INTRODUCTION
The notion that prognostic differences between treatment groups might explain apparent
differences in outcomes lies at the heart of clinical investigation. If clinicians
are to understand the research studies that guide their clinical practice, they must
grasp this concept. Further, clinicians should understand statistical adjustment for
differences in prognostic variables. This tip describes approaches to conveying these
concepts to learners.
As with other articles in this series, educators experienced in teaching evidence-based
medicine developed these tips and used them extensively to clarify statistical concepts
to learners solving clinical problems or critically appraising studies and reviews.
An article from the Canadian Medical Association Journal described the development
of this series and pertinent background information.1 For each of the tips we provide
guidance on when to use them, a teaching script, a “bottom line,” and a summary card.
For each tip we identify the appropriate target audience and provide time estimates
for the exercise.
We present qualitative introductions to the concepts of confounding variables and
adjusted analysis, followed by quantitative examples illustrating the potential impact
of adjustment. These demonstrations are characteristically interpolated into clinically
centered discussions with clinical learners. We do not in the course of using them
routinely attempt to address performing or analyzing multivariable or multivariate
analyses with such learners. We consider learner mastery of the concept of relative
risk to be prerequisite for understanding the tips, particularly for tip 3. A previously
published manuscript addressed teaching relative risk.2
TEACHING TIP 1: UNDERSTANDING CONFOUNDING VARIABLES
When to Use This Tip
This tip is suitable for those early in the process of learning critical appraisal.
This exercise takes 10 to 15 minutes to teach and has the following specific goals:
Explain the concept of a “prognostic variable”
Teach how randomization can minimize confounding
This tip is used when appraising the adequacy of randomization in a trial or for teaching
the concepts of randomization and prognostic variables.3
Begin by asking the learners why clinical trials are randomized. Typical initial answers
include to “reduce bias” or “ensure validity.” Eventually, learners respond, “to ensure
that the control and experimental groups are similar or balanced.” Focus on this answer
and ask “similar (or balanced) with respect to what?” Typical answers include “age
and sex.” Ask which patient characteristics, aside from age and sex, should ideally
be balanced. Look for any answer relating to patient prognosis such as severity of
disease, smoking history, or comorbid condition. Distribute or cite a specific therapy
article to focus this discussion on a specific patient population. Depending on the
context at hand, the learners may already have a suitable article in front of them.
Ask the learners why the 2 groups should be balanced with respect to age, sex, disease
severity, habits, and/or comorbidities. To illustrate the answer, contrast the above
variables (likely to be prognostic) with variables unlikely to be prognostic—asking
whether the experimental and control groups need to be balanced with respect to eye
color or shoe size. Of course the answer is no. The key is to help learners identify
why not. Ask why age (or sex, habits, etc.) is different from eye color. Learners
might respond that “they are related to developing the disease” or “they affect the
response to treatment.”
Eventually, someone will articulate that some patient attributes help predict future
events. Reinforce the concept that age, sex, disease severity, habits, and comorbidities
predict subsequent clinical events—they are prognostic factors. Now focus on the future
event by asking “prognostic of what?” Learners may need coaching to identify that
investigators are interested in prognostic factors for the relevant outcome(s) for
their study. You then state that randomization is designed to balance groups for the
relevant prognostic factors. Ideally, all treatment evaluations would compare 2 populations
identical in all prognostic factors related to the outcome of interest. This would
ensure that the only relevant baseline difference between the intervention group and
the control group is whether they receive treatment. This enables clinicians to clearly
evaluate the effect of an intervention on the outcome of interest (treatment effect).
The reason we are more concerned about imbalance in age than in eye color or shoe
size is that increasing age is likely associated with a higher risk for most important
adverse outcomes, whereas differences in shoe size and eye color very likely are not
so associated. A different distribution of age in the 2 groups can bias the results;
a difference in distribution of eye color would likely not bias the results.
For example, in a recent study, critically ill patients with acute lung injury and
acute respiratory distress syndrome (ARDS) were randomly assigned to either a lower
positive end-expiratory pressure (PEEP) or a higher PEEP.4 By chance, the mean age
of the lower PEEP group was significantly younger than the mean age of the higher
PEEP group (49 vs 54 years). The results showed a rate of death from any cause of
24.9% in the lower PEEP group and of 27.5% in the higher PEEP group. The results raised
the question of whether the mortality differences were attributable to the intervention
or to the age differences. At the heart of this question is the concept of confounding
variables. When the distribution of a known prognostic factor differs in the groups
under comparison, it becomes a potentially confounding variable—which, in the absence
of adjustment, can lead to overestimating or underestimating the true treatment effect.
Then ask learners whether the problem of confounding could be solved by matching groups
with respect to all known prognostic variables. Typically, learners raise concerns
about the feasibility of achieving an exact match between the 2 groups with respect
to all such variables. The preceptor should acknowledge these barriers, but persist
in asking whether, if feasibility barriers can be overcome, matching would be an appropriate
alternative to randomization. Eventually, a learner volunteers that unmeasured or
unknown confounders could still be unbalanced across the groups. Reinforce this concept
with an example such as The Nurses’ Health Study, an observational cohort study of
hormone replacement therapy (HRT) to prevent cardiovascular events.5 Because the nurses
were not randomized to HRT or control, we cannot know why only some nurses chose HRT.
There were many known, and likely many unknown, prognostic factors imbalanced between
the 2 groups. The adjusted analysis, which controlled for the known confounding variables
(such as smoking history, hypertension, etc.), demonstrated an apparent decrease in
cardiovascular events with HRT. However, a large randomized controlled trial (producing
2 groups homogeneous for known and unknown prognostic factors) found an increased
cardiovascular risk in women on HRT.6 The difference in results is almost certainly
caused by unknown or unmeasured prognostic factors because women choosing HRT in the
Nurses Health Study were destined to have a lower rate of cardiovascular events irrespective
of using HRT. The benefit was no longer apparent in a randomized study designed to
balance prognostic factors. This example demonstrates the limitations of adjustment
or matching and reinforces the benefits of randomization.
The Bottom Line
Randomization is the optimal approach for balancing the intervention and control groups
with respect to patient characteristics associated with the outcome of interest.
Such characteristics are called prognostic variables, and if unbalanced between groups,
confounding variables.
See Appendix 1 for the summary card on this tip.
TIP 2: UNDERSTANDING ADJUSTMENT—QUALITATIVE DEMONSTRATION
When to Use This Tip
Adjusted analysis arises in 2 contexts: randomized trials, especially if prognostic
variables are unbalanced, and observational studies. In either situation, users of
the medical literature must consider the issue of adjustment when critically appraising
an article. Tips 2 and 3 help facilitate learners’ understanding of adjusted analyses.
Tip 2 is suitable for beginners or intermediate learners who understand the concept
of why randomized trials provide the best way of balancing prognostic factors, and
thus understand the essential concept of confounding. This exercise takes about 15 minutes
to teach.
This tip has the following goal:
Demonstrate the fundamental logic underlying adjusted analyses.
The Script
Present the group with the following problem. A trial contains an intervention and
a control group with dissimilar ages. You suspect that age is associated with the
outcome of interest (and thus is a prognostic, and potentially confounding, variable)
in this study. The distribution of age is as follows: in the treatment group, 80%
of subjects are young and 20% are old. In the control group, 20% are young and 80%
are old.
In this trial, treated patients appear to have superior outcomes to untreated patients.
Ask the group for possible explanations. Students usually observe, “Treated patients
are younger.” You agree, and reiterate that spurious treatment effects can result
from a prognostic imbalance. Another possible explanation for the observed outcomes
is that “treatment really works.” For purposes of clarity in this exercise, you should
probably ignore the third possible answer—chance.
Next, ask the learners how to differentiate between the possibilities of a true benefit
versus a spurious apparent benefit as a result of confounding. Learners often struggle
with this challenge and answer “regression” or “logistic regression,” but are unable
to further elaborate. You might need to provide the answer: calculate estimates of
effect separately for the prognostic groups. In this case, the estimates of treatment
effect for the young treatment, young control, old treatment, and old control groups
are calculated separately. Next, combine effects across the young and old groups to
calculate an overall “adjusted” effect. This process may be described as “creating
a level playing field,” “creating 2 comparisons in which groups are homogenous for
the prognostic variable,” “creating 2 comparisons in which patients in treatment and
control group are prognostically similar,” or “creating an unconfounded analysis.”
The same process can be followed for several variables. Inform the learners that this
study also has patients with and without diabetes that may influence the outcome of
interest. A volunteer (or the preceptor) may list the 4 unconfounded comparisons that
result: old diabetic treatment, old diabetic control; young diabetic treatment, young
diabetic control; old non-diabetic treatment, old non-diabetic control; and young
non-diabetic treatment, young non-diabetic control.
This process could continue for as many such prognostic groups (within the limits
of sample size) as necessary. This principle can be extended to categorical variables
with more than 2 categories (e.g., cancer stages) or to continuous variables (e.g.,
age). In each case, the principle is to create prognostically homogeneous groups,
make comparisons between treatment and control within these groups, and then combine
treatment effect estimates across the groups to obtain an adjusted estimate of the
treatment effect. Computer programs for making such adjusted comparisons are widely
available.
We return to the previous example of critically ill patients with acute lung injury
and ARDS who were randomly assigned to either a lower PEEP or a higher PEEP.4 By chance,
the mean age of the lower PEEP group was significantly lower than the mean age for
the higher PEEP group (49 vs 54 years). The unadjusted results showed a rate of death
from any cause of 24.9% in the lower PEEP group and of 27.5% in the higher PEEP group.
However, the adjusted death rates are in the opposite direction: 27.5% in the lower
PEEP group and 25.1% in the higher PEEP group.
THE BOTTOM LINE
Studies that do not balance groups with respect to known prognostic factors may underestimate
or overestimate treatment effects.
The principle of an adjusted analysis involves creating groups that are homogeneous
for known prognostic variables and then combining intervention effect estimates across
groups.
See Appendix 1 for the summary card for this tip.
TIP 3: UNDERSTANDING ADJUSTMENT—QUANTITATIVE DEMONSTRATION
When to Use This Tip
This tip is useful for any learner who has worked through tips 1 and 2. Typically,
this follows immediately after tip 2. Use this tip for intermediate to advanced learners
or anyone who is particularly interested in a deeper understanding and who already
understands the concept of relative risk.4 This exercise takes 15 to 20 minutes.
This tip has the following goal:
Reinforcing the concepts of confounding variables and adjustment.
Return to the potentially confounded comparison presented above in tip 2. Ask the
group to make the following assumption: the event rate is 10% in the young and 20%
in the old and there is no treatment effect. Ask the group to help construct a 2 × 2
table with 100 patients in the treatment and 100 patients in the control groups. How
many events can we expect in treatment patients (80 young and 20 old)? The answer
is
\documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
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\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}$$ {\left( {80 \times 0.1} \right)} + {\left( {20 \times 0.2} \right)}
= 8 + 4 = 12 $$\end{document}
. Enter this in a 2 × 2 table (Table 1). Lead the group through the same calculations
for the control group (20 young and 80 old):
\documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
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\usepackage{amssymb}
\usepackage{amsbsy}
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\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}$$ {\left( {20 \times 0.1} \right)} + {\left( {80 \times 0.2} \right)}
= 2 + 16 = 18 $$\end{document}
. Use these numbers to complete the 2 × 2 (Table 1).
Table 1
A 2 × 2 Table Used in Demonstration of Tip 3
Dead
Alive
Treated
12
88
Control
18
82
Risk in treatment group: 12 of 100 or 12%; risk in control group: 18 of 100 or 18%;
relative risk = 12%/18% = 0.67.
Now ask the group to calculate the relative risk. Remind the group that the relative
risk is the risk of an outcome in 1 group divided by the risk of the outcome in the
other group. Facilitate the process by asking the group to state the risk in the treatment
group (12%) and the risk in the control group (18%). Therefore, the relative risk,
obtained by dividing the risk in the treatment group by the risk in the control group,
is 0.67.
Next, direct the group back to the unconfounded comparison. Ask them to calculate
the mortality risks for the treated (n = 80) and control (n = 20) young patients.
Assuming no effect of treatment on mortality risk, 10 % (n = 8) of the 80 younger
treated patients and 10% (n = 2) of the younger control patients died. Because the
mortality risks in the 2 groups are both 10% the corresponding relative risk is 1.0.
Next, calculate the mortality risks among the old patients. Again, assuming no treatment
effect on mortality risk, 20% (n = 4) of the 20 old treated patients and 20% (n = 16)
of the 80 old control patients died; this also yields a relative risk of 1.0. This
is demonstrated in Table 2.
Table 2
Demonstration of Effect of Adjustment for Age on Observed Relative Risk
Patients
Young patients
Treatment: 80 patients × 10% mortality = 8 deaths,
Risk in treatment group: 8 of 80 = 0.1 or 10%
Control: 20 patients × 10% mortality = 2 deaths,
Risk in control group: 2 of 20 = 0.1 or 10%
Relative Risk = Risk in treatment group/Risk in control group = 0.1/0.1 = 1.0
Old patients
Treatment: 20 patients × 20% mortality = 4 deaths,
Risk in treatment group: 4 of 20 = 0.2 or 20%
Control: 80 patients × 20% mortality = 2 deaths,
Risk in control group: 16 of 80 = 0.2 or 20%
Relative Risk = Risk in treatment group/Risk in control group = 0.2/0.2 = 1.0
This example points out that an adjusted analysis combines the relative risk for 1
prognostically homogeneous group (the young, 1.0) with the relative risk in another
prognostically homogeneous group (the old, 1.0) to generate the relative risk for
the entire group (1.0). You may mention that this is called a stratified or adjusted
analysis.
Ask the group to reflect on the relative risk of 0.67 generated for the entire patient
pool. The group will conclude that the apparent difference in treated patients was
due completely to the confounding variable (age). Point out to the learners that the
analysis could be adjusted for more than 1 factor as demonstrated conceptually in
Tip 2. In fact, this is the principle that computers follow when performing multivariable
analyses
Bottom Line
Imbalance of prognostic variables between groups can create spurious treatment effects.
Adjusted analysis seeks to better estimate the true effect of treatment.
See Appendix 1 for the summary card for this tip.
Report on Field Testing
We field tested the tips to verify the clarity and practicality of the descriptions.
Field testing frequently generates examples of the kinds of variations in approach
that occur when an experienced teacher of evidence-based medicine adapts the approaches
to their own style, context, and learner level. S.K. conducted a field test of all
3 tips with 25 resident learners, half of whom were interns. Overall, these tips were
rated highly by the learners and by S.K. The objectives were felt to be clear and
the learners were able to articulate the major teaching points from the exercises.
Preparatory time was approximately 2 hours. The field test utilized a board, data
projector, and a handout.
Trainees from prior field tests have consistently requested that teaching tips were
grounded in an article or specific case example to best appreciate the relevance of
the content. Thus, S.K. opted to include a brief review of the NEJM article4 as an
adjunct to Tip 1. Learners were asked to review the abstract, baseline characteristics
for confounders, and then Table 5 of that article, which demonstrates the adjusted
and unadjusted analysis. This required an additional 10 minutes. Tip 1 was recommended
for beginners, and was appropriate based on field testing. S.K. recommended an abbreviated
version of Tip 1 for more experienced learners. Tip 2 was recommended for beginner
or intermediate learners and this also seemed appropriate based on field testing.
Tip 3 was recommended for intermediate to advanced learners, and indeed the more novice
learners required coaching through the mathematical formulas associated with Tip 3.
Based on learner feedback, the concepts of relative risk (or risk ratio) and number
needed to treat might be helpful prerequisites to this series of exercises.
The overall strength of the tips was the stepwise building on the same concept from
an introductory to an advanced level. One point of clarification was required during
the first tip: the difference between the authors’ intent for randomization and the
actual achievement of balanced prognostic factors. In addition, S.K. felt it may be
useful in the future to add a coin flip exercise to Tip 1, to randomize the learners.
After the 2 groups are randomly allocated to either heads or tails, examine the distribution
of males versus females, married versus single, etc., to illustrate that sometimes
randomization falls short of its intention to have equal groups. S.K. also suggests
a modified approach to Tip 3 by using a completed 2 × 2 table to calculate overall
relative risk and number needed to treat to see the effect of a given treatment. She
would then alert the group to the fact that the treatment and control populations
were confounded. Finally, she would have the learners sort out the contribution of
the confounding variable. S.K. believes that the impact of a confounding variable
might be powerfully demonstrated this way.
CONCLUSION
Randomization is performed in clinical trials to achieve balance in prognostic factors.
Confounding variables are imbalances in prognostic factors. These imbalances can lead
to overestimating or underestimating the impact of an intervention under study. The
known confounding variable can be adjusted for by performing the calculations of risk,
risk difference, and relative risk for populations after stratifying by the additional
prognostic factor.
Electronic Supplementary Material
Video object (mpg 140 MB)