Likelihood 2005/5/22

Likelihood  probability I am likelihood I am probability

Two meaning of likelihood ratio To statistician, likelihood is a mathematical function*: For x successes in n Bernoulli trials To clinican, likelihood is a notion, a ratio, an odds: * LR = [True positive rate]/[False positive rate]

DiseaseNo Disease Positive test Positive Negative test Negative

DiseaseNo Disease Positive test True Positive Negative test True Negative

DiseaseNo Disease Positive test False Positive Negative test False Negative

Validation of the test DiseaseNo Disease Positive test TrueFalse Positive Negative test FalseTrue Negative Known

Sensitivity who have the disease will have a positive test DiseaseNo Disease Positive test TPFP Negative test FNTN Disease Positive test Sensitivity Sn = = TP + FN TP

Specificity who have no disease will have a negative test DiseaseNo Disease Positive test TPFP Negative test FNTN No Disease Negative test Specificity Sp = = FP + TN FP

Clinical setting DiseaseNo Disease Positive test TrueFalse Positive Negative test FalseTrue Negative unknown only the test result is known

DiseaseNo Disease Positive test TPFP Negative test FNTN Disease Positive test Positive Predictive value PPV = = TP + FP TP Positive Predictive Value who have positive test will have disease

Negative Predictive Value who have negative test will not have disease DiseaseNo Disease Positive test TPFP Negative test FNTN No Disease Negative test Negative Predictive Value NPV = = TN + FN

Assumption the prevalence of disease among the population of patient likely to be tested is the same as in the sample

DiseaseNo Disease Positive test TPFP Negative test FNTN Disease Positive test Positive Likelihood LR+ == TP + FP TP Positive Likelihood how a positive test more likely in patient who have disease than who do not have the disease Positive test No Disease FN FP + TN Sensitivity 1- Specificity

DiseaseNo Disease Positive test TPFP Negative test FNTN Disease Negative test Negative Likelihood LR- == TP + TN FN Negative test No Disease FN FP + TN Negative Likelihood how a negative test more likely in patient who have disease than who do not have the disease 1- Sensitivity Specificity

Disease Negative test Negative Likelihood LR- == TP + TN FN Negative test No Disease FN FP + TN Disease Positive test Positive Likelihood LR+ == TP + FP TP Positive test No Disease FN FP + TN What is the advantage of Likelihood? Sensitivity 1- Specificity 1- Sensitivity Specificity One single parameter incorporate Sn and Sp without prevalence!

Disease Negative test Negative Likelihood LR- == TP + TN FN Negative test No Disease FN FP + TN Disease Positive test Positive Likelihood LR+ == TP + FP TP Positive test No Disease FN FP + TN What is the advantage of Likelihood? This is 1/pre-test odds! Post-test Odds only give FN rate, not NPV

Therefore… Pre-test Odds Post-test Odds LR+ ×= Prevalence Post test probability PPV = Odds = p/(1-p) p=odds/(1+ odds)

But the converse is not true Pre-test Odds Post-test Odds LR - ×= Prevalence Post test probability FN rate = This is NOT NPV

DiseaseNo disease Positive Test TPFN Negative Test FPTN Prevalence = = Accuracy TP + FP + TN + FN TP FP Disease + Accurate results TP TN +

Exam paper 2004 June 1 D+D- T T D+D- T T TTT: Sn 0.9, Sp 0.75 TTT2: Sn 0.95, Sp 0.70 Prevalence = 0.4; pre-test odds =0.4/(1-0.4) =0.4/0.6= 2/3 =0.67 B4: LR+ = 0.9/(1-0.75) = 3.6 LR- = (1-0.9)/0.75 = B4: LR+ = 0.95/(1-0.70) = 3.17 LR- = (1-0.95)/0.7 = 0.07 B1: post-test Odds = 0.67 X 3.6 = 2.4 PPV = 2.4/ (2.4+1) = B1’: simply, PPV = 380/( ) =0.68 B2: NPV = 450/(40+450) =0.918 B3: Accuracy = ( )/1000=0.81B3: Accuracy = ( )/1000=0.8

What would happen if prevalence decrease? Examination paper 2003/6/2 B2b B2c

DiseaseNo Disease Positive test TPFP Negative test FNTN DiseaseNo Disease Positive test ab Negative test cd Sn= a a + c Sp= b b + d +PV= a a + b -PV= d c + d p= a + c a + b+ c + d LR+= a a + c d b + d LR-= c a + c d b + d No change

Advantage of Likelihood ratio as a measure of the usefulness of a test 1.comprise both sensitivity and specificity in one single parameter 2.do not depend on the disease prevalence 3.multilevel likelihood ratios enable us summarize the information contained in a test results over all the entire possible values. Test results can be represented by the degree of abnormality, rather than crude presence or absence of it. 4.Calculation of pretest and posttest odds is easier. 5.easier to calculate the overall probability of disease when a series of diagnostic tests is used.

Disadvantage of LR Use of odds instead of probability is more difficult. calculation of post-test probability requires maths or use of nomogram

Why use Odds but not probability? Why use OR but not Relative risk?

Odds Odds ratio is ratio of probability is ratio of Odds is ratio of ratios of probabilities

Odds Grand Round /5/19

Reference elihood.htmlhttp://mathworld.wolfram.com/MaximumLik elihood.html htmlhttp:// html Diagnostic test 4: likelihood ratios, BMJ 2004;329;