Measures of effect
 So far, χ2 test – testing whether there is an
association between two proportions using a 2x2
(or 2xn) table
 We are often interested in the relative difference
between two proportions rather than the actual
difference
 The effect estimates that we present are then
ratios: there are three main measures we will use:
◦ Rate ratio
◦ Risk ratio
◦ Odds ratio
Relative measures of effect (relative
risk)
We have 2 groups of individuals:
 An exposed group (group with risk factor
of interest) and unexposed group
(without such factor of interest)
 We are interested in comparing the
amount of disease (mortality or other
health outcome) in the exposed group to
that in the unexposed group
Risk/rate
 Measures the strengths of association
between the risk factor and disease
 Incidence rate or Risk in exposed (r1)
 Incidence rate or Risk in unexposed (r0)
Risk ratio
• we calculate the risk ratio (RR) as:
RR=r1/r0
Risk difference
• the absolute difference between two risks (or
rates)
RD = r1 – r0
Example: cohort study of oral
contraceptive use and heart attack
Myocardial infarction
Yes No Total
OC use
Yes 25 400 425
No 75 1500 1575
Total 100 1900 2000
Risk (exposed) = 25/425=0.059
Risk (unexposed) = 75/1575=0.048
Relative risk = 0.059/0.048 = 1.23
 We can also have different strata of
exposure.We may calculate ratio measures
for each strata – we compare measure of
frequency in each level with measure of
frequency in the baseline (unexposed) level.
 Example: Death rates from CHD in smokers
and non-smokers by age
Age Smokers
rate
Nonsmokers
rate
Rate ratio
35-44 0.61 0.11 5.5
45-54 2.40 1.12 2.1
55-64 7.20 4.90 1.5
65-74 14.69 10.83 1.4
75-84 19.18 21.20 0.9
85+ 35.93 32.66 1.1
ALL AGES 4.29 3.30 1.3
What can you say about this table?
Age Smokers
rate
Nonsmokers
rate
Rate ratio
35-44 0.61 0.11 5.5
45-54 2.40 1.12 2.1
55-64 7.20 4.90 1.5
65-74 14.69 10.83 1.4
75-84 19.18 21.20 0.9
85+ 35.93 32.66 1.1
ALL AGES 4.29 3.30 1.3
The rate ratio decreases with increasing age. It may
suggest that the effect of smoking on the rate of CHD is
higher in younger ages.
 Alternative measure of risk
Odds ratio
The odds of disease is the number of cases divided by
the number of non-cases
Cases
Odds = ------------
Non cases
Odds ratio (OR) is ratio of odds of disease among
exposed (oddsexp) and odds of disease among
unexposed (oddsunexp)
OR= oddsexp/ oddsunexp
We can calculate
• Odds (exposed) Oexp=25/400
• Odds (unexposed) Ounexp=75/1500
• Odds ratio OR = Oexp / Ounexp = 1.25
Myocardial infarction
Yes No Total
OC use
Yes 25 400 425
No 75 1500 1575
Total 100 1900 2000
Odds ratio as an approximation to
the risk ratio
 For a rare disease, odds ratio is
approximately equal to the risk ratio
(because denumerators are very similar)
 For a common conditions, OR overestimates
the true RR
Measures of population impact
 Population attributable risk (PAR) is
the absolute difference between the risk
(or rate) in the whole population and the
risk or rate in the unexposed group
PAR = r – r0
Population attributable risk fraction
(PARF or PAR%)
 It is a measure of the proportion of all cases
in the study population (exposed and
unexposed) that may be attributed to the
exposure, on the assumption of a causal
association
 It is also called the aetiologic fraction, the
percentage population attributable risk or
the attributable fraction
 If r is rate in the total population
PAF = PAR/r
PAR = r – r0
PAF = (r-r0)/r
Risk or rate difference
the absolute difference between two risks (or
rates)
RD = r1 – r0
Measure of the absolute effect
Similar for rates = rate difference = incidence
rate in exposed – incidence rate in unexposed
Measure of
effect
Use of the measure How to interpret results
Risk
Difference
Public Health
Interested in excess disease burden
due to factor (“Attributable risk”)
Close to 0 = little effect
Large difference = large effect
Risk Ratio Epidemiology
Causation
“This factor doubles the risk of the
disease”
Close to 1 = little effect
Large ratio = large effect
Close to 0 = large effect!Odds Ratio As for Risk Ratio
“This factor doubles the odds of the
disease”
Only possibility (case-control study)
More advanced statistical methods
(logistic regression)
Exercise
 50 persons attended a garden party
 25 of them developed diarrhoea in the
next 3 days
 What was the risk of diarrhoea among
the participants of the party?
Exercise – cont.
 30 party visitors had a BBQ (minced
meat)
 24 of them developed diarrhoea
 20 people did not eat BBQ
 1 of them developed diarrhoea
 How would you calculate RR related to
eating BBQ?
Exercise – cont.
 Risk among unexposed R0:
 1/20
 Risk among exposed R1:
 24/30
 Relarive risk RR=R1/R0=(24/30)/(1/20)=16
Summary of this part
1. Construct 2-way table to examine
association between two categorical variables
2. Conduct Chi-squared test to assess the
association between two categorical variables
3. Calculate measures of the effect for binary
data
– Risk difference
– Risk ratio (relative risk)
– Odds ratio