Vahid Ashoorion MD. ,MSc, vahidashoorion@yahoo.com Refining Probability Test Informations Vahid Ashoorion MD. ,MSc, vahidashoorion@yahoo.com Dr. Vahid Ashoorion

Which one of these test is the best for SLE Dx? Sensitivity% Specificity% ANA 99 80 dsDNA 70 95 ssDNA 50 Histone 30-80 Nucleoprotein 58 Sm 25 RNP 87-94 PCNA 5 Dr. Vahid Ashoorion

Diagnostic Tests Characteristics: Sensitivity Specificity Predictive Value Likelihood Ratio Dr. Vahid Ashoorion

Sensitivity and specificity Remember: Sensitivity & Specificity can be used for diagnostic tests that have only two outcome (dichotomous tests) Sensitivity & Specificity are meaningful only when the studied population underwent an acceptable “gold standard” that used to “Rule in” or “ Rule out” the disease. Dr. Vahid Ashoorion

a b c d Disease Present Absent TP=True Positive FP= False Positive FN=False Negative d TN=True Negative Positive Test Result Negative Dr. Vahid Ashoorion

Sensitivity & Specificity Sensitivity & Specificity are easily derived by thinking Vertically Sensitivity: the proportion of patients with the disease who have a positive test result Specificity: the proportion of patients without the disease who have a negative test result Dr. Vahid Ashoorion

Specificity a/a+c a b c d Sensitivity d/b+d Disease Present Absent TP=True Positive b FP= False Positive c FN=False Negative d TN=True Negative Positive Test Result Negative Sensitivity a/a+c d/b+d Dr. Vahid Ashoorion

Information for a dichotomous test Disease Present Absent True positive A False positive B False negative C True negative D Positive Test Result Negative Sensitivity = A / (A+C) Specificity = D / (B+D) Dr. Vahid Ashoorion

Information for a dichotomous test Disease Present Absent True positive A = 103 False positive B = 16 False negative C = 12 True negative D = 211 Positive Test Result Negative Sensitivity = A / (A+C) Specificity = D / (B+D) Dr. Vahid Ashoorion

Information for a dichotomous test Disease Present Absent True positive A = 103 False positive B = 16 False negative C = 12 True negative D = 211 Positive Test Result Negative Sensitivity=103/(103+12)=89% Specificity=211/(16+211)=93% Dr. Vahid Ashoorion

Sensitivity & Specificity Limitation Sensitivity & Specificity describe the proportion of positive & negative test results in a population in whom we already know who has the disease or not. So We don’t know who has the disease before the test Dr. Vahid Ashoorion

The Usefulness of Predictive Value It is based on both Sensitivity & Specificity AND Prevalence of target disease in the population being evaluated. We care more about how “good” a test is at “predicting” who has the disease and who doesn’t, we will now think horizontally across in the table Dr. Vahid Ashoorion

Predictive values PPV : the proportion of patients with a positive test result who have the disease NPV : the proportion of patients with a negative test result who do not have the disease Dr. Vahid Ashoorion

Information for a dichotomous test Disease Present Absent True positive A False positive B False negative C True negative D a/a+b Positive Test Result d/c+d Negative Sensitivity = A / (A+C) Specificity = D / (B+D) PPV = A / (A+B) NPV = D / (C+D) Dr. Vahid Ashoorion

Information for a dichotomous test Disease Present Absent True positive A = 103 False positive B = 16 False negative C = 12 True negative D = 211 Positive Test Result Negative Sensitivity=103/(103+12)=89% PPV = A / (A+B) Specificity=211/(16+211)=93% NPV = D / (C+D) PPV = 103 / (103+16) = 86% NPV = 211 / (12+211) = 94% Dr. Vahid Ashoorion

Predictive values Limitation: predictive values are dependent on the fixed prevalence (pretest probability) of disease in the studied population. If the pretest probability of the disease is equal to prevalence of disease then the post test probability of disease will be equal to PPV (e.g in screening) Dr. Vahid Ashoorion

Homework1: Prevalence of a disease =5% Test Sensitivity:98% Test Specificity:80% What is Positive Predictive Value? What is Negative Predictive Value? Dr. Vahid Ashoorion

c=0.1 a=4.9 b=19 d=76 5 95 Disease Presence Absence PPV= 20% Test NPV= Positive PPV= 20% Test NPV= 99.8% Negative a+b+c+d=100 5 95 Dr. Vahid Ashoorion

Homework2: Prevalence of a disease =10% Test Sensitivity:98% Test Specificity:80% What is Positive Predictive Value? What is Negative Predictive Value? Dr. Vahid Ashoorion

c=0.2 a=9.8 b=18 d=72 10 90 Prevalence:5% 10% PPV:20% 35% NPV:99.8% 99.7% Disease Presence Absence a=9.8 b=18 c=0.2 d=72 Positive PPV= 35% Test NPV= 99.7% Negative a+b+c+d=100 10 90 Dr. Vahid Ashoorion

Properties of Diagnostic Tests Effect of prevalence on predictive values As prevalence decreases so does (+) PV, and (-) PV increases The PV can be improved by selecting more sensitive or specific tests, however, don’t expect any dramatic improvement More sensitive test improves (+) PV (fewer false-negative results) More specific test improves (-) PV (fewer false-positive results) Dr. Vahid Ashoorion

Likelihood Ratio: The Final Frontier Probability of an event depends on new information applied to what is previously known about the event “WHAT WE THINK AFTER” “WHAT WE THOUGHT BEFORE” + ”TEST INFORMATION” = Pretest Probability Posttest Probability Likelihood Ratio Dr. Vahid Ashoorion

Why Likelihood Ratios Are Useful? We don’t have truly perfect test ( Gold Standard) Test results only increase or decrease our likelihood (probability) of disease. Diagnostic tests with different level or categories of results can give us more Informations LR from different, independent tests can be used together sequentially to easily calculate a single estimate of a patient’s post test probability of disease Dr. Vahid Ashoorion

Some Rules When magnitude of LR applied to pretest probability directly affect the magnitude of post-test probability. In diagnostic tests with multiple levels/categories of results, each possible level/category has its own LR with a value ranging from 0-+∞ Dr. Vahid Ashoorion

Posttest probability of Disease LR Posttest probability of Disease No Disease 0.1 Lower 1 Unchanged 10 Higher +∞ Disease Certain Dr. Vahid Ashoorion

With Over Without (WOWO) Likelihood of a particular test result in someone with the disease LR= Likelihood of a particular test result in someone without the disease A test has a result: A Likelihood of test result “A” in Pt with the disease LR= Likelihood of test result “A” in Pt without the disease Dr. Vahid Ashoorion

a=207 True Positive b=231 False Positive c=44 False Negative d=399 Pulmonary Embolism Present Absent a + b = 438 a=207 True Positive b=231 False Positive c=44 False Negative d=399 True Negative Positive V/Q Scan Negative c + d = 443 a+c=251 b+d=630 Dr. Vahid Ashoorion

With Over Without (WOWO) Likelihood of a Positive test result in Pts with PE LR(+)= Likelihood of a Positive test result in Pts without PE Sensitivity a/a+c b/b+d 1-Specificity Dr. Vahid Ashoorion

Sensitivity 1-Specificity LR(+)= Dr. Vahid Ashoorion

Homework3: What is the LR(+) for a V/Q scan using data in slide #29? 207/251 231/630 What is the LR(-) for a V/Q scan using data in slide #29? 44/251 399/630 =2.4 =0.26 Dr. Vahid Ashoorion

What should we do with different levels/categories of results? Scan Category PE No PE High Probable 102 14 Intermediate Probability 106 217 Low Probability 39 273 Near NL/NL 5 126 Total 251 630 Dr. Vahid Ashoorion

Homework4: Calculate the LR for each test result by the use of generic equation: LR (High Probable)=102/251=18.3 14/630 LR( Intermediate Probability)=105/251=1.2 217/630 LR (Low Probability)=39/251=0.4 273/630 LR (Near NL/NL)= 5/251 =0.1 126/630 Dr. Vahid Ashoorion

Putting The Equation Back Together Using LR: “WHAT WE THINK AFTER” There are two methods we can apply LR to refine probability: Using Nomogram Simple Math Dr. Vahid Ashoorion

Nomogram for interpreting Diagnostic test result 0.1 0.2 0.5 1 2 5 10 20 30 40 50 Pre-test probability Post-test 99 95 90 80 70 60 Likelihood ratio 100 0.05 0.02 0.01 0.005 0.002 0.001 200 500 1000 Nomogram for interpreting Diagnostic test result Dr. Vahid Ashoorion

Homework5: Ms Klott’s pretest probability is 10%: What is her post test probability of having a pulmonary embolism? What is her post test probability if she had an intermediate probability V/Q scan? What is her post test probability if she had NL V/Q scan? Dr. Vahid Ashoorion

Using LR with simple math First: We should learn how to getting odd straight Odds are a ratio of proportions: The probability of Sth happening The probability of Sth not happening Odds= P 1-p Odds= Dr. Vahid Ashoorion

Let’s think about Odds Visually What proportion of the pie do you take? What proportion of the pie you don’t take? What is the ratio of the proportion you take to the proportion you don’t take? Dr. Vahid Ashoorion

Converting Probability to Odds and Vice Versa Odds= Probability 1-Probability Probability= Odds 1+Odds Dr. Vahid Ashoorion

Homework6: Probability Odds 0.01 .01 0.1 1/9 0.5 1 3/4 3 5/6 5 19/20 Fill in The Table Below Through Converting Between Probabilities and Odds Probability Odds 0.01 .01 0.1 1/9 0.5 1 3/4 3 5/6 5 19/20 19 Dr. Vahid Ashoorion

Some Simple Rules When either probability or odds is low (<0.1) they are essentially interchangeable values. When the probability is 0.5 the odds are 1 Probability is limited to values between 0-1, whereas odds range from 0 to +∞ Dr. Vahid Ashoorion

Putting It All Together Pret. p=0.003 Postt p: 0.054 Odds=p/(1-p) P=odds/(odds+1) = Pret. Odds: 0.003  LR: 19.2 Postt. Odds: 0.0576 Pretest odds likelihood ratio=posttest odds Dr. Vahid Ashoorion

Four steps to estimate post-test probability: Estimate the pretest probability Convert pretest probability to pretest odds Multiply the pretest odds by the likelihood ratio to get posttest odds Convert the post test odds to a posttest probability Dr. Vahid Ashoorion

Let’s compare Nomogram results and Simple Math Pretest probability=10% Pretest Odds=1/9 LR=18 Posttest Odds=2 Posttest Probability=2/3=67% Dr. Vahid Ashoorion

Table 2a: Likelihood Ratios of Tests for the Diagnosis of Appendicitis Dr. Vahid Ashoorion

Table 2b: Likelihood Ratios of Tests for the Diagnosis of Appendicitis Dr. Vahid Ashoorion

Table 3: Likelihood Ratios of Tests for the Diagnosis of Acute MI in Patients Admitted for suspected MI Dr. Vahid Ashoorion

Which one of these test is the best for SLE Dx? Sensitivity Specificity LR(+) ANA 99 80 4.95 dsDNA 70 95 14 ssDNA 50 1.6 Histone 30-80 1.1 Nucleoprotein 58 1.16 Sm 25 RNP 87-94 3.8-8.3 PCNA 5 1 Dr. Vahid Ashoorion

Thank You Dr. Vahid Ashoorion