4. 2) Matching
▪ Instead of restriction, one could also ensure that the study groups do not differ with
respect to possible confounders such as age and gender by matching the two
comparison groups.
▪ For example, for every inactive male between the ages of 40-50, we could find and
enroll an active male between the ages of 40-50.
▪ In this way, the groups we are comparing can artificially be made similar with
respect to these factors, so they cannot confound the relationship.
▪ This method actually requires the investigators to control confounding in both the
design and analysis phases of the study, because the analysis of matched study
groups differs from that of unmatched studies.
Methods to Control for Confounding – Study Design
5. 2) Matching (Cont.)
▪ Like restriction, this approach is straightforward, and it can be
effective.
▪ However, it has the following disadvantages:
1. It can be time-consuming and expensive.
2. It limits sample size.
Methods to Control for Confounding – Study Design
6. 3) Randomization in Clinical Trials
▪ It should be obvious why randomization is such a powerful method to
control and prevent confounding.
▪ If a large number of subjects are allocated to treatment groups by a random
method that gives an equal chance of being in any treatment group, then it is
likely that the groups will have similar distributions of age, gender,
behaviors, and virtually all other known and as yet unknown possible
confounding factors.
▪ Moreover, the investigators can get a sense of whether randomization has
successfully created comparability among the groups by comparing their
baseline characteristics.
Methods to Control for Confounding – Study Design
7. 3) Randomization in Clinical Trials
Methods to Control for Confounding – Study Design
Randomizing the exposure adjusts for confounding by eliminating the
influence of the confounder on the probability of receiving the exposure:
8. 3) Randomization in Clinical Trials (Cont.)
Example:
o Consider the question of whether a new antibiotic, Supramycin, causes a
rash.
o Investigators could identify a group of adults with acute bronchitis التهاب
شعبي and then randomly assign them to receive supramycin or
amoxicillin, which is an established antibiotic for bronchitis.
o Both antibiotics could be prepared in identical appearing capsules to
blind study subjects and investigators to the treatment assignment.
Methods to Control for Confounding – Study Design
9. 3) Randomization in Clinical Trials (Cont.)
o Data presented as mean (standard deviation) or number of subjects (percent).
o It can be detected from the table above that distributions of all side factors
including the history of eczema is approximately identical between the
treatment groups which is one tool for controlling the confounding.
o Baseline data from this hypothetical randomized trial are presented in following table:
Methods to Control for Confounding – Study Design
10. 3) Randomization in Clinical Trials (Cont.)
o The results indicate that participants who are randomized to Supramycin have a 60%
greater incidence of rash, compared to those who are randomized to Amoxicillin
(0.71% versus 0.44%).
o In the context of a large randomized trial, these results can be interpreted as,
“Supramycin causes a 60% greater risk of rash compared to Amoxicillin” because the
Supramycin and Amoxicillin groups differ only by the use of these antibiotic
medications.
o Results are presented in the following table:
Methods to Control for Confounding – Study Design
11. Limitation of random assignment:
1.Ethical reason:
Randomizing participants would be unethical when studying the effect of a
harmful exposure or when it is known for certain that the exposure is beneficial.
2. Practical reason:
Some exposures are very hard to randomize, like air pollution and education.
Also, random assignment is not an option when we are analyzing observational
data that we did not collect ourselves.
3. Financial reason:
Random assignment is a part of experimental designs where participants are
followed over time, which turns out to be highly expensive in some cases.
Methods to Control for Confounding – Study Design
3) Randomization in Clinical Trials (Cont.)
12. 4) Stratification
▪ Stratified analysis divides the contingency tables arising from a study into
groups (strata).
▪ The groups are defined by levels of the confounding variable.
▪ Since confounding is caused by intermixing, unmixing through
stratification will lead to a change in the estimated effect if the
unstratified (crude) estimate was distorted by confounding.
▪ Stratified analysis leads to a set of adjusted estimates, called stratum-
specific estimates.
▪ Stratum-specific estimates are adjusted for confounding.
Methods to Control for Confounding – Study Design
13. 4) Stratification (Cont.)
▪ There is, of course, drawbacks to this approach:
1. Since stratum-specific estimates derive from a subset of the sample
rather than the whole sample, they are subject to random error to a
greater extent. However, There are procedures to regain precision of
adjusted estimates in stratified analysis. These involve calculating pooled
estimates from the (adjusted) stratum-specific estimates.
2. The problem of small stratified tables is even worse when there are
multiple confounders. It is usually not possible to simultaneously stratify
on several confounders.
Methods to Control for Confounding – Study Design
14. 5) Regression
▪ Another method used to control for confounding is called regression.
▪ Regression is a mathematical model that can estimate the association between many
exposure variables and an outcome variable.
▪ Regression utilizes all of the study data, can account for multiple confounders
simultaneously, and can deal with different types of potential confounding variables,
such as those that are continuous and those that are dichotomous.
▪ Because of its flexibility, regression is the most commonly used method to deal with
confounding in the medical literature.
▪ Disadvantages of regression are that the methods can sometimes be difficult to
explain to a general audience, and that the results may be inaccurate if assumptions of
the mathematical models are not satisfied.
Methods to Control for Confounding – Study Design
16. ▪ Methods discussed so far are to control or adjust for confounding, we now
turn to the task of interpreting study results after adjustment.
▪ The result from the first row of this table can be interpreted as the
association of Supramycin use with rash prior to any adjustment. This result
is also called the ‘crude’ or ‘unadjusted’ relative risk. The result from the
second row can be interpreted as the association of supramycin use with rash
independent of previous eczema, and the result from the third row can be
interpreted as the association of supramycin use with rash independent of
previous eczema and age.
▪ Table compares the relative risk to rash of
Supramycin with respect to Amoxicillin.
Unadjusted versus Adjusted Association
17. ▪ From the above table, the association of Supramycin use with rash
changes considerably after adjustment for previous eczema.
▪ Adjustment for previous eczema substantially changes the relative
risk from 2.53 to 1.83.
▪ This change implies that the original association of supramycin
use with rash was confounded in part by previous eczema.
▪ On the other hand, further adjustment for age does not appreciably
change the relative risk (from 1.83 to 1.80), implying that once
previous eczema is controlled, age has minimal impact on the
association of Supramycin use with rash.
Unadjusted versus Adjusted Association
18. ▪ There is no general agreement as to how much change in the strength
of an association is required for a factor to be dealt with as a
confounder; some experts have argued for a 10% change.
▪ In the above example, the association of Supramycin use with rash
was substantially reduced by adjustment for previous eczema,
implying that previous eczema was in fact confounding the crude
association, and that analyses should adjust for previous eczema.
An alternative method to evaluate a potential confounding factor using the Stratified
Analysis is to compare associations before and after adjustment for that factor
Unadjusted versus Adjusted Association
20. ▪ The Cochran-Mantel-Haenszel method is a technique that generates an
estimate of an association between an exposure and an outcome after
adjusting for confounding.
▪ We stratify the data into two or more levels of the confounding factor. In
essence, we create a series of two-by-two tables showing the association
between the risk factor and outcome at two or more levels of the
confounding factor.
▪ Then we compute the adjusted estimator as a weighted average of the risk
ratios or odds ratios across the strata (i.e., across subgroups or levels of
the confounder).
Cochran-Mantel-Haenszel Adjusted Estimator
21. A general format of two-by-two tables in each stratum can be depicted as:
D + D - Total
E + a b n1
E - c d n2
Total m1 m2 n
Using the notation in this table estimates for a risk ratio or an odds ratio
would be computed as:
n1
n2 cn1
an2
Cochran-Mantel-Haenszel Adjusted Estimator in Stratified
Analysis
22. ❑ To explore and adjust for confounding, we can use a stratified
analysis in which we set up a series of two-by-two tables, one for each
stratum (category) of the confounding variable.
❑ Having done that, we can compute a weighted average of the estimates
of the risk ratios/odds ratios across the strata.
❑ The weighted average provides a measure of association that is
adjusted for confounding.
Cochran-Mantel-Haenszel Adjusted Estimator in Stratified
Analysis
23. The weighted averages for risk ratios and odds ratios are computed as
follows:
Where ai, bi, ci and di are the numbers of participants in the cells of the
two-by-two table in the ith stratum of the confounding variable.
ni represents the number of participants in the ith stratum.
(n2)i
(n1)i
Cochran-Mantel-Haenszel Adjusted Estimator in Stratified
Analysis
25. ▪ After all what have been introduce;
definition of confounding factor (C),
methods to control for confounding,
and an adjusted estimator of the
measure of association between the
exposure (E) and the outcome (D).
▪ A general algorithm is needed in
practice to judge whether C is
confounding the association between E
and D.
Confounding in practice
E
(Exposure)
C
(Confounder)
D
(Outcome)
26. This algorithm can be introduced in detailed steps as follows:
First, one should check whether the confounding variable is
associated with the exposure of interest. This occurs when
confounder distribution are different across exposed/non-
exposed groups. If YES then GO TO
Checking whether the confounding variable is itself a risk factor
for the outcome of interest (based on non-exposure data). This
occurs when different estimated risk factor for the outcome
across groups of the confounder in the sample of non-exposed
group. If YES then GO TO
Comparing the estimated measure of association before (crude
RR/OR) and after adjusting (ARR/AOR) for a potential
confounding. If the difference between the two measures of
association is 10% or more, then confounding was present. If it
is less than 10%, then there was little confounding.
Confounding in practice
27. Example 1
1. What is the value of the crude risk ratio
(relative risk)?
2. What is the age-adjusted value of the risk
ratio?
3. Is age is confounding the association of
smoking and death? (Is age a
confounder?) Why?
4. Repeat 1 and 2 in terms of odds ratio.
(HW)
Confounding in practice
28. Example 1
Solution
1. Crude value of the risk ratio (relative risk)
RR = (788/2181) / (762/2253) = 1.07
[Or: RR = (788*2253) / (762*2181) = 1.07]
The relative risk based on the combined sample suggests a weak association
between smoking and the 24-risk of death, that is smoking increases
slightly the risk of death by 7%.
Confounding in practice
30. Is age confounding the association of smoking and risk of death?
Age has different
distribution (%) across
smoker (exposed) and
non-smoker (non-
exposed) groups.
Smokers are younger
than non-smokers in this
data set.
1
Confounding in practice
31. Is age confounding the association of smoking and risk of death?
2
Confounding in practice
Based on the data of non-smokers
(non-exposed), approximately,
estimated risk ratio is doubled as
going up from an age group to the
higher one. This reflects a strong
relationship between age (as a risk
factor) and the outcome (death), and
this result is independent from the
exposure variable (smoking)
32. Crude risk ratio is different than adjusted risk ration with more than 10%
RR = 1.07
ARR = 1.38
ARR – RR = 138 – 107 = 31 %
3
Difference
between RR and
ARR is greater
than 10%
Age is a Confounder
Confounding in practice
