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Published byAlfred Horsfield Modified over 2 years ago

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Likelihood ratios Why these are the most thrilling statistics in Emergency Medicine

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Objectives Explore how we make diagnoses 2x2 tables, sensitivity and specificity Snout and Spin pre/post test probabilities and LRs

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Revision of terms Prevalence Sensitivity Specificity Truth table

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Prevalence How many people have the condition. Specific for the defined population In diagnostic testing Prevalence=Pre-test probability

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Sensitivity How good is the test at picking up the condition. Highly sensitive tests pick up everybody. SnOut - so SeNsitive that a negative test rules it OUT

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Specificity When the test is positive is it really positive (how many false positives are there) SPIN - so specific that when the test is positive it rules the diagnosis in

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Example Is it a Porsche? Sensitive test - does it have 4 wheels? Specific test - does it have a 3.2 Litre engine in the back Gold standard - does it have a certificate from the factory that says it is a Porsche?

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Truth table and calculations Sensitivity=a/a+c Specificity=d/d+b

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Why do we need to know more? The “performance” of tests depends on prevalence. We intuitively use pre-test probabilities to interpret tests How does this work? Likelihood ratios!!!!!!!!!!!!!!!!

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What answers do we really get from a Truth table? What does a +ve test result really mean? What does a -ve test result mean?

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Likely results A +ve test means you are more likely to have the condition A -ve result means you are less likely to have the condition How likely?

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What affects the accuracy of the test? How good the test is (sens/spec) How likely you were to have it before (prevalence) A combination of the above 2 gives the post test probability. Pre-test probability x the performance of the test = post test probability

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Likelihood ratios Take into account both specificity and sensitivity Differ depending on whether the test is +ve or -ve The positive likelihood ratio = Sens/1-Spec The negative likelihood ratio = 1-Sens/Spec

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Examples - calculating LRs What is the ability of ST elevation on the 12 lead ECG to detect Troponin >0.05 at >12 hours Sens= –a/a+c = 16/60 = 26% Spec= –d/d+b = 147/160 =92% +ve LR = –Sens/1-Spec = 3.25 -ve LR = –1-Sens/Spec = 0.8

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Examples - calculation 2 What is the ability of ST elevation on Body Surface Mapping to detect Troponin >0.05 at >12 hours Sens= –a/a+c = Spec= –d/d+b = +ve LR = –Sens/1-Spec = -ve LR = –1-Sens/Spec =

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Examples - calculation 2 What is the ability of ST elevation on Body Surface Mapping to detect Troponin >0.05 at >12 hours Sens= –a/a+c = 42% Spec= –d/d+b = 83% +ve LR = –Sens/1-Spec = 2.5 -ve LR = –1-Sens/Spec = 0.69

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Using LRs Pre-test probability x LR = Post-test probability Probabilities must be expressed as odds. Odds = probability/1-probability Use a table!!!!

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Example Low risk patient for trop rise >0.05 (prevalence 10%) in the ED has an ST rise on 12 lead ECG. How likely are they to eventually have a rise? Pre test odds = 0.1/1-0.1 = 0.11 Likelihood ratio for +ve result = 3.25 Post test odds = 0.11 x 3.25 = 0.36 Post test probability=0.36/1 + 0.36 = 26%

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Example 2 Low risk patient for trop rise >0.05 (prevalence 10%) in the ED has a normal12 lead ECG. How likely are they to eventually have a rise? Pre test odds = 0.1/1-0.1 = 0.11 Likelihood ratio for -ve result = 0.8 Post test odds = 0.11 x 0.8 = 0.08 Post test probability=0.08/1 + 0.08 = 8% In low risk groups negative result not very helpful

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Example 3 High risk patient with chest pain (prevalence 60% risk of Trop T>0.05) Positive ECG Pre-test odds = 0.6/1-0.6 = 1.5 LR +ve = 3.25 Post test odds = 1.5 x 3.25 = 4.875 post test probability = 4.875/1+4.875 = 83% ECG makes trop rise VERY likely. More active management?

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Example 4 High risk patient with chest pain (prevalence 60% risk of Trop T>0.05) Negative ECG Pre-test odds = LR -ve = 0.8 Post test odds = post test probability = You try

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Example 4 High risk patient with chest pain (prevalence 60% risk of Trop T>0.05) Negative ECG Pre-test odds = 0.6/1-0.6 = 1.5 LR -ve = 0.8 Post test odds = 1.5 x 0.8 = 1.2 post test probability = 1.2/1+1.2 = 54% A negative ECG is not a rule out in this group

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Nomograms Use nomogram to see how pre-test probability changes post test probability

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Have we got any further? Not really - mostly PPV / NPV so far. BUT - what if the LR changes for the same test?

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Different LRs Changing the level of “test positive” or “test negative” changes the Sensitivity, Specificity and LRs.

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Different LRs for CKMB mass This study used WHO definition of AMI as gold standard

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More Work Consider myocardial damage in chest pain patients. For low risk (10%) –What level rules out? –What level rules in? For High risk (50%) –What level rules out? –What level rules in?

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The EM/EBM method of diagnosis Risk assessment Estimate pre-test probabilities Organise test strategy based on risk Management based on post test probabilities Examples –DVT –PE –Cardiac chest pain –Headache –FAST –Back Pain

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Questions?

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Summary LRs are an extension of diagnostic statistics Interpreting tests with reference to the patient is a key stone of our speciality We intuitively use them all the time We should understand the principles We can use them to inform diagnostic strategies and pathways

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