Transcript Unit 6: Standardization and Methods to Control Confounding Unit 6 Learning Objectives: 1.

Unit 6:
Standardization and Methods
to Control Confounding
Unit 6 Learning Objectives:
1. Understand the “design” and “analysis”
methods used to control confounding.
--- Randomization
--- Restriction
--- Matching
--- Stratification
--- Multivariate analysis.
2. Understand pros and cons of the
methods used to control confounding.
Lesson 6 Learning Objectives (cont.):
3. Understand the rationale for rate adjustment
(standardization).
4. Apply and interpret the technique of direct
standardization.
5. Apply and interpret the technique of indirect
standardization.
6. Recognize differences between direct and
indirect standardization.
Assigned Readings:
Textbook (Gordis):
Chapter 4, pages 60-68 (Age
adjustment)
Chapter 15, pages 230-232 (More on
confounding)
Hennekens and Buring: Evaluating
the role of confounding. In
Epidemiology in Medicine, pages
304-323.
CONFOUNDING - REVIEW
DEFINITION: A third variable (not the
exposure or outcome variable of interest)
that distorts the observed relationship
between the exposure and outcome.
• Confounding is a confusion of effects that
is a nuisance and should be controlled for
if possible.
• Age is a very common source of
confounding.
CONFOUNDING - REVIEW
E
D
Confounding IS
present
CF
Confounding
NOT
present
E
?CF
D
CONFOUNDING
Reason for controlling confounding:
• To obtain a more precise (accurate)
estimate of the true association between
the exposure and disease under study.
• As a general rule, age and gender should
always be considered as potential
confounders of an association.
CONFOUNDING
POSITIVE CONFOUNDING:
• The confounding factor produces an
estimate that is more extreme (positive or
negative) than the true association.
NEGATIVE CONFOUNDING:
• The confounding factor results in an underestimate of the true association.
CONFOUNDING
METHODS TO CONTROL CONFOUNDING:
DESIGN:
1. Randomization
2. Restriction
3. Matching (Analysis also)
ANALYSIS:
4. Stratification
5. Multivariate Analysis
CONTROL OF CONFOUNDING
1. RANDOMIZATION (Design):
Definition: Subjects or groups of subjects
are randomly assigned to a hypothesized
preventive or therapeutic intervention.
Pro: With sufficient sample size, virtually
assures that both known and unknown
confounders are controlled.
Con: Sample size may not be large enough
to control for confounding since many
persons are unwilling to be randomized.
CONTROL OF CONFOUNDING
2. RESTRICTION (Design):
Definition: Study participation is restricted to
individuals who fall within a specified
category or categories of the confounder.
Pro: Straightforward, convenient, inexpensive
Con: Sufficiently narrow restriction range may
severely reduce the number of eligible
participants
Con: If restriction criteria are not sufficiently
narrow, possibility of residual confounding
exists
CONTROL OF CONFOUNDING
•
RESTRICTION (cont.):
Con: Does not permit evaluation of the
association between exposure and
disease for varying levels of the factor.
Note:Although restriction may limit
generalizability, it does not affect the
internal validity of any observed
association between the groups
included in the study.
CONTROL OF CONFOUNDING
3. MATCHING (Design/analysis);
Definition: All levels of the confounding factor are
allowable for study inclusion, but subjects are
selected in a way that potential confounders
are distributed equally among the study
groups.
Pro: Great intuitive appeal – may provide greater
analytic efficiency by insuring adequate
number of cases and controls at each level of
the confounder.
Con: Can be difficult, time consuming, and
expensive to find a comparison subjects with
right set of characteristics on each matching
variable.
CONTROL OF CONFOUNDING
•
MATCHING (cont.):
Con: Does not control potential
confounding by factors other than those
matched on
Con: Not needed as much as in the past
due to alternative techniques (e.g.
multivariate analysis)
CONTROL OF CONFOUNDING
INDICATIONS FOR MATCHING:
• Factors for which there would otherwise be
insufficient overlap between study groups
(e.g. nominal-level variables such as race).
• Small case series in which baseline
characteristics are likely to differ between
study groups.
• Most often employed in case-control studies.
CONTROL OF CONFOUNDING
•
MATCHING (ANALYSIS);
Note: Matching on several confounders can
make the study groups more alike on the
exposures of interest than would have
occurred had independent series of cases
and controls been selected.
• This requires use of statistical techniques
that make explicit provision for the
matched nature of the data (e.g.
conditional odds ratio)
CONTROL OF CONFOUNDING
•
STRATIFICATION (Analysis):
Definition: Evaluation of the exposure/disease
association within homogeneous categories
or strata of the confounding variable.
Pro: Intuitively appealing, straightforward,
and enhances understanding of intricacies
of the data
Con: Impractical for simultaneous control of
multiple confounders, especially those with
multiple strata
CONTROL OF CONFOUNDING
Hypothesis: Sedentary lifestyle is associated with risk of
myocardial infarction (cohort study)
E+
E-
D+
40
100
D80
750
120
850
970
RR = (40 / 120) / (100 / 850)
RR = 2.83
It appears that persons with a sedentary lifestyle
are 2.83 times more likely to experience
myocardial infarction compared to persons without
a sedentary lifestyle.
BUT WHAT ABOUT SMOKING?
CONTROL OF CONFOUNDING
NON-SMOKERS
E+
E-
D+
D-
5
50
25
525
SMOKERS
30
575
605
RR = (5 / 30) / (50 / 575)
RR = 1.92
E+
E-
D+
35
50
D55
225
90
275
365
RR = (35 / 90) / (50 / 275)
RR = 2.14
Is there evidence that smoking confounds
the relationship between sedentary
lifestyle and myocardial infarction?
CONTROL OF CONFOUNDING
CRUDE
STRATA 1
STRATA 2
RRMI = 2.83
RRNS = 1.92
RRSM = 2.14
In general:
If Strata 1 RR < Crude RR > Strata 2 RR
OR
If Strata 1 RR > Crude RR < Strata 2 RR
then confounding is present.
CONTROL OF CONFOUNDING
CRUDE
STRATA 1
STRATA 2
RRMI = 2.83
RRNS = 1.92
RRSM = 2.14
Now, the question is:
Should the stratum-specific estimates be
combined to obtain an unconfounded (adjusted)
estimate of the relationship between sedentary
lifestyle and risk of myocardial infarction?
CONTROL OF CONFOUNDING
CRUDE
STRATA 1
STRATA 2
RRMI = 2.83
RRNS = 1.92
RRSM = 2.14
Axiom: If the stratum-specific estimates are
similar (homogeneous), the estimates can be
combined to obtain an unconfounded (adjusted)
estimate.
However, if the stratum-specific estimates are
sufficiently different, they should not be
combined, as this would obscure useful
information (lecture 7).
CONTROL OF CONFOUNDING
CRUDE
STRATA 1
STRATA 2
RRMI = 2.83
RRNS = 1.92
RRSM = 2.14
Note: Statistical tests of homogeneity exist to test
the similarity of the stratum-specific estimates,
however, these tests are heavily affected by
sample size, and often under-powered.
Thus, the stratum-specific estimates should be
“eyeballed.”
CONTROL OF CONFOUNDING
CRUDE
STRATA 1
STRATA 2
RRMI = 2.83
RRNS = 1.92
RRSM = 2.14
Mantel-Haenszel pooled RR estimate
(uniform strata):
RRMH
Σ a(c + d) / T
= ----------------Σ c(a + b) / T
Where T = total sample in each stratum
CONTROL OF CONFOUNDING
CRUDE
STRATA 1
STRATA 2
RRMI = 2.83
RRNS = 1.92
RRSM = 2.14
RRMH
5(50 + 525) / 605 + 35(50 + 225) / 365
= -------------------------------------------------50(5 + 25) / 605 + 50(35 + 55) / 365
4.75 + 26.4
= -------------- =
2.48 + 12.3
31.1
-----14.8
=
2.10
CONTROL OF CONFOUNDING
CRUDE
ADJUSTED
RRMI = 2.83
RRMH = 2.10
Axiom: The magnitude of confounding is
evaluated by observing the degree of discrepancy
observed between the crude and adjusted
estimates.
•Presence of confounding should not be
assessed using a test of statistical significance.
•Generally, when the crude estimate changes by
at least 10%, meaningful confounding exists.
CONTROL OF CONFOUNDING
•
MULTIVARIATE ANALYSIS (Analysis):
Definition: A technique that takes into account a
number of variables simultaneously.
• Involves construction of a mathematical model
that efficiently describes the association
between exposure and disease, as well as
other variables that may confound or modify
the effect of exposure.
Examples: Multiple linear regression model
Logistic regression model
CONTROL OF CONFOUNDING
MULTIVARIATE ANALYSIS (Analysis):
Multiple linear regression model:
Y = a + b1X1 + b2X2 + …bnXn
Where:
n = the number of independent variables (IVs)
(e.g. Exposure(s) and confounders)
X1 … Xn = individual’s set of values for the IVs
b1 … bn = respective coefficients for the IVs
CONTROL OF CONFOUNDING
•
MULTIVARIATE ANALYSIS (Analysis):
Logistic regression model:
ln [Y / (1-Y)] = a + b1X1 + b2X2 + …bnXn
Where:
Y = probability of disease
n = the number of independent variables (IVs)
(e.g. exposure(s) and confounders)
X1 … Xn = individual’s set of values for the IVs
b1 … bn = respective coefficients for the IVs
CONTROL OF CONFOUNDING
•
MULTIVARIATE ANALYSIS (Analysis):
Pro: Can simultaneously control for multiple
confounders when stratified analysis is
impractical
Pro: With the logistic regression model, beta
coefficients can be directly converted to
odds ratios
Con: Process of efficient mathematical
modeling can
occur at the expense of clear understanding
of the data