Measures of Effect: An Introduction
Epidemiology Supercourse Astana, July 2012
Philip la Fleur, RPh MSc(Epidem)Deputy Director, Center for Life [email protected]
Come to Ottawa, Canada and get “Out and About”
Canadian Agency for Drugs and Technologies in Health (www.cadth.ca)
Emerg Med J 2003;20:164-168
ObjectivesUnderstand how to calculate and interpret and articulate measures of effect and morbidity
1. 2x2 Table• Risk• Odds• Relative Risk• Odds Ratio
2. Relative Risk Reduction and Absolute Risk Reduction3. Number needed to Treat and Number needed to Harm
SummaryOutcome Outcome Total
Exposure Yes No
Yes a b a + b
No c d c + d
Total a + c b + d N
1. 2x2 TableOutcome Outcome Total
Exposure Yes No
Yes a b a + b
No c d c + d
Total a + c b + d N
Risk
• Probability that an event will occur (Last 2001)• E.g. that a person will die within one year• Risk in Exposed = a/(a+b)• Risk in unexposed, “Baseline risk” = c/(c+d)
Outcome Outcome Total
Exposure Yes No
Yes a b a + b
No c d c + d
Total a + c b + d N
Odds• The ratio of the probability of occurrence of an
event to that of non-occurrence• E.g. odds of smokers developing a chronic cough• Odds in Exposed = a/b• Odds in unexposed, “Baseline odds” = c/d
Outcome Outcome Total
Exposure Yes No
Yes a b a + b
No c d c + d
Total a + c b + d N
Risk Versus OddsRisk Odds
Conversion:
Odds = Risk/(1-Risk)
Risk = Odds / (1 + Odds)
0.80 4.0 ⌂⌂⌂⌂/⌂0.67 2.0 ⌂⌂/⌂0.50 1.0 ⌂/⌂0.20 0.25 ⌂/⌂⌂⌂⌂0.10 0.11 ⌂/⌂⌂⌂⌂⌂⌂⌂⌂⌂
Would you swim here?
Develop a Question: PICO
Population: children under 5 years of age
Intervention (exposure): Swimming in the Ishim River
Comparator (control): Not swimming in the Ishim river
Outcome: Otitis Media
Question: What is the risk that a child under 5 will develop an ear infectionafter swimming in the Ishim river?
Odds Ratio
Outcome Outcome Total
Exposure Yes No
Yes a b a + b
No c d c + d
Total a + c b + d N
Odds Ratio
Odds of getting infection for swimmers: 40/60 = 0.67
Ear Infection
Ear Infection
Total
Swimming in Ishim
Yes No
Yes 40 60 100
No 5 95 100
Total 45 155 200
Odds of getting infection for non-swimmers: 5/95 = 0.052
Relative Risk
Outcome Outcome Total
Exposure Yes No
Yes a b a + b
No c d c + d
Total a + c b + d N
Relative Risk
Risk of getting infection for swimmers: 40/100 = 0.4
Ear Infection
Ear Infection
Total
Swimming in Ishim
Yes No
Yes 40 60 100
No 5 95 100
Total 45 155 200
Risk of getting infection for non-swimmers: 5/100 = 0.05
OR versus RR Key Messages
• Odds and Odds Ratios are difficult to conceptualize but statisticians prefer them in some situations because of their mathematical properties
• Odds Ratios always exaggerate the relative risk, but when baseline risk is low (e.g. <10%), the OR approximates the relative risk
• Relative Risk is a more intuitive measure and is becoming more common in medical literature
ObjectivesUnderstand how to calculate and interpret and articulate measures of effect and morbidity
1. 2x2 Table• Risk• Odds• Relative Risk• Odds Ratio
2. Relative Risk Reduction and Absolute Risk Reduction3. Number needed to Treat and Number needed to Harm
2. Relative Risk Reduction and
Absolute Risk ReductionObjectives•Learn how to interpret risk of events in the control (baseline group) and intervention groups (treatment group) from published studies.•Understand the concepts of relative risk reduction and absolute risk reduction and how they usually differ from one population to another.
Trial 1: High Risk Patients– New drug for acute myocardial
infarction to reduce mortality– First studied in a high risk
population:• 40% mortality at 30 days among
untreated• e.g., elderly, heart failure,
anterior wall infarction
Ref: http://www.cche.net/usersguides/ebm_tips.asp
Trial 1: High Risk Patients– New drug for acute myocardial
infarction to reduce mortality– First studied in a high risk
population:• 40% mortality at 30 days among
untreated• e.g., elderly, heart failure,
anterior wall infarction• 30% mortality among treated
– How would you describe the effect of the new drug?
Ref: http://www.cche.net/usersguides/ebm_tips.asp
Trial 1: High Risk Patients
Ref: http://www.cche.net/usersguides/ebm_tips.asp
Trial 2: Low Risk Patients– New drug for acute myocardial
infarction to reduce mortality– Later studied in a lower risk
population:• 10% mortality at 30 days among
untreated• e.g., younger, uncomplicated
inferior wall infarction
Ref: http://www.cche.net/usersguides/ebm_tips.asp
Trial 2: Low Risk Patients– New drug for acute myocardial
infarction to reduce mortality– Later studied in a lower risk
population:• 10% mortality at 30 days among
untreated• e.g., younger, uncomplicated
inferior wall infarction• 7.5% mortality among treated
– How would you describe the effect of the new drug?
Ref: http://www.cche.net/usersguides/ebm_tips.asp
Trial 2: Low Risk Patients
Ref: http://www.cche.net/usersguides/ebm_tips.asp
Summary Points for Relative Risk Reduction and Risk Difference
• Relative risk reduction is often more impressive than absolute risk reduction.
• The lower the risk in the control group, the larger the difference between relative risk reduction and absolute risk reduction.
ObjectivesUnderstand how to calculate and interpret and articulate measures of effect and morbidity
1. 2x2 Table• Risk• Odds• Relative Risk• Odds Ratio
2. Relative Risk Reduction and Absolute Risk Reduction3. Number needed to Treat and Number needed to Harm
3. Number Needed to TreatNumber Needed to Harm
Objectives•Learn how to calculate Number Needed to Treat (NNT) from an estimate of risk difference.•Increase awareness of the range of NNTs associated with common interventions.
Definitions
• Number Needed to Treat (NNT):– Number of persons who would have to receive
an intervention for 1 to benefit.
• Number Needed to Harm(NNH):– Number of persons who would have to receive
an intervention for 1 to be experience a adverse event.
Calculating NNT
If a disease has a mortality of 100% without treatment and therapy reduces that mortality to 50%, how many people would you need to treat to prevent 1 death?
Estimate NNT
CER% EER% ARR% NNT
How many 60-year-old patients with mild hypertension would you have to treat with diuretics for 5 years to prevent 1 stroke?
How many people with myocardial infarction would you have to treat with ß-blockers for 2 years to prevent 1 death?
How many people with acute myocardial infarction would you have to treat with streptokinase to prevent 1 person from dying in the next 5 weeks?
Ref: http://www.cche.net/usersguides/ebm_tips.asp
Estimate NNT
CER% EER% ARR% NNT
How many 60-year-old patients with hypertension would you have to treat with diuretics for 5 years to prevent 1 death?
How many people with myocardial infarction would you have to treat with ß-blockers for 2 years to prevent 1 death?
How many people with acute myocardial infarction would you have to treat with streptokinase to prevent 1 person from dying in the next 5 weeks?
Ref: http://www.cche.net/usersguides/ebm_tips.asp
Estimate NNT
CER% EER% ARR% NNT
How many 60-year-old patients with hypertension would you have to treat with diuretics for 5 years to prevent 1 death?
How many people with myocardial infarction would you have to treat with ß-blockers for 2 years to prevent 1 death?
How many people with acute myocardial infarction would you have to treat with streptokinase to prevent 1 person from dying in the next 5 weeks?
Ref: http://www.cche.net/usersguides/ebm_tips.asp
Calculation
NNT= 100/ARR (where ARR is %)or
NNT= 1/ARR (where ARR is proportion)
NNH= 100/ARI (where ARI is %)Or
NNH = 1/ARI (where ARI is proportion)
NNTs from Controlled Trials
Control Event %
Treatment Event %
Absolute Risk
Reduction%
NNT
Population: hypertensive 60-year-oldsTherapy: oral diureticsOutcome: stroke over 5 years
Population: myocardial infarctionTherapy: ß-blockersOutcome: death over 2 years
Population: acute myocardial infarctionTherapy: streptokinase (thrombolytic)Outcome: death over 5 weeks
1
2.5
2.8
100
40
36
2.9 1.9
9.8 7.3
12 9.2
Ref: http://www.cche.net/usersguides/ebm_tips.asp
Population: hypertensive 60-year-oldsOutcome: stroke over 5 years
Depiction of Results in Control Group
Ref: http://www.nntonline.net/
Population: hypertensive 60-year-oldsOutcome: stroke over 5 years
Depiction of Results in Treatment Group
Ref: http://www.nntonline.net/
Bottom Line
• It is easy to mis-estimate baseline risk and effects of therapy
• NNT is easily calculated from the absolute risk reduction (ARR)
• Awareness of threshold NNT can help anticipate the risk reduction to look for in a therapy.
SummaryOutcome Outcome Total
Exposure Yes No
Yes a b a + b
No c d c + d
Total a + c b + d N
References/Slide Sources1. Last JM. A Dictionary of Epidemiology, 4th ed. Oxford University Press, 20012. Guyatt G et al. Users’ Guides to the Medical Literature, 2nd ed. McGraw Hill,
20083. Guyatt G. Tips for Teachers of Evidence Based Medicine. Lecture on Odds and
Risk.4. Grimes and Schulz. Making Sense of Odds and Odds Ratios. Obs & Gyn
2008(111):423-65. Some Slides for Risk Reduction and NNT are from: Alexandra Barratt, Peter C.
Wyer, Rose Hatala, Thomas McGinn, Antonio L. Dans, Sheri Keitz, Virginia Moyer, Gordon Guyatt, Robert Hayward, for the EBM Teaching Tips Working Group (www.cche.net)
6. Smiley Diagrams from: Dr. Chris Cates EBM Website: www.nntonline.net