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

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

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

Revision of terms Prevalence Sensitivity Specificity Truth table

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

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

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

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?

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

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!!!!!!!!!!!!!!!!

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?

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?

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

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

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

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 =

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

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

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%

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

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?

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

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

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

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

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

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

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?

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

Questions?

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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