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

Gold Standard

+ve -ve

+ve A BNewtest

-ve C D

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

Gold Standard

+ve -ve

+ve A BNewtest

-ve C D

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

Gold Standard

+veTrop

T>0.05

-veTrop

T<0.05+ve 16 13New

Test12 leadECG

-ve 44 147

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 =

Gold Standard

+veTrop

T>0.05

-veTrop

T<0.05+ve 25 27New

TestBSM -ve 35 133

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

Gold Standard

+veTrop

T>0.05

-veTrop

T<0.05+ve 25 27New

TestBSM -ve 35 133

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 massCut-off for diagnostictest protocol

Sensitivity Specificity LR +ve LR -ve

CK mass>2 100% 48% 1.92 Infinite

CK mass>3 97% 79% 4.62 0.03

CK mass>5 92% 95% 18.4 0.08

CK mass>7 64% 98% 22 0.36

CK mass>9 56% 99% 44 0.44

CK mass>11 56% 99% 44 0.44

CK mass>13 50% 99% 50 0.51

CK mass>22 39% 100% infinite 0.61

This study used WHO definition of AMI as gold standard

More WorkCut-off for diagnostictest protocol

Sensitivity Specificity LR +ve LR -ve

CK mass>2 100% 48% 1.92 Infinite

CK mass>3 97% 79% 4.62 0.03

CK mass>5 92% 95% 18.4 0.08

CK mass>7 64% 98% 22 0.36

CK mass>9 56% 99% 44 0.44

CK mass>11 56% 99% 44 0.44

CK mass>13 50% 99% 50 0.51

CK mass>22 39% 100% infinite 0.61

• 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