Míry asociace a efektu 2
Podíl šancí, rozdíl rizik, atribuce rizika
Hynek Pikhart
 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
Odds of an outcome
 The analysis of the association between
exposure and outcome is often based on
ODDS and ODDS RATIOS
 Odds is the number of cases divided by the
number of non-cases
Odds ratio = measure of the magnitude of the
association
 It is defined as ratio of odds of outcome (e.g.
disease) among exposed (Odds1) and odds of
outcome (e.g. disease) among unexposed (Odds0)
Outcome
Exposure Yes No Total
Exposed D1 H1 N1
Unexposed D0 H0 N0
Total D H N

Hypertension
Occupation Yes No Total
Manual 96 144 240
Non-manual 72 228 300
Total 168 372 540
We can calculate
Odds (exposed) O1=96/144
Odds (unexposed) O0=72/228
Odds ratio (OR) = O1 / O0 = 0.67/0.32=2.11
Back to our example...
Risk (last session)
 Risk: Proportion of people with a certain
characteristic within a group
Mathematical:
Number of cases (d)
Risk (r) =
Population at risk (N)
r = d / N
Risk ratio
 Often we compare 2 groups – exposed and unexposed to a
risk factor
 Research question: Do exposed participants have a higher
risk of disease compared with unexposed participants?
◦ Risk in exposed (r1)
◦ Risk in unexposed (r0)
 Risk ratio (RR) = r1 / r0 = (d1 / N1) / (d0 / N0)
 RR measures the strength of association between risk factor
and disease
Example
Risk (exposed) = 96 / 240 = 0.40
Risk (unexposed) = 72 / 300 = 0.24
Risk ratio = 0.40 / 0.24 = 1.67
Hypertension
Employment Yes No Total
Manual 96 144 240
Non-manual 72 228 300
Total 168 372 540
Odds ratio → approximation of risk ratio
 Rare disease outcome: Odds ratio ~ risk
ratio
◦ Similar denominators
 Example of employment and hypertension
◦ OR = 2.11
◦ RR = 1.67
Rare disease → OR~RR
RR OR
Cases Cases
N Population N controls
~
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
Example
Exposure
Status
Diseased
No
Disease
Population Incidence
(Risk)
Exposed 500 9,500 10,000 0.050
Not Exposed 900 89,100 90,000 0.010
Column
Totals
1,400 98,600 100,000 0.014
Example – cont.
 Risk in exposed=0.05
 Risk in unexposed=0.01
 Risk ratio = 5
Example – cont.
 Risk in exposed=0.05
 Risk in unexposed=0.01
 Risk ratio = 5
 Odds in exposed=500/9500=0.0526
 Odds in unexposed=900/89100=0.0101
 Odds ratio=5.21
Example – cont.
 Risk in exposed=0.05
 Risk in unexposed=0.01
 Risk difference = 0.05-0.01=0.04
Example – cont.
 Risk in exposed=0.05
 Risk in unexposed=0.01
 Risk difference = 0.05-0.01=0.04
 PAR = r – r0 = 0.014-0.010=0.004
 PAF = PAR/r=0.004/0.014=0.286 (28.6% of
cases)
 0.286x1400=400 cases (80% of exposed
cases)
Example -cont
Exposure
Status
Diseased
No
Disease
Population Incidence
(Risk)
Exposed 5000 5,000 10,000 0.50
Not Exposed 9000 81,000 90,000 0.10
Column
Totals
14,000 86000 100,000 0.14
Example – cont.
 Risk in exposed=0.5
 Risk in unexposed=0.1
 Risk ratio = 5
Example – cont.
 Risk in exposed=0.5
 Risk in unexposed=0.1
 Risk ratio = 5
 Odds in exposed=5000/5000=1
 Odds in unexposed=9000/81000=0.111
 Odds ratio=9
Example – cont.
 Risk in exposed=0.5
 Risk in unexposed=0.1
 Risk difference = 0.5-0.1=0.4
Example – cont.
 Risk in exposed=0.5
 Risk in unexposed=0.1
 Risk difference = 0.5-0.1=0.4
 PAR = r – r0 = 0.14-0.10=0.04
 PAF = PAR/r=0.04/0.14=0.286 (28.6% of
cases)
 0.286x14000=4000 cases (80% of exposed
cases)
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
 Relative risk RR=R1/R0=(24/30)/(1/20)=16