Epidemiologie E350
Confounding a standardizace
Three major issues in interpretation of
any epidemiological study
•Chance (random variation) – statistics
•Bias (i.e. systematic error)
•Confounding
Confounding
•Situation when a third factor is associated with
both exposure and disease
•Association between exposure and disease
may not be causal; instead, it is due to a third
factor which is associated with both exposure
and disease.
Confounding
Exposure Disease
Confounding
factor
Example
Alcohol Lung cancer
Case-control study of alcohol and lung
cancer
Alcohol No alcohol
Cases 450 300
Controls 200 250
Estimated odds ratio = 1.9
The same data stratified by smoking:
Non-smokers Smokers
Alcohol No alcohol Alcohol No
alcohol
Cases 50 100 400 200
Controls 100 200 100 50
Estimated odds ratio 1.0 1.0
Alcohol and smoking in controls
Alcohol No alcohol
Smokers 100 50
Non-smokers 100 200
Non-drinkers: 1 in 5 were smokers,
Drinkers: 1 in 2 were smokers.
Confounding
Alcohol Lung cancer
Smoking
Most common confounders:
•Sex (men have higher mortality and more risk
factors)
•Age (risk of most diseases increases with age)
•Socioeconomic status (risk of most diseases
higher in lower SE groups)
•Ethnic group
•Smoking
•Alcohol
•etc...
Control of confounding
Design
•Randomisation
•Restriction
•Matching
Analysis (if data collected)
•Stratification
•Regression modelling
Step-by-step guide to the stratified
analysis
Example
• A study was undertaken to assess whether smokingh increased
risk of stomach cancer. Data were collected from 36,000
individuals
Stomach cancer
Yes No Total
Smokers 800 (4.0%) 19200 20000
Non-smokers 400 (2.5%) 15600 16000
Total 1200 34800 36000
Example
• X2=62.07 p<0.001
Odds(low) 800/19200
OR = ----------- = ------------ = 1.63
Odds(high) 400/15600
• 95% CI = 1.44-1.84 (Stata)
• The study found a significantly higher odds of cancer in
smokers
But is it real association?
• Smokers are more likely to be drinkers
• Drinking doubles the risk of stomach cancer
• THEREFORE
some of the higher risk in smokers could be because they tend
to drink more frequently (and have higher risk because of
drinking).
?
Smoking Stomach cancer
Alcohol
?
Confounding
• We say that alcohol is a confounding variable because it is
related both to the outcome variable and to exposure
(smoking)
• Ignoring alcohol in the analysis leads to misleading results
INDIVIDUALS
Drinkers
Non-drinkers
Test association between
smoking and cancer
X2 and OR
Test association between
smoking and cancer
X2 and OR
Pool these if OR similar across strata
= Mantel-Haenszel pooled X2 and OR
Example
DRINKERS Stomach cancer
Yes No Total
Smokers 140 6000 6140
Non-smokers 130 7800 7930
Total 270 13800 14070
DRINKERS Stomach cancer
Yes No Total
Smokers 660 13200 13860
Non-smokers 270 7800 8070
Total 930 21000 21930
Example
NON-DRINKERS Stomach cancer
Yes No Total
Smokers 140 (2.28%) 6000 6140
Non-smokers 130 (1.64%) 7800 7930
Total 270 13800 14070
DRINKERS Stomach cancer
Yes No Total
Smokers 660 (4.76%) 13200 13860
Non-smokers 270 (3.35%) 7800 8070
Total 930 21000 21930
Stratum specific calculations
NON-DRINKERS
X2=7.55 p=0.006
OR (95% CI) = 1.40 (1.09-1.79)
DRINKERS:
X2=25.19 p<0.001
OR (95% CI) = 1.44 (1.25-1.67)
Interpretation
•Stratum specific OR are lower than the crude
OR (1.44 and 1.40 vs 1.63)
•Stratum specif OR are similar to each other
•This means that it is logical and sensible to pool
them
•If they are different (very different) – we should
consider drinking to be an EFFECT MODIFIER
(the effect of smoking on cancer is modified by
drinking status)
Steps for dealing with possible
confounders
1. Calculate crude X2 and OR – DONE (X2 signif. and OR
calculated)
2. List possible confounders – we have chosen alcohol in our
example
3. Determine whether they are possible confounders
a. Association with exposure
b. Association with outcome
c. Not on causal pathway
Steps for dealing with possible
confounders
4. Do stratified analysis by possible confounder
5. Calculate pooled X2 and OR (= look at the association that
is adjusted for confounder)
6. If crude OR and pooled OR different – conclude that
variable is a confounder
Summary of results
• Results are best summarized in the table
Association
between smoking
and cancer
OR P-value Conclusion
Crude assoc. 1.63 <0.001 Odds of cancer 1.63 times higher
if smoker
Stratified anal.
Drinkers 1.44 <0.001 Odds of cancer 1.44 times higher
if smoker
Non-drinkers 1.40 0.006 Odds of cancer 1.40 times higher
if smoker
Adjusted for
drinking
1.43 <0.001 Confounded. Odds of cancer 1.43
times higher rather than 1.63
times higher if smoker
Interpretation of results
•There is still an association between smoking
and cancer but less strong than originally
showed (in crude analysis)
•The confounding variable (drinking) made the
association between smoking and cancer look
stronger that it is.
•There is NO STATISTICAL TEST to help you
decide whether change in odds ratios (1.63 to
1.43 in our example) is large enough to say
that variable is confounder.
Residual confounding
•Unmeasured confounding factors or
measurement error in confounding factors may
lead to residual confounding.
•The possibility of residual confounding cannot
be completely eliminated in observational
studies.
Standardisation
Standardisation in epidemiology
•A numerical (quantitative / statistical) approach
to remove confounding by a common
characteristic
•Age
•Sex
•Marital status
•Education
•The most common is standardisation of
mortality or incidence rates for age and sex
Trends in crude and age-standardized rates for diabetes
mellitus in men and women, China, 1990-2017
(Int J Env Res Public Health. 16. 158. 10.3390/ijerph16010158.)
Crude vs. standardised trends:
•Trends more dramatic for crude rates
•Diabetes strongly associated with older age
•Chinese population is ageing very fast
•Many more “old” people (e.g. 65+) in 2017 than
in 1990
•Population ageing distorts the comparisons
over time
•Age acts as confounding
Example
Comparison of all-cause mortality rates between
Sweden and Panama, 1962
Sweden Panama
Age
group
Number
deaths
Populati
on
Mortality
rate /
1000pyrs
Number
deaths
Populati
on
Mortality
rate /
1000pyrs
All ages 73555 7496000 9.8 8281 1075000 7.7
Sweden has mortality rate higher than Panama (9.8 vs 7.7)
Example
Sweden Panama
Age
group
Number
deaths
Populati
on
Mortality
rate /
1000pyrs
Number
deaths
Populati
on
Mortality
rate /
1000pyrs
All ages 73555 7496000 9.8 8281 1075000 7.7
0-29 3523 3145000 1.1 3904 741000 5.3
30-59 10928 3057000 3.6 1421 275000 5.2
60+ 59104 1294000 45.7 2956 59000 50.1
All age-specific mortality rates are lower in Sweden than in Panama
WHY?
WHY?
Sweden has an older population structure than Panama
Age group Sweden Panama
0-29 42% 69%
30-59 41% 26%
60+ 17% 5%
… and mortality increases with age
EXPOSURE OUTCOME
CONFOUNDER
Age is a confounding factor
Populations often
have different age
structures
Most disease
risks vary
with age
Age
Age is a confounding factor
Confounding in epidemiological studies
• At the design stage
• Statistical modelling
• Stratification
• At the analysis stage
• Randomisation
• Restriction
• Matching
Summarising stratum specific measures
of effect
• We want to summarise the effect of E on the risk of D,
allowing for the confounding effect of C.
• In order to get this adjusted rate ratio (or odds ratio, or risk
ratio) we pool the stratum-specific rate ratios (or odds ratios,
or risk ratios).
• A common method of doing this = the Mantel-Haenszel
method (known to us from session 6)
• Another major method which uses the principle of
stratification is standardisation. This method is commonly
used when comparing rates.
Example – cont.
•Ideally, we want to have summary measure for
each population which has been controlled for
different age structure
•Two possibilities:
•DIRECT standardisation
•INDIRECT standardisation
Direct vs. Indirect Standardisation
DIRECT
Uses
STANDARD
POPULATION
STRUCTURE
INDIRECT
Uses
STANDARD SET OF
AGE-SPECIFIC
RATES
Direct standardisation
We have “standard population” = hypothetical population with known
age structure
Q1: how many deaths would be expected in Sweden if it had
the same age distribution as this standard population
Q2: how many deaths would be expected in Panama if it had
the same age distribution as this standard population
Age (years) Population
0-29 56,000
30-59 33,000
60+ 11,000
All ages 100,000
Direct standardisation
Swedish age-specific rates Panama age-specific rates
Standard population
Expected deaths
and
DIRECTLY STANDARDISED
RATE
Expected deaths
and
DIRECTLY STANDARDISED
RATE
Example
Sweden Panama
Age
group
Number
deaths
Populati
on
Mortality
rate /
1000pyrs
Number
deaths
Populati
on
Mortality
rate /
1000pyrs
All ages 73555 7496000 9.8 8281 1075000 7.7
0-29 3523 3145000 1.1 3904 741000 5.3
30-59 10928 3057000 3.6 1421 275000 5.2
60+ 59104 1294000 45.7 2956 59000 50.1
Age specific rates in Sweden (per 1000 pyrs) Age specific rates in Panama (per 1000 pyrs)
0-29 1.1
30-59 3.6
60+ 45.7
0-29 5.3
30-59 5.2
60+ 50.1
Standard population
0-29 56,000
30-59 33,000
60+ 11,000
Age Expected deaths
0-29 0.0011 x 56,000=61.6
30-59 0.0036 x 33,000=118.8
60+ 0.0457 x 11,000=502.7
TOTAL 683.1
Age Expected deaths
0-29 0.0053 x 56,000=296.8
30-59 0.0052 x 33,000=171.6
60+ 0.0501 x 11,000=551.1
TOTAL 1019.5
Age-adjusted rates
• Sweden:
• 683.1/100,000=6.8 per 1,000 person years
• Panama:
• 1019.5/100,000=10.2 per 1,000 person years
These rates can be interpreted as the mortality rates
that these two countries would have if their age distributions
were changed from what they actually were to the age
distribution of the standard.
Direct standardisation
•A weighted average of the age-specific rates
•Weights = population in strata of standard
population
•Weights are the same = Age-standardised rates
can be directly compared
•We can calculate age-standardised rate ratio:
10.2/6.8=1.5
What standard population?
WHO
standard
populations
Indirect standardisation
•Let’s assume that the total number of deaths for
Panama is known but their distribution by age is
not available
•It is not possible to use the direct method of
standardisation.
Sweden Panama
Age
group
Number
deaths
Populati
on
Mortality
rate /
1000pyrs
Number
deaths
Populati
on
Mortality
rate /
1000pyrs
All ages 73555 7496000 9.8 8281 1075000 7.7
0-29 3523 3145000 1.1 NA 741000 -
30-59 10928 3057000 3.6 NA 275000 -
60+ 59104 1294000 45.7 NA 59000 -
Indirect standardisation
• It is possible to calculate how many deaths would be expected
in Panama and in Sweden if both these countries had the same
age-specific mortality rates as Sweden
• Swedish age-specific rates will be taken as a set of standard
rates
Swedish age-specific rates
Expected deaths
Panama populationSwedish population
Observed/Expected ratio
Expected deaths
Observed/Expected ratio
Age-spec rates in Sweden
0-29 1.1
30-59 3.6
60+ 45.7
Panama population
0-29 741,000
30-59 275,000
60+ 59,000
Swedish population
0-29 3,145,000
30-59 3,057,000
60+ 1,294,000
Age Expected deaths
0-29 0.0011 x 3,145,000=3,523
30-59 0.0036 x 3,057,000=10,928
60+ 0.0457 x 1,294,000=59,104
TOTAL 73,555
Age Expected deaths
0-29 0.0011 x 741,000=815.5
30-59 0.0036 x 275,000=990.0
60+ 0.0457 x 59,000=2,696.3
TOTAL 4,501.4
Total expected deaths (E) = 73,555
Total observed deaths (O) = 73,555
Total expected deaths (E) = 4,501
Total observed deaths (O) = 8,281
SWEDEN PANAMA
O/E (%) = 100 O/E (%) = 184
STANDARDISED MORTALITY RATIO
SMR
(rate ratio)
The SMR for Panama is equal to 184 = the number of observed
deaths was 84% higher than the number we would expect if the
Panama had the same mortality experience as Sweden.
Comparison of the methods
• Direct method uses STANDARD population structure
• Indirect method uses STANDARD set of age-specific rates
Data needed for each study population
•Direct method: number of cases by age group,
population numbers by age group (to be able to
calculate age specific rates)
•Indirect method: total number of cases only,
population number by age group
Method
• Direct method: select standard population, apply
age specific rates to standard population
• Indirect method: choose standard age-specific
rates and apply them to each study population
Which method preferable?
•Decision depends on what data are available
•The direct method requires stratum-specific rates
(e.g. age-specific rates) in all the populations under
study whereas the indirect method only requires
the total number of cases
•If stratum-specific rates are not available for the
study population, the indirect method may provide
the only feasible approach
Which method preferable?
•Indirect method preferred when there are small
numbers in age-specific groups. Rates in direct
adjustment would be based on these small
numbers and would be subjected to substantial
sampling variation.
•With indirect adjustments the summary rates are
more stable because we can choose the most
stable rates as the standard rates
STANDARDISED MEANS
• Same principle as with proportions/rates
• If continuous variable is related for example to age and age
structure differs in 2 populations the comparisons of means of
continuous variable might be misleading
SUMMARY
•Confounding is hugely important issue in
epidemiology
•Common alternative explanation for observed
association
•Can be controlled by design or analysis
Adjustment = analytical approach to control for
confounding
Standardisation - uses stratification method
•Two types of standardisation
•Direct x Indirect standardisation
•Standardized rates
•Standardized means