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Review and practice for the emergency medicine clin epi components of the Royal College or board exams. Risk ratios, odds ratios, 2X2 tables, sensitivity and specificity, PPV, NPV, likelihood ratios.
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Clin Epi Boot CampR5 review 2014
Outline
Studies: Exposures and outcomes
Odds vs. risks
Odds ratios and risk ratios
ARR/RRR/NNT
Sensitivity / specificity
PPV/NPV
Hierarchy of Studies
Exposure and Outcome
Crash2 trial
5000 followed to see if they developed heart disease and looked at if they smoked
20 pts with MS questioned about lead paint in their house
Exposure and Outcome
Crash2 trialExposure (Treatment): TXA
Outcome: Mortality
5000 followed to see if they developed heart disease and looked at if they smoked
Exposure: smoking
Outcome: Heart disease
20 pts with MS questioned about lead paint in their house
Exposure: lead paint
Outcome: MS
Cross Sectional
Defined by outcomes and exposures determined at same point in time
Attitudes of ED physicians towards homeless
Drug-assisted intubation by EMS providers
(often surveys)
Case-Control
Groups defined by outcomes
Compare children who LWBS from ED to those who didn’t and compare wait times
Look at cases of ketamine sedation including those involving laryngospasm and consider predictors
Cohort
Groups defined by exposures
Framingham: 5000 pts followed to see if they developed heart disease, asked about smoking, activity, cholesterol
Following pts with varying features of TIA to see who develops stroke
RCT
Groups defined by exposures
Only differs from cohort in that:
Exposure is introduced (C)
Groups are randomized (R)
Cohort
RCT
2 X 2 Tables
Outcome (+)
Outcome (-) Totals
Exposure (+)(Experimental group)
a b a+b
Exposure (-)(Control group)
c d c+d
Totals a+c b+d a+b+c+d
2 X 2 Tables
Outcome (+)
Outcome (-) Totals
Exposure (+)(Experimental group)
a b a+b
Exposure (-)(Control group)
c d c+d
Totals a+c b+d a+b+c+d“The truth always rises to
the top”
45 ED physicians worked over the last month, 25 on days, and 20 on nights. A total of 15 EPs who worked day shifts got gastro, and 5 EPs who worked night shifts got gastro.
What is the outcome?
What is the exposure?
45 ED physicians worked over the last month, 25 on days, and 20 on nights. A total of 15 EPs who worked day shifts got gastro, and 5 EPs who worked night shifts got gastro.
Fill in the 2X2 table.
45 ED physicians worked over the last month, 25 on days, and 20 on nights. A total of 15 EPs who worked day shifts got gastro, and 5 EPs who worked night shifts got gastro.
Gastro (+) Gastro (-) Totals
Day shift (+) 15 25
Day shift (-) 5 20
Totals 45
45 ED physicians worked over the last month, 25 on days, and 20 on nights. A total of 15 EPs who worked day shifts got gastro, and 5 EPs who worked night shifts got gastro.
Gastro (+) Gastro (-) Totals
Day shift (+) 15 10 25
Day shift (-) 5 15 20
Totals 20 20 45
Of 75 EM residents, 65 of them pass the exam. 10 people were at this lecture, and 9 of them were among the ones who passed.
What is the exposure?
What is the outcome?
Fill in the 2X2 table.
Of 75 EM residents, 65 of them pass the exam. 10 people were at this lecture, and 9 of them were among the ones who passed.
Pass (+) Pass (-) Totals
Lecture (+) 9 10
Lecture (-)
Totals 65 75
Of 75 EM residents, 65 of them pass the exam. 10 people were at this lecture, and 9 of them were among the ones who passed.
Pass (+) Pass (-) Totals
Lecture (+) 9 1 10
Lecture (-) 56 9 65
Totals 65 10 75
2000 pts with severe bleeding from trauma were randomized to get TXA or not – 1000 in each group. 500 pts in total died, and 75 of them had received TXA.
What is the exposure?
What is the outcome?
Fill in the 2X2 table.
2000 pts with severe bleeding from trauma were randomized to get TXA or not – 1000 in each group. 500 pts in total died, and 75 of them had received TXA.
Death (+) Death (-) Totals
TXA (+) 75 1000
TXA (-) 1000
Totals 500 2000
2000 pts with severe bleeding from trauma were randomized to get TXA or not – 1000 in each group. 500 pts in total died, and 75 of them had received TXA.
Death (+) Death (-) Totals
TXA (+) 75 925 1000
TXA (-) 425 575 1000
Totals 500 1500 2000
Risk
Risk is a proportion
Risk is a probability of something occurring
Risk represents incidence
Number of outcomes occurring out of all possible outcomes
Flip a coin 10 times: heads occur 5 times, do not occur 5 times
Risk of heads is 5/10 or ½ or 50%.
Risk
45 ED physicians worked over the last month, 25 on days, and 20 on nights. A total of 15 EPs who worked day shifts got gastro, and 5 EPs who worked night shifts got gastro.
Gastro (+) Gastro (-) Totals
Day shift (+) 15 10 25
Day shift (-) 5 15 20
Totals 20 20 45
What is the risk of getting gastro on day shift?What is the risk of someone on night shift getting gastro?
Risk
45 ED physicians worked over the last month, 25 on days, and 20 on nights. A total of 15 EPs who worked day shifts got gastro, and 5 EPs who worked night shifts got gastro.
Gastro (+) Gastro (-) Totals
Day shift (+) 15 10 25
Day shift (-) 5 15 20
Totals 20 20 45
Number of outcomes occurring on day shift = 15Number of total possible outcomes occurring on day shift = 25Risk = 15/25 or 60%
Risk
45 ED physicians worked over the last month, 25 on days, and 20 on nights. A total of 15 EPs who worked day shifts got gastro, and 5 EPs who worked night shifts got gastro.
Gastro (+) Gastro (-) Totals
Day shift (+) 15 10 25
Day shift (-) 5 15 20
Totals 20 20 45
Number of outcomes occurring on night shift = 5Number of total possible outcomes occurring on night shift = 20Risk = 5/20 or 25%
Odds
Odds are a ratio
Number of outcomes occurring vs. outcomes not occurring
Less intuitive
Flip a coin 10 times: heads occur 5 times, do not occur 5 times
Odds are 5:5 or 1:1
Odds
45 ED physicians worked over the last month, 25 on days, and 20 on nights. A total of 15 EPs who worked day shifts got gastro, and 5 EPs who worked night shifts got gastro.
Gastro (+) Gastro (-) Totals
Day shift (+) 15 10 25
Day shift (-) 5 15 20
Totals 20 20 45
What are the odds of someone on day shift getting gastro?What are the odds of someone on night shift getting gastro?
Odds
45 ED physicians worked over the last month, 25 on days, and 20 on nights. A total of 15 EPs who worked day shifts got gastro, and 5 EPs who worked night shifts got gastro.
Gastro (+) Gastro (-) Totals
Day shift (+) 15 10 25
Day shift (-) 5 15 20
Totals 20 20 45
Number of outcomes occurring = 15Number of outcomes not occurring = 10Odds = 15:10 = 3:2 or 1.5
Odds
45 ED physicians worked over the last month, 25 on days, and 20 on nights. A total of 15 EPs who worked day shifts got gastro, and 5 EPs who worked night shifts got gastro.
Gastro (+) Gastro (-) Totals
Day shift (+) 15 10 25
Day shift (-) 5 15 20
Totals 20 20 45
Number of outcomes occurring = 5Number of outcomes not occurring = 15Odds = 5:15= 1:3 or .33
Risk vs. Odds
Risk
What is the risk (probability) of drawing a diamond from a deck of cards?
Odds
What are the odds of drawing a diamond from a deck of cards?
Risk vs. Odds
Risk
What is the risk (probability) of drawing a diamond from a deck of cards?
13 diamonds out of 52 cards (or 1 out of 4)
13/52 = 25%
Odds
What are the odds of drawing a diamond from a deck of cards?
13 diamonds to 39 non-diamonds (or 1 to 3)
13:39 = 1:3 odds
More Examples
Risk
Of 75 EM residents, 65 of them pass the exam. 10 people were at this lecture, and 9 of them were among the ones who passed.
Pass (+) Pass (-) Totals
Lecture (+) 9 1 10
Lecture (-) 56 9 65
Totals 65 10 75
What is the risk of passing if you went to the lecture?What is the risk of passing if you didn’t go to the lecture?
Risk
Of 75 EM residents, 65 of them pass the exam. 10 people were at this lecture, and 9 of them were among the ones who passed.
Pass (+) Pass (-) Totals
Lecture (+) 9 1 10
Lecture (-) 56 9 65
Totals 65 10 75
Number of passes if you went to lecture = 9Number of total possible passes if you went to lecture = 10Risk = 9/10 or 90%
Risk
Of 75 EM residents, 65 of them pass the exam. 10 people were at this lecture, and 9 of them were among the ones who passed.
Number of passes if you didn’t go to lecture = 56Number of total possible passes if you didn’t go to lecture = 65Risk = 56/65 or 86%
Pass (+) Pass (-) Totals
Lecture (+) 9 1 10
Lecture (-) 56 9 65
Totals 65 10 75
Risk
2000 pts with severe bleeding from trauma were randomized to get TXA or not – 1000 in each group. 500 pts in total died, and 75 of them had received TXA.
Death (+) Death (-) Totals
TXA (+) 75 925 1000
TXA (-) 425 575 1000
Totals 500 1500 2000
What is the risk of dying among those who got TXA?What is the risk of dying among those who didn’t get TXA?
Risk
2000 pts with severe bleeding from trauma were randomized to get TXA or not – 1000 in each group. 500 pts in total died, and 75 of them had received TXA.
Death (+) Death (-) Totals
TXA (+) 75 925 1000
TXA (-) 425 575 1000
Totals 500 1500 2000
Number of deaths with TXA = 75Number of total possible deaths with TXA = 1000Risk = 75/1000 or 7.5%
Risk
2000 pts with severe bleeding from trauma were randomized to get TXA or not – 1000 in each group. 500 pts in total died, and 75 of them had received TXA.
Death (+) Death (-) Totals
TXA (+) 75 925 1000
TXA (-) 425 575 1000
Totals 500 1500 2000
Number of deaths without TXA = 425Number of total possible deaths without TXA = 1000Risk = 425/1000 or 42.5%
Odds
Of 75 EM residents, 65 of them pass the exam. 10 people were at this lecture, and 9 of them were among the ones who passed.
Pass (+) Pass (-) Totals
Lecture (+) 9 1 10
Lecture (-) 56 9 65
Totals 65 10 75
What are the odds of someone at the lecture passing?What are the odds of someone not at the lecture passing?
Odds
Of 75 EM residents, 65 of them pass the exam. 10 people were at this lecture, and 9 of them were among the ones who passed.
Pass (+) Pass (-) Totals
Lecture (+) 9 1 10
Lecture (-) 56 9 65
Totals 65 10 75
Number of outcomes occurring = 9Number of outcomes not occurring = 1Odds = 9:1
Odds
Of 75 EM residents, 65 of them pass the exam. 10 people were at this lecture, and 9 of them were among the ones who passed.
Pass (+) Pass (-) Totals
Lecture (+) 9 1 10
Lecture (-) 56 9 65
Totals 65 10 75
Number of outcomes occurring = 56Number of outcomes not occurring = 9Odds = 56:9 or 6.2:1
Odds
2000 pts with severe bleeding from trauma were randomized to get TXA or not – 1000 in each group. 500 pts in total died, and 75 of them had received TXA.
Death (+) Death (-) Totals
TXA (+) 75 925 1000
TXA (-) 425 575 1000
Totals 500 1500 2000
What are the odds of someone who got TXA dying?What are the odds of someone who didn’t get TXA dying?
Odds
2000 pts with severe bleeding from trauma were randomized to get TXA or not – 1000 in each group. 500 pts in total died, and 75 of them had received TXA.
Death (+) Death (-) Totals
TXA (+) 75 925 1000
TXA (-) 425 575 1000
Totals 500 1500 2000
Number of outcomes occurring = 75Number of outcomes not occurring = 925Odds = 75:925 or 3:37 or 0.08:1
Odds
2000 pts with severe bleeding from trauma were randomized to get TXA or not – 1000 in each group. 500 pts in total died, and 75 of them had received TXA.
Death (+) Death (-) Totals
TXA (+) 75 925 1000
TXA (-) 425 575 1000
Totals 500 1500 2000
Number of outcomes occurring = 425Number of outcomes not occurring = 925Odds = 425:925 or 17:37 or 0.46:1
Risk Ratios and Odds Ratios
Looks at strength of association
We know there’s a risk of gastro on day shift – how much more than from night shift?
You are more likely to pass after a lecture – how much more likely?
You are less likely to die with TXA in trauma – how much less?
Risk Ratio
Risk ratio = relative risk (same thing) = RR
Observational Studies:Relative risk = risk in exposed
risk in nonexposed
Experimental Studies:Risk of event in experimental group = a/a+b = EER
Risk of event in control group = c/c+d = CER
Relative risk = EER/CER
Risk Ratio
45 ED physicians worked over the last month, 25 on days, and 20 on nights. A total of 15 EPs who worked day shifts got gastro, and 5 EPs who worked night shifts got gastro.
Gastro (+) Gastro (-) Totals
Day shift (+) 15 10 25
Day shift (-) 5 15 20
Totals 20 20 45
What is the relative risk?
Risk Ratio
45 ED physicians worked over the last month, 25 on days, and 20 on nights. A total of 15 EPs who worked day shifts got gastro, and 5 EPs who worked night shifts got gastro.
Gastro (+) Gastro (-) Totals
Day shift (+) 15 10 25
Day shift (-) 5 15 20
Totals 20 20 45
Risk of gastro in day shift: 15/25 = .6Risk of gastro in night shifts: 5/20 = .25Risk ratio = .6/.25 = 2.4
Risk Ratio
45 ED physicians worked over the last month, 25 on days, and 20 on nights. A total of 15 EPs who worked day shifts got gastro, and 5 EPs who worked night shifts got gastro.
Gastro (+) Gastro (-) Totals
Day shift (+) 15 10 25
Day shift (-) 5 15 20
Totals 20 20 45
ED physicians on day shift were 2.4 X more likely to get gastro than those on night shift.
Odds Ratio
Odds ratio = OR
Observational Studies:Odds ratio = odds in exposed
odds in nonexposed
Experimental Studies:Odds of event in experimental group = a/b
Odds of event in control group = c/d
Odds ratio = a/b / c/d
* if you’re interested, this comes out to the cross-product, or
a x d / b x c
Odds Ratio
45 ED physicians worked over the last month, 25 on days, and 20 on nights. A total of 15 EPs who worked day shifts got gastro, and 5 EPs who worked night shifts got gastro.
Gastro (+) Gastro (-) Totals
Day shift (+) 15 10 25
Day shift (-) 5 15 20
Totals 20 20 45
What is the odds ratio?
Odds Ratio
45 ED physicians worked over the last month, 25 on days, and 20 on nights. A total of 15 EPs who worked day shifts got gastro, and 5 EPs who worked night shifts got gastro.
Gastro (+) Gastro (-) Totals
Day shift (+) 15 10 25
Day shift (-) 5 15 20
Totals 20 20 45
Odds of gastro in day shift: 15/10 = 1.5Odds of gastro in night shifts: 5/15 = 0.33Odds ratio = 1.5/.33 = 4.5
Odds Ratio
45 ED physicians worked over the last month, 25 on days, and 20 on nights. A total of 15 EPs who worked day shifts got gastro, and 5 EPs who worked night shifts got gastro.
Gastro (+) Gastro (-) Totals
Day shift (+) 15 10 25
Day shift (-) 5 15 20
Totals 20 20 45
Odds ratio = 15/10 / 5/15 = 15 X 15 / 5 X 10 = 4.5
Odds Ratio
45 ED physicians worked over the last month, 25 on days, and 20 on nights. A total of 15 EPs who worked day shifts got gastro, and 5 EPs who worked night shifts got gastro.
Gastro (+) Gastro (-) Totals
Day shift (+) 15 10 25
Day shift (-) 5 15 20
Totals 20 20 45
The odds of getting gastro from day shift were 4.5:1 compared to night shift
Risk Ratio
Of 75 EM residents, 65 of them pass the exam. 10 people were at this lecture, and 9 of them were among the ones who passed.
Pass (+) Pass (-) Totals
Lecture (+) 9 1 10
Lecture (-) 56 9 65
Totals 65 10 75
What is the risk ratio?What is the odds ratio?
Risk Ratio
Of 75 EM residents, 65 of them pass the exam. 10 people were at this lecture, and 9 of them were among the ones who passed.
Pass (+) Pass (-) Totals
Lecture (+) 9 1 10
Lecture (-) 56 9 65
Totals 65 10 75
Risk in exposed (event) group = 9/10 = .9Risk in non-exposed (control) group = 56/65 = .86Risk Ratio = 0.9/0.86 = 1.05
Odds Ratio
Of 75 EM residents, 65 of them pass the exam. 10 people were at this lecture, and 9 of them were among the ones who passed.
Pass (+) Pass (-) Totals
Lecture (+) 9 1 10
Lecture (-) 56 9 65
Totals 65 10 75
Odds in exposed (event) group = 9:1 = 9Odds in non-exposed (control) group = 56:9 = 6.2Odds Ratio = 9/6.2 = 1.45
or:9X9 / 56X1 = 1.45
Risk
2000 pts with severe bleeding from trauma were randomized to get TXA or not – 1000 in each group. 500 pts in total died, and 75 of them had received TXA.
Death (+) Death (-) Totals
TXA (+) 75 925 1000
TXA (-) 425 575 1000
Totals 500 1500 2000
What is the relative risk?What is the odds ratio?
Risk
2000 pts with severe bleeding from trauma were randomized to get TXA or not – 1000 in each group. 500 pts in total died, and 75 of them had received TXA.
Death (+) Death (-) Totals
TXA (+) 75 925 1000
TXA (-) 425 575 1000
Totals 500 1500 2000
Risk in exposed (event) group = 75/1000 = .075Risk in non-exposed (control) group = 425/1000 = .425Risk Ratio = .075 / 0.425 = 0.18
Odds
2000 pts with severe bleeding from trauma were randomized to get TXA or not – 1000 in each group. 500 pts in total died, and 75 of them had received TXA.
Death (+) Death (-) Totals
TXA (+) 75 925 1000
TXA (-) 425 575 1000
Totals 500 1500 2000
Odds in exposed (event) group = 75:925 = 0.08Odds in non-exposed (control) group = 425:575 = 0.74Odds Ratio = 0.08/0.74 = 0.11
or:75X575 / 425X925 = 0.11
ARR
Absolute risk reduction = difference in event rates
ARR = risk difference
ARR = CER – EER
If the control group has an outcome rate of 15%, and the treatment/exposure group has an outcome rate of 10%, what is the ARR?
ARR
Absolute risk reduction = difference in event rates
ARR = risk difference
ARR = CER – EER
If the control group has an outcome rate of 15%, and the treatment/exposure group has an outcome rate of 10%, what is the ARR?
ARR = 15%-10% = 5%
NNT
Number needed to treat = the number of patients needed to treat to prevent one bad outcome
NNT = 1 / ARR
Highly tied to ARR
If the absolute risk reduction is 10% - ie. The control group has deaths in 20% of patients, and the treatment group has deaths in 10% of patients, then how many patients would you have to treat to prevent one death?
NNT
Number needed to treat = the number of patients needed to treat to prevent one bad outcome
NNT = 1 / ARR
Highly tied to ARR
If the absolute risk reduction is 10% - ie. The control group has deaths in 20% of patients, and the treatment group has deaths in 10% of patients, then how many patients would you have to treat to prevent one death?
NNT = 1/.1 = 10
ARR
Of 2000 residents at a school, half of them had their call cut in half. By the end of residency, 18 of them had dropped out, 8 of whom had had the reduction in call.
Draw the 2X2 table
ARR
Of 2000 residents at a school, half of them had their call cut in half. By the end of residency, 18 of them had dropped out, 8 of whom had had the reduction in call.
Dropped out Didn’t drop out
Totals
Call reduced (+)
8 992 1000
Call not reduced
10 990 1000
Totals 18 1982 2000
ARR
Of 2000 residents at a school, half of them had their call cut in half. By the end of residency, 18 of them had dropped out, 8 of whom had had the reduction in call.
Dropped out Didn’t drop out
Totals
Call reduced (+)
8 992 1000
Call not reduced
10 990 1000
Totals 18 1982 2000What are the event rates (risk)?
ARR
Of 2000 residents at a school, half of them had their call cut in half. By the end of residency, 18 of them had dropped out, 8 of whom had had the reduction in call.
Dropped out Didn’t drop out
Totals
Call reduced (+)
8 992 1000
Call not reduced
10 990 1000
Totals 18 1982 2000EER = 8/1000 = 0.008CER = 10/1000 = 0.01
ARR
Of 2000 residents at a school, half of them had their call cut in half. By the end of residency, 18 of them had dropped out, 8 of whom had had the reduction in call.
Dropped out Didn’t drop out
Totals
Call reduced (+)
8 992 1000
Call not reduced
10 990 1000
Totals 18 1982 2000What is the relative risk?
ARR
Of 2000 residents at a school, half of them had their call cut in half. By the end of residency, 18 of them had dropped out, 8 of whom had had the reduction in call.
Dropped out Didn’t drop out
Totals
Call reduced (+)
8 992 1000
Call not reduced
10 990 1000
Totals 18 1982 2000RR = 8/1000 / 10/1000 = 0.8
ARR
Of 2000 residents at a school, half of them had their call cut in half. By the end of residency, 18 of them had dropped out, 8 of whom had had the reduction in call.
Dropped out Didn’t drop out
Totals
Call reduced (+)
8 992 1000
Call not reduced
10 990 1000
Totals 18 1982 2000What is the absolute risk reduction?
ARR
Of 2000 residents at a school, half of them had their call cut in half. By the end of residency, 18 of them had dropped out, 8 of whom had had the reduction in call.
Dropped out Didn’t drop out
Totals
Call reduced (+)
8 992 1000
Call not reduced
10 990 1000
Totals 18 1982 2000ARR = CER – EER = 0.01-0.008 = 0.002 or 0.2%
ARR
Of 2000 residents at a school, half of them had their call cut in half. By the end of residency, 18 of them had dropped out, 8 of whom had had the reduction in call.
Dropped out Didn’t drop out
Totals
Call reduced (+)
8 992 1000
Call not reduced
10 990 1000
Totals 18 1982 2000What is the NNT?
ARR
Of 2000 residents at a school, half of them had their call cut in half. By the end of residency, 18 of them had dropped out, 8 of whom had had the reduction in call.
Dropped out Didn’t drop out
Totals
Call reduced (+)
8 992 1000
Call not reduced
10 990 1000
Totals 18 1982 2000NNT = 1/ARR = 1/0.002 = 200
RRR
Relative risk reduction = a proportion comparing the risk between different groups
RRR = CER-EER / CER
RRR = ARR / CER
RRR
Relative risk reduction = a proportion comparing the risk between different groups
Intuitively easy to understand but tells you nothing about the actual risk of the outcome
Eg. Of all 5th year ED residents in the country who took the Kingston course, say 1% of people failed the exam, and of those who didn’t take it, 2% failed.
RRR = CER – EER / CER = 1%/2% = 50%
So the relative risk reduction is 50%! 2% to 1% - that’s cutting the risk in half! If you didn’t take the Kingston course, you have a 50% greater risk of failing!
RRR
Relative risk reduction = a proportion comparing the risk between different groups
Intuitively easy to understand but tells you nothing about the actual risk of the outcome
But the absolute risk reduction is only 1%. If you only start out with a miniscule risk of failing, relative risk reductions are deceiving.
RRR
Of 2000 residents at a school, half of them had their call cut in half. By the end of residency, 18 of them had dropped out, 8 of whom had had the reduction in call.
Dropped out Didn’t drop out
Totals
Call reduced (+)
8 992 1000
Call not reduced
10 990 1000
Totals 18 1982 2000What is the RRR?
RRR
Of 2000 residents at a school, half of them had their call cut in half. By the end of residency, 18 of them had dropped out, 8 of whom had had the reduction in call.
Dropped out Didn’t drop out
Totals
Call reduced (+)
8 992 1000
Call not reduced
10 990 1000
Totals 18 1982 2000RRR = CER-EER / CER = 10/1000 – 8/1000 / 10/1000= .002 / .01 = 0.2= 20%
More Examples
ARR/RRR
Of 75 EM residents, 65 of them pass the exam. 10 people were at this lecture, and 9 of them were among the ones who passed.
Pass (+) Pass (-) Totals
Lecture (+) 9 1 10
Lecture (-) 56 9 65
Totals 65 10 75
What is the relative risk reduction?What is the absolute risk reduction?What is the NNT?
ARR/RRR
Of 75 EM residents, 65 of them pass the exam. 10 people were at this lecture, and 9 of them were among the ones who passed.
Pass (+) Pass (-) Totals
Lecture (+) 9 1 10
Lecture (-) 56 9 65
Totals 65 10 75
RRR = CER-EER/CER = 56/65 - 9/10 / 56/65 = .86-.9/.86 = 0.047 = 4.7%ARR = CER-EER = 56/65 - 9/10 = 0.04 = 4%NNT = 1/ARR = 25
ARR/RRR
2000 pts with severe bleeding from trauma were randomized to get TXA or not – 1000 in each group. 500 pts in total died, and 75 of them had received TXA.
Death (+) Death (-) Totals
TXA (+) 75 925 1000
TXA (-) 425 575 1000
Totals 500 1500 2000
What is the relative risk reduction?What is the absolute risk reduction?What is the NNT?
ARR/RRR
2000 pts with severe bleeding from trauma were randomized to get TXA or not – 1000 in each group. 500 pts in total died, and 75 of them had received TXA.
Death (+) Death (-) Totals
TXA (+) 75 925 1000
TXA (-) 425 575 1000
Totals 500 1500 2000
RRR = CER-EER/CER = 425/1000 – 75/1000 / 425/1000 = .35/.425 = 0.82 = 82%ARR = CER-EER = 425/1000 - 75/1000 = 0.35 = 35%NNT = 1/ARR = 1/.35 = 2.9
Diagnostic Tests
Sensitivity and specificity are measures of a test and do not change with the patient population
Diagnostic Tests
Disease (+) Disease (-) Totals
Test (+) a b a+b
Test (-) c d c+d
Totals a+c b+d a+b+c+d
“The truth always rises to the top”
Sens and Spec
Sensitivity and specificity are measures of a test and do not change with the patient population
Sensitivity is about the population that has disease. Disease (+) Disease (-) Totals
Test (+) a b
Test (-) c d
Totals a+c b+d
Sens = a/ a+c
Sens and Spec
Sensitivity and specificity are measures of a test and do not change with the patient population
Sensitivity is about the population that has disease.
Sensitivity = ability of the test to correctly identify those who have disease
Sensitivity = the proportion of patients with disease who will have a positive test
“given a patient with disease, what is the probability of a positive test?”
Sens and Spec
Sensitivity and specificity are measures of a test and do not change with the patient population
Specificity is about the population that does not have disease. Disease (+) Disease (-) Totals
Test (+) a b
Test (-) c d
Totals a+c b+d
Spec = d/ b+d
Sens and Spec
Sensitivity and specificity are measures of a test and do not change with the patient population
Specificity is about the population that does not have disease.
Specificity = ability of the test to correctly identify those who do not have disease
Specificity = the proportion of patients without disease who will have a negative test
“given a patient without disease, what is the probability of a negative test?”
PPV and NPV
PPV and NPV
PPV and NPV are far more clinically relevant
Why?
Like us, they start with a test result and tell us the likelihood of disease given that test result
They are highly influenced by prevalence and change with patient populations
PPV and NPV
PPV is about the population that has a positive test
Disease (+) Disease (-) Totals
Test (+) a b a+b
Test (-) c d c+d
Totals a+c b+d
PPV = a/ a+b
PPV and NPV
PPV is about the population that has a positive test
PPV = the proportion of patients who test positive who actually have disease
PPV = given a positive test, the likelihood that this patient actually has disease
“given a positive test, what is the probability of having disease?”
PPV and NPV
NPV is about the population that has a negative test
Disease (+) Disease (-) Totals
Test (+) a b a+b
Test (-) c d c+d
Totals a+c b+d
NPV = d/ c+d
PPV and NPV
NPV is about the population that has a negative test
NPV = the proportion of patients who test negative who actually do not have disease
NPV = given a negative test, the likelihood that this patient actually does not have disease
“given a negative test, what is the probability of not having disease?”
Diagnostic Tests
An ED physician tests the use of u/s to detect appendicitis in the ED. Of 100 patients, 45 of them ultimately have appendicitis on CT. U/S correctly identified 30, but there were also 20 false positives.
Disease (+) Disease (-) Totals
Test (+) a b
Test (-) c d
Totals a+c b+d
Fill in the 2X2 table.
Diagnostic Tests
An ED physician tests the use of u/s to detect appendicitis in the ED. Of 100 patients, 45 of them ultimately have appendicitis on CT. U/s correctly identified 30, but there were also 20 false positives.
Disease (+) Disease (-) Totals
Test (+) 30 20 50
Test (-) 15 35 50
Totals 45 55 100
What is the sensitivity?What is the specificity?
Diagnostic Tests
An ED physician tests the use of u/s to detect appendicitis in the ED. Of 100 patients, 45 of them ultimately have appendicitis on CT. U/s correctly identified 30, but there were also 20 false positives.
Disease (+) Disease (-) Totals
Test (+) 30 20 50
Test (-) 15 35 50
Totals 45 55 100
Sens = 30/45 = 67%Spec = 35/55 = 64%
Diagnostic Tests
An ED physician tests the use of u/s to detect appendicitis in the ED. Of 100 patients, 45 of them ultimately have appendicitis on CT. U/s correctly identified 30, but there were also 20 false positives.
Disease (+) Disease (-) Totals
Test (+) 30 20 50
Test (-) 15 35 50
Totals 45 55 100
What is the PPV?What is the NPV?
Diagnostic Tests
An ED physician tests the use of u/s to detect appendicitis in the ED. Of 100 patients, 45 of them ultimately have appendicitis on CT. U/s correctly identified 30, but there were also 20 false positives.
Disease (+) Disease (-) Totals
Test (+) 30 20 50
Test (-) 15 35 50
Totals 45 55 100
PPV = 30/50 = 60%NPV = 35/50 = 70%
Diagnostic Tests
A general surgery resident decides to take this same test and validate it. The test still has a sensitivity of 67%, and specificity of 64%, but in the 50 pts he sees, 45 of them end up having appendicitis.
Disease (+) Disease (-) Totals
Test (+)
Test (-)
Totals
Fill in the 2X2 table
Diagnostic Tests
A general surgery resident decides to take this same test and validate it. The test still has a sensitivity of 67%, and specificity of 64%, but in the 50 pts he sees, 45 of them end up having appendicitis.
Disease (+) Disease (-) Totals
Test (+) 30 2 32
Test (-) 15 3 18
Totals 45 5 50
What is the PPV?What is the NPV?
Diagnostic Tests
A general surgery resident decides to take this same test and validate it. The test still has a sensitivity of 67%, and specificity of 36%, but in the 50 pts he sees, 45 of them end up having appendicitis.
Disease (+) Disease (-) Totals
Test (+) 30 2 32
Test (-) 15 3 18
Totals 45 5 50
PPV = 30/32 = 94%NPV = 3/18= 17%
Diagnostic Tests
A patient is really worried that he might have Ebola. His naturopath did a test that has a 98% sensitivity for Ebola, and it came back positive. However, you look up this test and find it has a 5% specificity, and the prevalence of Ebola in the region is 0.01%
Disease (+) Disease (-) Totals
Test (+)
Test (-)
Totals
Given this positive test, what is the likelihood of this patient having disease?
Diagnostic Tests
A patient is really worried that he might have Ebola. His naturopath did a test that has a 98% sensitivity for Ebola, and it came back positive. However, you look up this test and find it has a 5% specificity, and the prevalence of Ebola in the region is 0.01%
Disease (+) Disease (-) Totals
Test (+) 98 949905 950003
Test (-) 2 49995 49997
Totals 100 999900 1000000
PPV = 98/950003 = 0.01%
Likelihood Ratios
Ratio between the probability of observing the result in a patient with disease and the probability of observing the result in a patient without disease
Advantages:Combine sens and spec
Can calculate probability of disease for an individual pt
Can be calculated for several levels of test or finding
(+) Likelihood Ratios
Ratio between the probability of having a positive test in a patient with disease and the probability of having a positive test in a patient without disease
LR (+) = sens / (1-spec) = TP/FP
> 10 greatly increase probability of disease (rule in)
<0.1 greatly decreases probability of disease (rule out)
(eg CT in appendicitis – LR(+) = 37, highly useful for ruling in disease)
(-) Likelihood RatiosRatio between the probability of having a negative test in a patient with disease and the probability of having a negative test result in a patient without disease
LR (-) = 1-sens / spec = FN/TN
> 10 greatly increase probability of disease (rule in)
<0.1 greatly decreases probability of disease (rule out)
(eg. D-dimer – LR(-) is 0.05, useful for negative result. LR(+) is around 2.4 – not useful for positive result)
Likelihood Ratios
2 options to use likelihood ratio to calculate post-test probability1. Convert to pre-test odds, multiply by LR,
convert post-test odds to probability
2. Use Fagan nomogram