Download - Outcome Measures in Epidemiology
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Measures Used To Compare Groups
Dr. N. Birkett,School of Epidemiology, Public Health and Preventive Medicine,
University of Ottawa
SUMMER COURSE:INTRODUCTION TO
EPIDEMIOLOGY
AUGUST 25, 1330-1500
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Session OverviewMethods of comparing studies
• Risk/rate ratios• Odd ratios• Difference measures• Number needed to treat• Attributable risk
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ONE BIG WARNING!!!!!The textbook (4th edition) has rotated their 2X2 tables from the normal approach.
That is, they have the outcomes as the rows and the exposure as the columns.
BE WARNED. This could cause confusion with my tables which use the more common approach.
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Comparing studies (1)• Two main types of outcome measures
• Incidence (either risk or rate)• Prevalence
• How do you determine if an exposure is related to an outcome?• Study 2 groups• Need to compare the measure in the two groups.
• Differences• Ratios (we’ll start with this one).
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Comparing studies (2)• Ratios (we’ll start with this one).
• Ratio measures have NO units.• All ratio measures have the same interpretation
• 1.0 = no effect• < 1.0 protective effect• > 1.0 increased risk
• Values over 2.0 are of strong interest
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Comparing studies: Cohorts (3)RISK RATIORisk in exposed = 1,000/10,000Risk in Non-exposed = 100/10,000If exposure increases risk, you would expect the risk in the exposed to be larger than the risk in the unexposed. How much larger can be assessed by the ratio of one to the other:
Disease
Exp
Yes No
Yes 1,000 9,000 10,000
No 100 9,900 10,000
1,100 18,900 20,000
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Comparing studies: Cohorts (4)RISK RATIORisk in exposed = a/(a+b)Risk in Non-exposed = c/(c+d)
If exposure increases risk, you would expect the risk in the exposed to be larger than the risk in the unexposed. How much larger can be assessed by the ratio of one to the other:
Disease
Exp
Yes No
Yes a b a+b
No c d c+d
a+c b+d N
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Comparing studies: Cohorts (5)RISK RATIORisk in exposed = 42/122 = 0.344Risk in Non-exposed = 43/345 = 0.125
Death
Apgar
Yes No
0-3 42 80 122
4-6 43 302 345
85 382 467
0-3: Very low4-6: Moderate7-10: Normal
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Comparing studies: Cohorts (6)RISK DIFFERENCERisk in exposed = 1,000/10,000Risk in Non-exposed = 100/10,000If exposure increases risk, you would expect the risk in the exposed to be larger than the risk in the unexposed. How much larger can be assessed by the difference between the two:
Disease
Exp
Yes No
Yes 1,000 9,000 10,000
No 100 9,900 10,000
1,100 18,900 20,000
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Comparing studies: Cohorts (7)RISK DIFFERENCERisk in exposed = a/(a+b)Risk in Non-exposed = c/(c+d)
If exposure increases risk, you would expect the risk in the exposed to be larger than risk in the unexposed. How much larger can be assessed by the difference between the two:
Disease
Exp
Yes No
Yes a b a+b
No c d c+d
a+c b+d N
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Comparing studies: Cohorts (8)RISK DIFFERENCERisk in exposed = 42/122 = 0.344Risk in Non-exposed = 43/345 = 0.125
Death
Apgar
Yes No
0-3 42 80 122
4-6 43 302 345
85 382 467
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Comparing studies: Cohorts (9)Which comparative measure do you use?• Depends on the circumstances.
• Risk Ratio RELATIVE risk measure• Risk Difference ABSOLUTE risk measure
• Post-menopausal estrogens & endometrial cancer• RR = 2.3• RD = 2/10,000
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Comparing studies: Cohorts (10)RATE RATIORate in exposed = 1,000/9,500Rate in Non-exposed = 100/9,950
If exposure increases the rate of getting the disease, you would expect the rate in the exposed to be larger than the rate in the unexposed. How much larger can be assessed by the ratio of one to the other:
Exp
# Diseased
Person-years
Yes 1,000 9,500
No 100 9,950
1,100 19,450
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Comparing studies: Cohorts (11)RATE RATIORate in exposed = A/Y1
Rate in Non-exposed = B/Y2
If exposure increases the rate of getting the disease, you would expect the rate in the exposed to be larger than the rate in the unexposed. How much larger can be assessed by the ratio of one to the other:
Exp
# Diseased
Person-years
Yes A Y1
No B Y2
A+B Y1+Y2
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Comparing studies: Cohorts (12)RATE RATIORate in exposed = 42/101 = 0.416Rate in Non-exposed = 43/323.5 = 0.133
Apgar
# Diseased
Person-years
0-3 42 101
4-6 43 323.5
85 424.5
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Comparing studies: Cohorts (13)RATE DIFFERENCERate in exposed = 1,000/9,500Rate in Non-exposed = 100/9,950
If exposure increases the rate of getting the disease, you would expect the rate in the exposed to be larger than the rate in the unexposed. How much larger can be assessed by the difference between the two:
Exp
# Diseased
Person-years
Yes 1,000 9,500
No 100 9,950
1,100 19,450
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Comparing studies: Cohorts (14)RATE DIFFERENCERate in exposed = A/Y1
Rate in Non-exposed = B/Y2
If exposure increases the rate of getting the disease, you would expect the rate in the exposed to be larger than the rate in the unexposed. How much larger can be assessed by the difference between the two:
Exp
# Diseased
Person-years
Yes A Y1
No B Y2
A+B Y1+Y2
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Comparing studies: Cohorts (15)RATE DIFFERENCERate in exposed = 42/101 = 0.416Rate in Non-exposed = 43/323.5 = 0.133
Apgar
# Diseased
Person-years
0-3 42 101
4-6 43 323.5
85 424.5
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Comparing studies: Cohorts (16)Some Issues• What does RR mean
• Can mean either• risk ratio or • rate ratio.
• Some people think this is pedantic rather than correct • Need to tell which from context.• Sometimes referred to as Relative Risk (generic term).
• Are risk differences or ratios preferred?• RR’s are much more common• Both have a role to play.
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Comparing studies: Case-control (1)CAN NOT COMPUTE A RISK RATIO!• Can not estimate incidence from a case-control study.• Can not directly compute risk differences.• Why? We choose the subjects based on their outcome status.
Usually, that means making the number of cases and controls equal. Hence, the ‘incidence’ in the case-control study is fixed at 0.50. In real world, it is most likely much lower (1/100,000).
So, what do we do?• Cornfield & Haenzel provided solution in 1960.
• They looked at the ODDS of exposure.• The ratio of the odds of exposure in the cases and controls is almost the same as the
RR, if the disease is rare.
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Comparing studies: Case-control (2)ODDS RATIOOdds of exposure in cases = 900/100Odds of exposure in controls = 400/600If exposure increases rate of getting disease, you would to find more exposed cases than exposed controls. That is, the odds of exposure for cases would be higher. How much higher can be assessed by the ratio of one to the other:
Disease
Exp
Yes No
Yes 900 400 1,300
No 100 600 700
1,000 1,000 2,000
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Comparing studies: Case-control (3)ODDS RATIOOdds of exposure in cases = a/cOdds of exposure in controls = b/dIf exposure increases rate of getting disease, you would to find more exposed cases than exposed controls. That is, the odds of exposure for case would be higher. How much higher can be assessed by the ratio of one to the other:
Disease
Exp
Yes No
Yes a b a+b
No c d c+d
a+c c+d N
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Comparing studies: Case-control (4)Death
Apgar
Yes No
0-3 42 18 60
4-6 43 67 110
85 85 170
NOTE:Risk ratio = 2.76Rate ratio = 3.13
ODDS RATIOOdds of exposure in cases = 42/43 = 0.977Odds of exposure in controls = 18/67 = 0.269
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Comparing studies: Case-control (5)Cohort aside:• You can compute an OR for a cohort. Why would you do
so?• OR’s are the key outcome measure for logistic regression, one of
the most common analysis methods used in epidemiology• Unless disease is common, the OR and the RR from the cohort will
be very similar.• But, where possible, rate ratios are preferred.
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Number needed to treat (1)Consider a clinical trial of a new drug. How many people do we need to treat to prevent one death?
• Incidence rate for the control group is 2 cases per 5 person years. • Incidence rate for the experimental group is 1 case per 5 person
years.
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Number needed to treat (2)• Treat five people for one year:
• Control therapy: 2 deaths• Exp therapy: 1 death• PREVENTED = 1 death
NNT = 5.
• What is the risk difference:• 2/5 – 1/5 = 1/5
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Number needed to treat (3)For diseases with rare outcomes, you will need to treat many people to prevent one outcome, even if the reduction in risk is high:
Relative risk reduction = 0.1IR (Old Rx) = 10/1,000IR (New Rx) = 1/1,000RD = 9/1,000NNT = 1000/9
= 111
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Attributable risks (1)• How much lung cancer can be attributed to smoking?• Measure of exposure IMPACT rather than strength.• There are many AR measures, often with similar names.
Makes things confusing. One book used the same abbreviation for 4 different measures in five pages!
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Attributable risks (2)In exposed subjects
ExpUnexp
RD or Attributable Risk Iexp
Iunexp
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Attributable risks (3)• In the exposed group, the impact of the exposure on
outcome depends on RR only:
• A value of ‘0’ shows no impact.• You shouldn’t compute AR’s unless causation has been
established.
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Attributable risks (4)However, my actual interest was:
In the general population, how much lung cancer was due to smoking?
Depends on two factors:• Strength of the smoking/lung cancer relationship (RR).• How common smoking is in the population (exposure prevalence).
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Attributable risks (5)
ExpUnexp
Attributable Risk,population
Iexp
Iunexp
Population
Ipop
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Attributable risks (5)
ExpUnexp
Attributable Risk,population
Iexp
Iunexp
Population
Ipop
Exposure is uncommon
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Attributable risks (5)
ExpUnexp
Attributable Risk,population
Iexp
Iunexp
Population
Ipop
Exposure is common
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Attributable risks (6)• Risk in the population is a weighted average of
• risk in exposed people• risk in unexposed people.
• The weight is the prevalence of the risk factor in the population:
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Attributable risks (6)Formulae for Population Attributable Risk (PAR)• Usually expressed as a %
• The percent reduction in risk in the population if the risk factor could be completely eliminated:
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Summary: comparisons• Cohort studies
• Relative risk• Relative rate• Risk/rate differences
• Case-control study• Odds-ratio
• Number needed to treat• Attributable risk/fraction
• Measure of the impact of exposure to exposed people or to general population.