = 0.7
A negative PSA does not decrease the likelihood of
Prostate Cancer
Resources
OmeRad EBM
http://omerad.msu.edu/ebm/Diagnosis/Diagnosis6.html
Wikipedia
https://en.wikipedia.org/wiki/Likelihood_ratios_in_diagnostic_testing
References
Desai (2014) Clinical Decision Making, AMIA’s CIBRC Online Course
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