clinical epidemiology bootcamp

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

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?


Fill in the 2X2 table.


Gastro (+) Gastro (-) Totals

Day shift (+) 15 25

Day shift (-) 5 20

Totals 45



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.





Pass (+) Pass (-) Totals

Lecture (+) 9 10

Lecture (-)

Totals 65 75



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.





Death (+) Death (-) Totals

TXA (+) 75 1000

TXA (-) 1000

Totals 500 2000



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



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



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



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



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



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



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



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



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


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%


Lecture (+) 9 1 10

Lecture (-) 56 9 65

Totals 65 10 75

Risk



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



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



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



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



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



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



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



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



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



Day shift (+) 15 10 25

Day shift (-) 5 15 20

Totals 20 20 45

What is the relative risk?

Risk Ratio



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



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



Day shift (+) 15 10 25

Day shift (-) 5 15 20

Totals 20 20 45

What is the odds ratio?

Odds Ratio



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



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



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



Lecture (+) 9 1 10

Lecture (-) 56 9 65

Totals 65 10 75

What is the risk ratio?What is the odds ratio?

Risk Ratio



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



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



TXA (+) 75 925 1000

TXA (-) 425 575 1000

Totals 500 1500 2000

What is the relative risk?What is the odds ratio?

Risk



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



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


Dropped out Didn’t drop out

Totals

Call reduced (+)

8 992 1000

Call not reduced

10 990 1000

Totals 18 1982 2000

ARR



Totals

Call reduced (+)

8 992 1000

Call not reduced

10 990 1000

Totals 18 1982 2000What are the event rates (risk)?

ARR



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



Totals

Call reduced (+)

8 992 1000

Call not reduced

10 990 1000

Totals 18 1982 2000What is the relative risk?

ARR



Totals

Call reduced (+)

8 992 1000

Call not reduced

10 990 1000

Totals 18 1982 2000RR = 8/1000 / 10/1000 = 0.8

ARR



Totals

Call reduced (+)

8 992 1000

Call not reduced

10 990 1000

Totals 18 1982 2000What is the absolute risk reduction?

ARR



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



Totals

Call reduced (+)

8 992 1000

Call not reduced

10 990 1000

Totals 18 1982 2000What is the NNT?

ARR



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


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


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



Totals

Call reduced (+)

8 992 1000

Call not reduced

10 990 1000

Totals 18 1982 2000What is the RRR?

RRR



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



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



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



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



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 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 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


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


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


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


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.


Test (+) a b

Test (-) c d

Totals a+c b+d


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.


Test (+) 30 20 50

Test (-) 15 35 50

Totals 45 55 100

What is the sensitivity?What is the specificity?

Diagnostic Tests



Test (+) 30 20 50

Test (-) 15 35 50

Totals 45 55 100

Sens = 30/45 = 67%Spec = 35/55 = 64%

Diagnostic Tests



Test (+) 30 20 50

Test (-) 15 35 50

Totals 45 55 100

What is the PPV?What is the NPV?

Diagnostic Tests



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.


Test (+)

Test (-)

Totals

Fill in the 2X2 table

Diagnostic Tests



Test (+) 30 2 32

Test (-) 15 3 18

Totals 45 5 50

What is the PPV?What is the NPV?

Diagnostic Tests



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%


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%


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

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