Measures of Effect: An Introduction

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

http://www.cadth.ca/

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


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


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


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

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

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


untreated• e.g., elderly, heart failure,

anterior wall infarction• 30% mortality among treated

– How would you describe the effect of the new drug?



Trial 1: High Risk Patients



Trial 2: Low Risk Patients– New drug for acute myocardial

infarction to reduce mortality– Later studied in a lower risk


untreated• e.g., younger, uncomplicated

inferior wall infarction



Trial 2: Low Risk Patients– New drug for acute myocardial

infarction to reduce mortality– Later studied in a lower risk


untreated• e.g., younger, uncomplicated

inferior wall infarction• 7.5% mortality among treated

– How would you describe the effect of the new drug?



Trial 2: Low Risk Patients



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.

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?



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?


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


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

Measures of Effect: An Introduction

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