Effect modification and confounding
Intended Learning Outcomes
By the end of the session, you are expected to be able to:
1. Define concept of effect modification (interaction) and
confounding
2. List and explain the steps required to identify effect
modification in a dataset
3. Be able to interpret results tables and identify evidence of
effect modification
4. Summarise how confounding may affect results, and ways to
deal with confounding in observational studies
5. Define the concept of residual confounding in contrast to the
general concept of confounding
6. Evaluate confounding in published observational studies 2
Influences on health
• Rare to have simple exposure and outcome with
no other influences
• Health status and risk of most diseases is subject
to multiple influences (e.g. CHD)
• One-variable-at-a-time approach (2x2 table)
• Public health & intervention
• Associations may vary according to other factors
3
Alternative explanations for your results
• Chance
Bias (yesterday)
• Effect
modification
• Confounding
4
• Strive to avoid at design stage
• Control or adjust at analysis stage
• Identify at design stage
• Carefully describe and
discuss at analysis stage
• Strive to avoid at design stage
• Control or adjust at analysis stage
Biological Interaction
Last’s Dictionary of Epidemiology (4th Ed)
Biological interaction is the interdependent operation
of two or more causes to produce, prevent or control
disease
Factor 1 Outcome
+ Factor 2
5
Examples of biological interaction
1. Antibiotic tetracycline and tooth
discolouration
• Tetracycline is associated with discoloration
of teeth but mainly among children <8 years
• effect of antibiotic (exposure) on tooth colour
(outcome) is modified by age (effect modifier)
6
2. Measles and vaccination
• Exposure to measles virus is associated with
measles infection if not vaccinated or has not had
measles
• Here immune status = effect modifier
Statistical interaction
when the association between exposure and
outcome of interest varies according to the level
of a third factor (the effect modifier)
Exposure Outcome
Note: may not imply biological interaction
7
Effect modifier (the 3rd factor)
Examples of statistical interaction
8
Energy from total fat and coronary heart
disease (CHD)
Energy from total fat is associated
with CHD among younger women
(HR=2.68, 95%CI 1.40,5.12) but
not among older women (HR=1.22,
95%CI 0.86,1.71) (Source:
Jakobsen et al. Am J Epidemiol. 2004)
0
0.5
1
1.5
2
2.5
3
<50 yrs 50+ yrs
Low fat high fat
Effort Reward Imbalance (ERI) and
depressive symptoms among children
(China)
10
School-related stress (ERI school
questionnaire) is associated with depressive
symptoms among low SES children
compared to high SES children (Source: Guo
et al. Int J Environ Res Public Health. 2014)
Measuring effect of association
• Absolute risk or rate (differences)
• Relative risk or rate (ratios)
11
Additive and multiplicative models
Absolute risk = Additive model (acts in additive way)
• When the absolute difference in risk or rate between those
with and without the exposure varies according to a third
variable
Relative risk = Multiplicative model (acts in a multiplicative way)
• When the risk ratio, rate ratio or odds ratio for an
association between exposure and disease varies
according to a third variable
Generally interested in interactions on a relative scale
12
How can we determine whether interaction is
present?
Adopt a statistical approach – two options
1. Assess homogeneity of effects
2. Compare observed and expected effects
13
Option 1 – Assessing homogeneity of effects
Crude Crude 2 x 2 table
Calculate crude measure of effect
Stratify by 3rd variable
Stratum 1 Stratum 2 Calculate measure of effect
for each stratum (values of 3rd variable)
Test whether stratum specific
measures of effect are similar (p-value
from homogeneity test)
Not sig. Sig. p-value
Investigate other possible Evidence of
influences of 3rd variable effect modification
(later in the session) (Stratified NOT
pooled estimates reported)
14
Assessing homogeneity of effects. Example 1
Additive model (absolute risk difference)
• Factor A = 0.9 - 0.4 = 0.5
• No factor A = 0.3 – 0.2 = 0.1
Multiplicative model (risk ratios)
• Factor A = 0.9/0.4 = 2.25
• No factor A = 0.3/0.2 = 1.5 15
Exposure Factor A No factor A
Yes Risk = 0.9 0.3
No 0.4 0.2
Evidence of
interaction
Evidence of
interaction
Absolue risk of disease according to exposure and factor A
• Case-control study of history of blood pressure (BP) and
myocardial infarction (MI)
• Crude OR for association between BP & MI =1.4
• Age-specific stratum estimates
<=60 years OR = 0.97
>60 years OR =1.87
• Evidence of effect modification on the multiplicative
(relative) scale
• Test for homogeneity, p-value = 0.01
16
Assessing homogeneity of effects. Example 2
How can we determine whether interaction is
present?
Two options
1. Assess homogeneity of effects
2. Compare observed and expected effects
17
Comparison of observed & expected effects. Example 1.
18
Exposure
Factor A (the 3rd factor)
Yes No
Yes 0.9 0.3
No 0.4 0.2
Risk of obesity according to presence / absence of 2 variables
What is the background risk?
Observed excess risk:
• due to only exposure0.3 - 0.2 = 0.1
• due to only factor A 0.4 - 0.2 = 0.2
• due to both 0.9 - 0.2 = 0.7
Expected excess risk due to both 0.1 + 0.2 = 0.3
On additive scale, there is evidence of effect modification
because joint observed effect ≠ expected effect
Measure of effect = risk difference
Model = Additive model
Joint observed effect
Combined
independent effects
0.2
Exposure
Factor A
Yes No
Yes 0.9 0.3
No 0.4 0.2
What is the background risk?
Observed risk ratio (RR)
• due to only exposure 0.3 / 0.2 = 1.5
• due to only factor A 0.4 / 0.2 = 2.0
• due to both 0.9 / 0.2 = 4.5
Expected risk ratio due to both 1.5 x 2.0 = 3.0
Suggests effect modification with regard to risk ratio
Because joint observed RR ≠ expected RR (Obs RR = exp RR x 1.5)
Measure of effect = risk ratio
Model = multiplicative model
Interaction term
Risk of obesity according to the presence or absence of 2 variables
Comparison of observed & expected effects. Example 1 (cont)
19
Joint observed
effect
Combined
indep. effects
NOTE: The
effect of A is
greater in the
presence of
exposure, and
vice versa.
0.2
Reciprocal nature of effect modification
• For any given outcome and two predictor variables, it is a
purely arbitrary decision which predictor variable will be
the exposure, and which the potential effect modifier.
• Effect modification is reciprocal. In any of examples, the
exposure and other factor (or variable) could have be
labelled the other way round, and the same effect would
still have been seen.
20
Positive and negative interaction
Synergism or positive interaction (interaction term > 1)
• Presence (or higher values) of Factor A strengthens the
association between exposure and disease
• the combined effect is greater than the sum (or product) of
the parts
Antagonism or negative interaction (interaction term < 1)
• Presence (or higher values) of Factor A weakens the
association between exposure and disease.
• the combined effect is less than the sum (or product) of
the parts
21
Ischemic heart disease mortality rates, smoking and age
in British doctors study
Age
(years)
Annual death rate
per 100,000 men
Non-smokers Heavy smokers
<45 7 104
45-54 118 393
55-64 531 1025
All <65 166 427
22
Source: Table V of Doll & Peto 1976, BMJ 2, 1525-1536
http://www.bmj.com/content/2/6051/1525
Ischemic heart disease mortality rates, smoking and age
in British doctors study
Age
(years)
Annual death rate
per 100,000 men Odds ratio (heavy
vs non-smokers)
Non-smokers Heavy smokers
<45 7 104 104/7 =14.9
45-54 118 393 393/118 = 3.3
55-64 531 1025 1025/531 = 1.9
All <65 166 427 2.7
Odds ratio
(55-64 vs <45)
531/7 = 75.9 1025/104 = 9.9
23
24
Summary of results
Association between
smoking and CHD
OR Conclusion
Crude assoc. 2.7 Odds of CHD 2.7 times higher among smokers
compared to non-smokers
Stratified anal.
<45 14.9 Among those aged <45, odds of CHD 14.9 times
higher among smokers than non-smokers
45-54
55-64
3.3
1.9
Among those aged 45-54, odds of CHD 3.3 times
higher among smokers than non-smokers
Among those aged 55-64, odds of CHD 1.9 times
higher among smokers than non-smokers
Test of homogeneity p <
0.001
Evidence against null hypothesis → heterogeneity
→ interaction between smoking and age in the
association with CHD
What is confounding?
A situation in which the effects of two processes are not
separated.
The distortion of the apparent effect of an exposure on
risk, brought about by the association with other factors
that can influence the outcome. (Last’s Dict. Epi., 4th
ed, 2001)
Latin verb: confundere = to mix up, to confuse
Potential alternative explanation(s)
CONFOUNDING (confusing one thing with another) arises
when there are important differences between groups
being compared. The differences are associated with the
variable or factor of interest, and with the health
outcome of interest.
Confounding must be considered in the evaluation of
epidemiological associations.
A confounding variable (confounding factor, or
confounder) is a third variable that correlates (positively
or negatively) with both the exposure and outcome.
Statistical definition of a ‘confounder’
To be a confounder, a variable must:
be related to exposure;
be related to outcome;
and not lie on the causal pathway between exposure and
outcome
mediation
The confounding triangle: 2 exposures
and an outcome
Yellow fingers Lung cancer
?smoking
???
Davey Smith and Phillips BMJ 1992
β-carotene intake and cardiovascular mortality
Egger et al BMJ 1998
Example of
spurious
findings
produced by
confounding
The critic’s view
“The disparity between observational studies and
RCTs…is probably explained by a failure to
appreciate the complex and important
differences between adults with high vitamin
concentrations and those with lower. High
intake of antioxidant vitamins might not be
causally related to cardiovascular and other
diseases, but rather serves as a proxy indicator
of a host of [protective] factors.”
Lawlor et al Lancet 2004
Difference between systematic error and
confounding
Systematic error, as the name implies, is intrinsic to study
design and methods – the result of weaknesses in
scientific approach
Confounding is intrinsic to the population and units of
observation e.g. people, places, being studied – it is not a
study artefact, it is ‘out there’
Dealing with confounding
Two ways to deal with confounding:
At the design stage or at the analysis stage
In both cases:
Confounding must be addressed at the design stage of a
study. If potential confounding factors are not
measured, the study will be weak, even uninterpretable.
1. Minimising by design
randomisation e.g. drug trial
restriction e.g. exclude ever-smokers
matching e.g. case-control study
Minimising by design
Randomised controlled trials (RCT) have strongest protection
against differences in the groups being compared
Confounding factors (measured and unmeasured) tend to be
evenly distributed across groups
RCTs are the gold standard design to establish a causal
relationship between cause and effect, but are not always
feasible.
It is not ethical to randomise interventions thought to be
harmful.
2. Controlling in analysis
stratification
standardisation
multivariable analysis (adjustment)
Controlling in analysis: stratification
Data analysed and results presented according to subgroups
of related characteristics.
Confounding is indicated if an association between exposure
and outcome is seen in the whole sample but not in the
subgroups
e.g. examine the effect of SES in smokers and non-smokers
INDIVIDUALS
SMOKERS
NON-SMOKERS
Test association between
SES and cancer
Test association between
SES and cancer
Combine these if the effect similar
across strata
Study evaluating the
association between SES
and stomach cancer
Summary of results
Association
between SES
and cancer
OR P-value Conclusion
Crude assoc. 1.63 <0.001 Odds of cancer 1.63 times higher
if low SES
Stratified anal.
Smokers 1.44 <0.001 Odds of cancer 1.44 times higher
if low SES
Non-smokers 1.40 0.006 Odds of cancer 1.40 times higher
if low SES
Adjusted for
smoking
1.43 <0.001 SES-cancer effect is confounded
by smoking. OR=1.43 for low SES
rather than 1.63
Multivariable analysis
Probably the most common method
The only feasible way to deal with several potential
confounding factors at the same time
Unmeasured confounding factors or measurement error in
confounding factors may lead to leftover confounding
(residual confounding)
Multivariable analysis to test confounding
Is A a confounding factor for the effect of B on O?
calculate a crude estimate of the effect of B on O e.g. ageand
sex-adjusted HR, OR or RR
repeat the analysis controlling for potential confounder A
(age-, sex- and confounder-A adjusted HR, OR or RR)
Compare the two estimates, if different, A is a confounder
Standardisation
When comparing different populations, or different
time periods, there is always the danger that age
structure of the compared populations differ.
Risk of most diseases increases with age.
Age acts as a confounder.
Cancer death rates are much lower in Mexico than in the UK.
One explanation is that risk factors are much less common in
Mexico
Another explanation is the difference in cancer mortality
is not genuine.
Cancer rates are higher in older people. The higher the proportion
of older persons in a population, the higher the crude cancer
mortality rate, even if age-specific death rates are the same.
Age standardised death rates: example
Hypothetical example: cancer mortality rate (MR) in three
populations with symmetrical, young and old population
structures
Symmetrical Young OldAge
group
% MR % MR % MR
25-44
45-64
65+
Total
33%
33%
33%
100%
10
100
500
203
50%
30%
20%
100%
10
100
500
135
20%
30%
50%
100%
10
100
500
282
Direct standardisation
Standardisation is based on a standard age structure, that of
the whole sample or of some external population
Calculate a weighted average of the age-specific death rates in
each sub-group (country, region, social class, etc.), using as
weights the proportions of the entire sample in age bands,
e.g. age 30-34.9
The adjusted (weighted) rate in each sub-group is comparable
because it is the rate that would be observed if the age
structure was the same in each group.
Age
2000 US Standard
Million
2000 US Standard Population
(Census P25-1130)
European Standard Million
World Standard
Million
00 years 13,818 3,794,901 16,000 24,000
01-04 years 55,317 15,191,619 64,000 96,000
05-09 years 72,533 19,919,840 70,000 100,000
10-14 years 73,032 20,056,779 70,000 90,000
15-19 years 72,169 19,819,518 70,000 90,000
20-24 years 66,478 18,257,225 70,000 80,000
25-29 years 64,529 17,722,067 70,000 80,000
30-34 years 71,044 19,511,370 70,000 60,000
35-39 years 80,762 22,179,956 70,000 60,000
40-44 years 81,851 22,479,229 70,000 60,000
45-49 years 72,118 19,805,793 70,000 60,000
50-54 years 62,716 17,224,359 70,000 50,000
55-59 years 48,454 13,307,234 60,000 40,000
60-64 years 38,793 10,654,272 50,000 40,000
65-69 years 34,264 9,409,940 40,000 30,000
70-74 years 31,773 8,725,574 30,000 20,000
75-79 years 26,999 7,414,559 20,000 10,000
80-84 years 17,842 4,900,234 10,000 5,000
85+ years 15,508 4,259,173 10,000 5,000
Total 1,000,000 274,633,642 1,000,000 1,000,000
http://seer.cancer.gov/stdpopulations/stdpop.19ages.html
23.9
21.6
21.3
20.7
20.0
20.0
17.5
17.4
16.2
16.2
16.0
15.8
15.7
15.3
14.8
14.4
13.5
9.7
9.0
0 5 10 15 20 25 30
Italy
Luxembourg
Finland
Spain
Age standardised death rate per 100,000 population
C H M U
Directly standardised death rates from breast cancer
Selected countries 1998*, Females aged under 65
Greece
France
Netherlands
Denmark
Canada
United Kingdom
Ireland
Sweden
Austria
Portugal
Belgium
Germany
USA
Japan
Source: WHO Annual of Statistics, HFA Indicators (ICD 174)
England
# Rates are calculated using the European Standard Population to take account of
differences in age structure.
#
Brstcerv.ppt (02/2000)
* Data for 1998 except for Belgium 1995.
Indirect standardisation
Standardisation is based on age-specific disease rates in the
reference population (group), weighted by the age structure of the
study population
Calculate the expected number of deaths in the group of interest
that would be obtained if it experienced the same age-specific
rates as the reference group
The adjusted (weighted) number of deaths in the group of interest
is compared to the observed number:
Standardised mortality ratio (SMR)
= Observed deaths * 100 %
------------------------
Expected deaths
Mortality from amenable and non-amenable
causes Czech Republic 1985-1995
50
60
70
80
90
100
110
1985 1990 1995
Non-amenable
Amenable
50
60
70
80
90
100
110
1985 1990 1995
Non-amenable
Amenable
Men, 1985=100 Women, 1985=100
Blazek & Dzurova, 2000
M Bartley, Health inequalities, 2nd edition pp 48-60, 70-73
R Bhopal, Concepts of epidemiology, 2002 pp194-9
Further reading for those wanting to know more
about age standardisation
Confounding - summary
Condition for confounding – risk factor and
confounding factor are correlated with each other, and
both are correlated with outcome
Confounding leads to spurious findings
Confounding should be considered at the design stage
of all studies. It can be minimised by design
– randomisation
– matching
Or in analysis, if the necessary measurements are
available
– stratification
– multivariable adjustment
Residual confounding
Last 4th ed, 2001
Confounding that persists after unsuccessful attempts to
adjust for it. The sources of residual confounding are
insufficiently detailed information, improper categorization,
and misclassification of one or more confounding
variables. It is a variable-specific concept.
“we only rarely have the information needed to fully adjust for
confounding”
Olsen and Basso AJE 1999
Calculating attenuation
If a risk estimate is unaffected by controlling (adjusting) for
potential confounders then it is robust
If the risk estimate is largely abolished by adjustment it is not
an independent risk factor
The extent to which an effect is reduced is called the
attenuation
RRunadj – RRadj
Attenuation = -------------------------- x 100%
RRunadj - 1
Confounding – yes or no?
A rule of thumb: if an effect is attenuated by 10% or more,
then confounding is probably important
Model (279 cases, total N=4291 ) HR 95% CI P
Age, sex, CRP>10 mg/L 1.40 (1.29-1.51) <0.0001
+ occupational status 1.39 (1.28-1.50) <0.0001
+ prevalent CHD, infectious symptoms 1.39 (1.28-1.50) <0.0001
+ BMI categories, waist circumference 1.22 (1.11-1.33) <0.0001
+ systolic BP, diastolic BP, BP treatment 1.20 (1.10-1.32) <0.0001
+ serum HDL-cholesterol, TG 1.17 (1.07-1.28) 0.001
Hazard ratio for diabetes per doubling of serum CRP at age 49
with sequential adjustments. 13 year follow-up
Whitehall II study
Brunner et al PLoS Med 2008
CRP-T2D effect attenuated by 53% on adjustment
53% on adjustment
Confounding vs. interaction
Confounding
• Alternative explanation
• Distorts the “truth”
• Efforts to remove it to get
nearer to the “truth”
• When present, stratum
specific effects are similar
to each other but different
from the overall crude
effect.
Effect modification
• One factor modifies effect
of another factor
• It is genuine, not artefact
• Property of the relationship
between factors
• We should detect and
describe it but not remove
it.
Difference between interaction and
confounding
Confounding: stratum-specific effects of the risk factor
of interest will be smaller (usually) but they will be similar
Interaction/effect modification: also examined by
stratification. As the label ‘effect modification’ indicates,
the stratum-specific effects will be different. If very
different, this is called strong interaction.
Steps in testing an association
1. Is there an association?
2. If yes, is it due to confounding?
3. If not, is the association similar in strata formed on the
basis of potential effect modifiers?
4a. If yes, there is no effect modification/interaction
4b. If no, effect modification/interaction is present
Conclusions: association does not mean causation
Associations are often observed: when alternative
explanations (chance, bias, confounding) have been
considered and rejected, the association may be causal
Strength of association (effect size), replication and
biological plausibility are further considerations
Note that the precise biological mechanisms linking
smoking and lung cancer were not known 40 years ago,
however the evidence on other dimensions of the link was
powerful
These issues will be explored in the session on causality