Intermediate Methods in Epidemiology
2008
Exercise No. 3 - Interaction
Major topics to be covered in this laboratory exercise:
Identification and assessment of interaction in case-control studies.
Part I deals with an unmatched incidence-based case-control study, and covers
the different approaches used to assess the additive and multiplicative models.
Part II deals with a matched case-control study in which interaction between a
matched variable and the exposure under study is evaluated.
This laboratory exercise assumes familiarity with the following topics:
Estimation of unmatched and matched odds ratios.
Use of stratification in unmatched and matched case-control studies.
Department of Epidemiology - Johns Hopkins University - Copyright 2001
PART I:
Unmatched incidence-based case-control study
This part of the exercise is based on a cohort study conducted in Bruneck (Bolzano Province,
Italy) to determine risk factors of incident atherosclerosis (Kiechl et al: Circulation 2001;
103:1064-70.) The study population was a sex-age-stratified random sample of individuals in
the community who were 40-79 years old. A total of 826 individuals who participated in the
baseline examination (1990) returned and completed a follow-up examination 5 years later. At
both examinations, the presence of carotid atherosclerosis was assessed using a highresolution duplex ultrasound scan. The development of new carotid plaques (“incident
atherosclerosis”) was assessed in all subjects. Blood samples were drawn at the baseline exam
and levels of inflammatory markers (C-reactive protein, CRP) were measured. “Chronic
infection” was defined based on history of chronic obstructive pulmonary disease, chronic
bronchitis, chronic sinusitis, urinary tract infections, other chronic infections.
The figure reproduced in the next page (figure 3) shows selected stratified results from this
study. Based on the numbers shown in the bottom of the bars of the figure, please, complete
the cells in the table below.
Table 1 - Odds ratio* for incident atherosclerosis by CRP levels and history of chronic infection
Chronic infection
No
CRP
>1mg/L
1mg/L
Incident
atherosclerosis
No
atherosclerosis
______
______
Yes
Incident
atherosclerosis
No
atherosclerosis
______
______
______
______
______
______
OR
OR
* Notice that the odds ratios that you calculate will be different than those shown in figure 3 of the original article
because the latter were age-, sex- and baseline atherosclerosis adjusted OR’s.
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You will start examining the possibility that interaction is present by using the homogeneity
approach (Strategy #1 in your hand-out.)
(1) Calculate the crude OR’s for high CRP (>1 mg/L) for each stratum of chronic
infection.
(2) Are the odds ratios homogeneous for the two chronic infection categories?
(3) Solely on the basis of your response to Question 2 above, what can you conclude
regarding presence and type (additive or multiplicative) of interaction?
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Now, you will examine presence of interaction by estimating the expected joint effect, and
comparing it with the observed joint effect of chronic infection and CRP (Strategy #2 in your
hand-out..)
Remember that the formulas to calculate the expected joint effects are:
For the additive model:
EXPECTED OR++ = OR+- + OR-+ - 1.0
And, for the multiplicative model:
EXPECTED OR++ = OR+- x OR-+
[Note: the OR’s denoted by ‘+-‘ and ‘-+’ relate to the independent effects of chronic infection and
CRP, respectively].
So that you can estimate the expected joint effect, you need to build a table which will allow you
to calculate the independent effects of CRP and chronic infection:
Chronic
infection
High CRP
No
No
No
Yes
Yes
No
Yes
Yes
Atherosclerosis
Controls
OR
OR
1.0
1.0
1.0
[Note that, in this table, you are asked to separate the effects of both risk factors. This is
accomplished by using the category where both risk factors are absent as the reference with an
OR of 1.0, and calculating the odds ratios across the two independent categories (“no/yes” and
“yes/no”). The last column is included at this point for your information: its odds ratios are the
same that you have already calculated for table 1, that is, the OR’s for high CRP stratified by
chronic infection.]
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(4) What is the independent effect of high CRP (that is, when the risk factor “chronic
infection” is absent)?
OR for high CRP =
(5) What is the independent effect of chronic infection (that is, in individuals with
normal/low CRP levels)?
OR for chronic infection =
(6) What is the expected joint additive effect of high CRP and chronic infection?
Expected joint additive effect OR =
(7) What is the expected joint multiplicative effect?
Expected joint multiplicative effect OR =
(8) What is the observed joint effect OR?
Observed joint effect OR =
(9) Compare the expected OR’s with the observed OR. Assuming no random
variability, what can you conclude regarding presence and type of interaction?
(10) In the abstract of the paper (see above), the authors stated that “Among subjects
with chronic infections, atherosclerosis risk was highest in those with prominent
inflammatory response.” In view of your above calculations, do you agree with
this conclusion? What does it say about the presence/absence of interaction?
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PART II:
Matched case-control study
This exercise is based on a hypothetical case-control study, which aims at examining the role of
an exposure X (whose presence or absence are denoted by the symbols + or - ) on disease Y.
The potential effect modifier (A third variable=) is sex.
SEX
CASES
CONTROLS
female
+
-
female
-
+
female
+
-
female
-
+
male
+
-
male
+
-
male
+
-
male
-
+
(1) Calculate the overall OR using the matched pair approach (ratio of discrepant
pairs):
ORoverall =
(2) Calculate the OR’s for males and females separately:
ORmale =
ORfemale =
(3) Are the OR’s homogeneous by sex?
(4) What can you conclude regarding presence and type of interaction between sex
and exposure?
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(5) Is it possible to apply the additive interaction formula,
[Expected OR++ = OR+- + OR-+ - 1.0] using data from table 1? Why?
(6) Is there confounding by sex? Are you now convinced that confounding and
interaction are distinct phenomena?
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