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					Epi 203: Epidemiologic Methods
Problem Set 9: Confounding and Interaction I
ANSWER KEY

Due: 11/23/10 at 1:30 pm section
Possible points: 30



1. Recently, there have been several notable hypotheses generated regarding the following
exposures and outcomes/conditions. For each, describe at least one factor that you would
consider as a potential confounding factor (either causing positive or negative confounding)
when evaluating/planning a study regarding the putative causal association between the exposure
and the outcome. For each potential confounding factor you list, state whether this would cause
positive or negative confounding. For each scenario, draw a directed acyclic graph (DAG).

a) Exposure: cell phone use while driving; Outcome: motor vehicle accidents (1 pt)

Answer:
-Age: younger drivers are at higher risk for MVAs (perhaps because of more reckless driving) and may also be more
apt to be cell phone users. (positive confounding)
-Socioeconomic Status: higher socioeconomic status may be causally related to cell phone use and also ownership of
own cars with more safety features (e.g., anti-lock brakes); the presence of this confounding factor may serve to
attenuate a possible association. (negative confounding)
-Presence of children in the car: it is possible that drivers with children in the car are more apt to be cell phone users
because of the need to schedule and coordinate the children’s activities; children in the car may be themselves be
distracting and a risk factor for an MVA. (positive confounding)

Note: This is not a complete list of correct answers, other answers may be acceptable for questions 1a-1d.
Note: Being distracted while on the cell phone would not be a correct response because this is presumably an
intermediary factor on the causal pathway between cell phone use and motor vehicle accidents.




                                                                   Cell phone use

                                             Age


                                                                             ?
                                    Driving experience/
                                         risk-taking



                                                                       MVA




                              Ques 1a




b) Exposure: cell phone use; Outcome: brain tumors (1 pt)

Answer:
-Age: among adults, cell phone users are likely to be younger than non-users. Older age is associated with greater
risk of brain tumors. (negative confounding).
-Predilection for technology: Conceivably, a predilection for technology might cause people to use cell phones, and
a predilection for technology might cause people to be more exposed to other by-products of the high technology
Epi Methods: Problem Set 9                                1                 Confounding and Interaction I
world we live in (e.g., computer monitors or printers), which conceivably could be the culprit in brain tumors.
(positive confounding)
-Socioeconomic status: higher SES is associated with more cell phone use; higher SES may also be associated with
greater access to care and hence greater likelihood of being diagnosed with brain tumor if it occurs (this assumes
that not all brain tumors get diagnosed before death) (positive confounding)


                                    Cell phone use
                                                                         Technology-philic   Cell phone use
                                                                            personality



              Age                                                   Use of other energy
                                               ?                    emitting technology
                                                                                                      ?
                                                                          devices




                                      Brain tumor
                                                                                              Brain tumor




  Ques 1b                                                     Ques 1b




c) Exposure: Chlamydia pneumoniae infection; Outcome: coronary heart disease. (Clinical note:
Chlamydia pneumoniae infection is a respiratory infection.) (1 pt)

Answer:
-Smoking: Smoking is likely a risk factor for C. pneumoniae infection and also a risk factor for CHD. (positive
confounding)
-Age: Age is associated with both a history of C. pneumoniae infection and CHD. (positive confounding)



                                C. pneumoniae infection




            Smoking
                                               ?




                                         CHD




  Ques 1c




d) Exposure: use of cloth diapers (via a mechanism of less absorption that makes child
uncomfortable and more apt to become toilet trained); Outcome: earlier achievement of “potty”
training (1 pt)

Answer:
-Familial socioeconomic status: Families with higher SES may be more able to afford cloth diapers and/or favor
their use on environmental grounds and may also have more time/resources to devote to toilet training (likely
positive confounding).
Note: An example of an intermediary, not a confounder, would be the extra work involved in use of cloth diapers
which gives parents greater incentive to start toilet training. Presumably, this is not the pathway one is interested in
investigating and, hence, even though it is not a confounding factor, the extra work involved is an extraneous factor
which one would want to control for. Therefore, “extra work” is an intermediary factor on an extraneous pathway.



Epi Methods: Problem Set 9                                2                    Confounding and Interaction I
                                      Family SES            Use of cloth diapers




                           Time spent toilet training
                                                                         ?




                                                            Early potty training




                     Ques 1d




Epi Methods: Problem Set 9                              3              Confounding and Interaction I
2. A case-control study was conducted to assess whether drinking coffee (specifically, the
ingestion of the components in coffee) is causally related to the occurrence of coronary artery
disease (CAD). Coffee consumption was measured as either “High Coffee” use of “Low
Coffee” use. The results, stratified on smoking status, are summarized below: (adapted from
Kleinbaum 2003)

Non-smokers                                                     Smokers
                    CAD         No CAD                                               CAD             No CAD
High coffee         40          45                              High coffee          150             65
Low coffee          65          150                             Low coffee           45              40


a) Calculate the crude odds ratio and two stratum-specific odds ratios. Show your calculations.
(2 pt)
Answer:
Crude
                   CAD         No CAD
High coffee        190         110
Low coffee         110         190
                   OR = (190/110) / (110/190) = 2.98


Non-smokers                                                 Smokers
                   CAD          No CAD                                           CAD                No CAD
High coffee        40           45                          High coffee          150                65
Low coffee         65           150                         Low coffee           45                 40
                   OR = (40/65) / (45/150) = 2.05                                OR = (150/45) / (65/40) = 2.05

b) Assess whether
  i. smoking is related to coffee consumption among those without CAD.
  ii. smoking is related to CAD among subjects with low coffee consumption.
Show your work. (2 pt)
Answer:

                   High coffee     Low coffee                                        CAD             No CAD
Smokers            65              40                           Smokers              45              40
Non-smokers        45              150                          Non-smokers          65              150
                   OR = (65/45) / (40/150) =                                         OR = (45/65) / (40/150) = 2.60
                   5.42
Answer:
   i.         Smoking is related to coffee consumption.
   ii.        Smoking is related to CAD.



c): If you knew nothing else, are the data given in the question and your calculations in item (b)
sufficient evidence for you to conclude that smoking is a confounder in the relationship between
coffee use and CAD? Explain your answer. (1 pt)

Answer: The available data alone don’t tell us whether smoking is a confounder. They just tell us that smoking
could be a confounder. The available data are actually compatible with at least 3 different DAGs as shown below:
1. smoking as the common cause; 2. one with behavioral factors as the common cause; and 3. one with smoking
mediating an extraneous directed path from coffee. You will need to bring in some external prior knowledge to

Epi Methods: Problem Set 9                          4                 Confounding and Interaction I
decide upon the 3 possibilities. It is also possible that the data observed do not stem from either of these 3 DAGs
and instead are caused by chance.




                        Smoking
                                                   Coffee consumption




                                                                 ?




                                                           CAD




   Question 2c) – possibility 1




                  Behavioral factors
                                                   Coffee consumption




                     Smoking
                                                                 ?




                                                           CAD



   Question 2c) – possibility 2




Epi Methods: Problem Set 9                            5                 Confounding and Interaction I
                                                        Coffee consumption




                      Smoking
                                                                    ?




                                                              CAD




    Question 2c) – possibility 3




d) Drawing upon all of your own knowledge about this system, show the DAG that you believe
best depicts the system under study. Justify your selection (1 pt)

Answer: Different answers are acceptable depending upon justification, but the DAG that is most likely given most
people’s prior knowledge is one where unmeasured behavioral factors cause both smoking and coffee consumption.
It is unlikely that either smoking causes coffee use or vice versa but if students state such a causal relationship with
conviction, then it is acceptable. This question points out how prior substantive knowledge is critical to draw a
DAG but this knowledge may not always be clear cut.




                                   Behavioral factors
                                                                    Coffee consumption




                                      Smoking
                                                                                   ?




                                                                             CAD




                  Question 2d)




Epi Methods: Problem Set 9                               6                   Confounding and Interaction I
3. A case-control study was conducted to examine the relation between use of estrogen
replacement therapy (ERT) and development of ovarian cancer among peri- and postmenopausal
women. The following data were collected about the other potential risk factors of ovarian
cancer. The data were collected among women who did not use ERT. (adapted from Kleinbaum
2003)

Factor                                                       Odds ratio for development of ovarian cancer
Age at menarche
    <12 yrs                                                  1.0 (reference)
    12 yrs                                                   0.99
    13 yrs                                                   0.99

Number of live births
   0                                                         1.0 (reference)
   1                                                         0.95
   2-3                                                       0.75
   4                                                         0.65

Education
    <High school                                             1.0 (reference)
    High school                                              1.92
    College                                                  3.48

Based only on the data in the above table, indicate whether each of the following statements is
true or false and justify your answer.

a) Age at menarche is unlikely to be a confounder of the relationship between ERT and ovarian
cancer. (1 pt)

Answer: True. Age at menarche is essentially unrelated to ovarian cancer in these data (no association). Therefore,
it is unlikely that it could be a confounder in the relationship between ERT use and ovarian cancer. It is also
acceptable to state that it is possible that age at menarche is truly a confounder but that sampling error is preventing
us from seeing this relationship in this particular study sample.

b) Number of live births is unlikely to be a confounder of the relationship between ERT and
ovarian cancer. (1 pt)

Answer: False. There appears to be a dose-response relationship between number of live births and reduction of
ovarian cancer. In particular, those women with 4 live births appear to have a 35% reduction in the odds of ovarian
cancer compared to women with no live births. This is a clinically important effect size, and therefore number of
live births can be considered to be associated with the outcome variable. Even if there is just a modest association
between number of live births and ERT use, there is likely to be some degree of confounding in the relationship
between ERT use and ovarian cancer. We certainly cannot say, with the data at hand, that it is unlikely that number
of live births could be a confounder.

c) Education is definitely a confounder of the relationship between ERT and ovarian cancer. (1
pt)

Answer: False. Although education is clearly a strong predictor of ovarian cancer, we are not told of its relationship
with ERT use. Therefore, we simply do not know, using the available data, if it will confound the relationship
between ERT use and ovarian cancer. This illustrates how factors need to be associated with both the exposure and
outcome under study to be definitely considered confounders.


Epi Methods: Problem Set 9                            7                  Confounding and Interaction I
4. Consider the following abstract:

Risk factors for cervical intraepithelial neoplasia in southwestern American Indian women.
    The authors assessed risk factors for cervical intraepithelial neoplasia (CIN) among southwestern American
    Indian women using case-control methods. Cases were New Mexico American Indian women with biopsy-
    proven grade I (n = 190), grade II (n = 70), or grade III (n = 42) cervical lesions diagnosed between November
    1994 and October 1997. Controls were American Indian women from the same Indian Health Service clinics
    with normal cervical epithelium (n = 326). All subjects underwent interviews and laboratory evaluations.
    Interviews focused on history of sexually transmitted diseases and sexual behavior (i.e. number of partners).
    Laboratory assays included polymerase chain reaction-based tests for cervical human papillomavirus infection,
    tests for gonorrhea and chlamydia, wet mounts, and serologic assays for antibodies to Treponema pallidum,
    herpes simplex virus, and hepatitis B and C viruses. In multiple logistic regression analysis, the strongest risk
    factors for CIN among American Indian women were any human papillomavirus infection (OR = 5.8; 95% CI:
    3.3, 10.0), and low income (OR = 3.3; 95% CI: 1.7, 6.2). Unlike previous research, this study found no strong
    associations between CIN and sexual behavior (number of partners) after adjustment for the above other factors
    associated with CIN.
(Substantive note: Human papillomavirus is a causal agent of CIN)

The authors felt it was notable that unlike previous research, this study found no strong
association between CIN and sexual behavior (as measured by number of sexual partners).
Assuming this was not because of chance, selection bias, or measurement bias, can you explain
why no association was found? Draw a DAG. (2 pts)
Answer: The abstract suggests that there was no effect of sexual activity in an analysis that included adjustment for
HPV infection. HPV infection resides immediately on the causal pathway between sexual activity and CIN. In
other words, it is not the sexual activity per se that is responsible for CIN, it is the infection (HPV) that is spread by
sexual activity. Adjusting (or controlling) for HPV infection means that one is looking at the effect of sexual
activity in persons with the same classification (or status) for HPV infection. It is therefore not surprising that after
adjustment for HPV, there is no longer an effect of sexual activity. This illustrates what occurs when one adjusts for
factors residing on the causal pathway in question.




                                                                     # sexual partners




                                                                      HPV infection      ?




                                                                            CIN



                   Question 4




Epi Methods: Problem Set 9                             8                  Confounding and Interaction I
5. Observational studies are often performed to evaluate already-licensed drugs for new
indications. Confounding by indication refers to the specific type of confounding that may occur
in such observational studies because those patients who are prescribed drugs are generally
different from those who are not prescribed the drug. Specifically, the reasons why certain
patients with a given disease/condition are prescribed drugs, and others are not, may be related to
the outcome of interest. Consider an observational study to evaluate an antibiotic for its ability
to prevent post-operative infections following coronary artery bypass surgery.

a) Name one factor that you would want to measure as a potential confounding factor that might
result in an underestimation of the effect of the antibiotic in preventing infection. Explain your
answer and draw a DAG. (1 pt).

Answer: It is possible that those patients deemed to be at highest risk for post-op infection (e.g., diabetics or older
patients) might be most apt to be prescribed the antibiotic. Because those receiving the antibiotic are at higher risk
of post-op infection than those not prescribed, this is apt to underestimate the effect of the antibiotic.




                                                           Antibiotic use




                          Diabetes                                   ?




                                                           Post op infection




                   Question 5a)




b) Name another factor that you would want to measure as a potential confounding factor that
might result in an overestimation of the effect of the antibiotic in preventing infection. Explain
your answer and draw a DAG. (1 pt)

Answer: Very cautious and careful surgeons may be more likely to prescribe antibiotics for their patients. These
same surgeons might also have a surgical technique that results in a smaller incidence of post-op infections. This
would therefore spuriously lead to an underestimation of post-op infection in those who received antibiotics. Not
controlling for surgeon characteristics would result in an overestimate of the effect of antibiotic use on infection.
Documenting the actual surgeon involved in the case (and perhaps some other factors such as length of surgery) will
be necessary to deal with this potential confounder.




Epi Methods: Problem Set 9                             9                    Confounding and Interaction I
                             Antibiotic use




       Careful Surgeon                 ?




                             Post op infection




    Question 5b)




Epi Methods: Problem Set 9            10         Confounding and Interaction I
6. You have been awarded a lucrative grant from a large food manufacturing corporation to
study whether the consumption of irradiated food is causally related to the development of a
variety of malignancies via a mechanism of mutation of human genes. This is to address public
concern about the safety of food irradiation. The design will be observational (case-control due
to the rarity of most cancers). The company’s chief executive officer has insisted you not
measure body mass index (BMI) as part of your study as he is concerned that you might find that
eating his product is associated with obesity during the course of your analysis. How would you
respond to the executive officer’s request not to measure BMI? Draw a DAG. (2 pts)

Answer: The scientific question is whether the components of the irradiated food per se are in some way capable of
causing cancer via alteration of human genes. In this case, BMI is extraneous and should be considered as
downstream from the true common cause (some unmeasured behavioral factor) of both irradiated food consumption
and cancer. Presumably you are not interested in whether eating this type of food is associated with eating more
food in general (or exercising less) and hence a higher body mass index, which is known to be associated with a
greater risk for some cancers. Hence, if you do not measure and control for body mass index , you may end up
observing an association between the consumption of irradiated food and cancer, but one that is caused by the
confounding influence of behavioral factors. Such a finding would surely force the company to stop production of
these foods when, in fact, they might be entirely safe in terms of causing cancer.




                                     Behavioral factors
                                                                 Irradiated food
                                                                    consumed



                                                                              ?
                                              BMI




                                                                     Cancer




                Question 6




Epi Methods: Problem Set 9                          11                Confounding and Interaction I
7. Consider the following data:
The Pima-Papago group of Native Americans has long been known to have a high prevalence of type 2 (non-insulin-
dependent) diabetes mellitus. In a sample of 4,920 individuals self-reporting as Pima-Papago but who also have
varying extents of Caucasian racial background, there is a very strong negative (inverse) association between a
particular genetic haplotype for immunoglobulin (Gm3;5,13,14) and the occurrence of type 2 diabetes (crude
prevalence ratio = 0.27, 95% confidence interval 0.18-0.40).

One might conclude from this observation that the presence of this haplotype protects against the
occurrence of type 2 diabetes mellitus (DM). Investigations using other populations which were
more homogeneous in terms of racial background could not replicate this finding. Can you think
of a way that confounding could explain the association between the Gm haplotype and
prevalence of type 2 DM in the study described? Draw a DAG. (2 pts)
Answer:
Without knowing anything else about the biology or genetics of this system, one should be able to infer that the Gm
haplotype may be associated with a person’s genetic ancestry. In turn, genetic ancestry could be associated with
another gene that is actually the true culprit in preventing diabetes development. Or, genetic ancestry may be
associated with behavioral or environmental factors that are actually the true culprit in preventing diabetes
development. This is a classic example of how confounding can introduce bias into studies of genetic epidemiology.
In more detail,

    1) The haplotype in question (Gm 3;5,13, 14) is associated with genetic ancestry (racial background).
       Specifically, Gm3;5,13,14 is more prevalent in those of Caucasian ancestry.
    2) Genetic ancestry (racial background) is also associated with risk of type 2 diabetes (DM). From other
       studies, it is known that the Pima and Papago tribes, the Native Americans included in this study, have a
       higher risk of type 2 DM than Caucasians.
    3) The participants in this study have a range of racial admixture, including people whose ancestry is mostly
       Pima-Papago and those whose ancestry is mostly Caucasian. When the analysis was stratified by degree
       of racial admixture, there was no longer an association between the Gm haplotype and type 2 DM. (The
       prevalence ratio was 0.91 for full Pima-Papago participants and 0.89 for full Caucasian.) Thus, the results
       reported above (prevalence ratio = 0.27 for the Gm haplotype Gm3;5,13,14) are confounded by the degree
       of Caucasian admixture among the Native Americans in this study population. (See tables below)
    4) This indicates that the reason for increased risk of type 2 DM in the Pima-Papago tribes compared with
       Causcasians is not due to the Gm haplotype but to some other factor, genetic or behavioral/environmental,
       that differs between Caucasians and the Pima-Papago population.

(Knowler et al. Am J Hum Genet. 1988 Oct;43(4):520-6.)


A. Crude prevalence of type 2 DM according to Gm marker

Gm marker                  Prevalence of diabetes
Present                    7.8%
Absent                     29.0%

Crude prevalence ratio = 7.8% / 29.0% = 0.27

B. Stratify by degree of admixture, into these stratum-specific tables, to calculate prevalence ratio for each
stratum:

0% Pima-Papago                      50% Pima-Papago                        100% Pima-Papago
Gm         Prevalence of            Gm marker Prevalence of                Gm         Prevalence of
marker     diabetes                             diabetes                   marker     diabetes
Present    17.8%                    Present     28.3%                      Present    35.9%
Absent     19.9%                    Absent      28.8%                      Absent     39.3%
Prevalence 0.89                     Prevalence 0.98                        Prevalence 0.91
ratio                               ratio                                  ratio



Epi Methods: Problem Set 9                          12                Confounding and Interaction I
        Genetic ancestry/
        racial background


                                               Gm haplotype
                                               (Gm3;5,13,14)
                              Unidentified
                              genetic factor
                                                         ?



            Unidentified                           Type 2
          environmental or                         diabetes
          behavioral factor




   Question 7




Epi Methods: Problem Set 9                        13           Confounding and Interaction I
8. A cohort study has been conducted to assess whether regular jogging prevents sudden cardiac
death in middle-aged men. The data analyst notes that 30% of joggers had pulse rates below 60
beats/minute at their study enrollment exams, versus only 10% of sedentary subjects. A slow
pulse rate at enrollment is also found to be a protective factor for sudden cardiac death (rate ratio
= 0.6) among both joggers and non-joggers. Should the investigator adjust for pulse rate in
evaluating the causal effect of jogging on the risk of sudden cardiac death? Why or why not?
Draw one or more DAG to explain your answer. (2 pts)
Answer: In the initial analyses it would be advisable not to adjust for pulse rate since this is likely a mechanism (or
marker for a mechanism) for the protective effect of jogging. In other words, it is an intermediary factor. You might
want to adjust for pulse rate in subsequent models to see if there is an effect that is mediated by a pathway other than
lowering the pulse rate. Note: Credit is also given for hypothesizing that jogging might be caused by upstream
behavioral factors that are also responsible for lowering of the pulse rate via other mechanisms (e.g., swimming).
Hence, adjusting for pulse rate would be incorrect in this scenario and instead adjusting for the other behavioral
factors would be necessary.



                                                                     Jogging
  Initial analysis with
  pulse rate as
  intermediary. Do not
  adjust for pulse rate.
                                                                     Pulse rate ?




                                                                   Cardiac death




Subsequent analysis with
adjustment for pulse rate
as an extraneous
pathway. Goal is to                                                  Jogging

evaluate presence of
another mechanistic
pathway.                                         Pulse rate                 ?




                                                                     Cardiac death




Epi Methods: Problem Set 9                            14                  Confounding and Interaction I
Presence of confounding
                          Behavioral factors          Jogging
by behavioral factors.
Do not adjust for pulse
rate.

                                Swimming
                                                      Pulse rate ?




                                                    Cardiac death
                 .




Epi Methods: Problem Set 9                     15      Confounding and Interaction I
9. There is growing interest in whether inflammation is important in the pathogenesis of
coronary artery disease (CAD) and whether the presence of certain inflammatory diseases
outside of the heart can influence the risk of development of CAD. Specifically, there is interest
in the role of periodontal disease. To address this, a cohort study was performed to evaluate the
independent association between periodontal disease (inflammation of the gums and other soft
tissue in the mouth) and the occurrence of CAD. The unadjusted (crude) analysis found that
those persons with periodontal disease at baseline have a higher rate of CAD than persons
without periodontal disease. Assessment of plasma level of C-reactive protein (CRP) was also
performed at baseline. CRP level is known to be elevated in many inflammatory conditions and
has also been associated with the development of coronary artery disease. In this cohort study,
after adjustment for CRP level, the association between periodontal disease and coronary artery
disease was no longer present. Using the causal diagrams (DAGS) that were demonstrated in
class, sketch out two scenarios that would explain why adjustment for CRP resulted in no longer
seeing an effect for periodontal disease. In which scenario would you predict that treating
periodontal disease would reduce the incidence of coronary artery disease? (2 pts)

Answer:

There are at least two scenarios that could explain this. The first is that CRP is an intermediary variable along the
causal pathway. In this scenario, treatment of periodontal disease would be expected to decrease incidence of CAD.




                                                   Periodontal disease




                                              Inflammation (measured by CRP)      ?




                                                 Coronary artery disease
     Question 9 – CRP as an
     intermediary




The second scenario is that CRP is a proxy for a confounding variable in the sense that it is a marker for a genetic
predisposition for developing inflammatory conditions. In other words, certain people may be more prone to
develop inflammation, including both periodontal disease and coronary artery disease, and these people have higher
CRP levels. Having a high CRP level may therefore be thought of as the “cause” rather than the result of
periodontal disease. The interpretation of this scenario is very different from the first scenario. Here, periodontal
disease is not independently causally related to CAD. Specifically, treatment of periodontal disease would not be
expected to influence occurrence of CAD.




Epi Methods: Problem Set 9                           16                  Confounding and Interaction I
                                                    Periodontal disease




           Genes             Inflammation         CRP               ?




                                                  Coronary artery disease
     Question 9 – CRP as a
     confounder




It is important to note that these two scenarios cannot be distinguished by simply performing the adjusted and
unadjusted analysis that was described in the question above. This example illustrates how intermediary variables
and confounding variables can behave the same way numerically such that some external data or understanding of
the system must also be available to distinguish them.




Epi Methods: Problem Set 9                         17                   Confounding and Interaction I
10. Consider the following DAG:


          gender

                                     Exercise




                                    High stress

                                                      Anxiety disorder


                                  Blood pressure


     Question 10

                                       CHD




a) Which factor(s) would you control for if you want to know the causal effect of exercise on
blood pressure? (1 pt)
Answer: gender

b) If you want to know the causal association between high stress and blood pressure would you
consider gender to be a confounder? Explain. (1 pt)

Answer: Yes. Note that the effect of gender on stress is mediated via exercise.

c) If you wanted to know the causal association between high stress and blood pressure would
you have to control for gender to prevent confounding? Are there any other options to prevent
confounding by gender? (1 pt)

Answer: No, you would not have to control for gender. Although gender is a confounder, the path could be blocked
by controlling for exercise instead.

d) What would you control for if you want to estimate the overall causal effect of gender on
CHD, irrespective of mechanism? (1 pt)

Answer: Nothing.

e) After submitting a manuscript in which you examine the causal association between gender
and blood pressure, a reviewer suggests that CHD may be a confounder of the association
because prior studies have shown that it is associated with both gender and blood pressure. The
reviewer suggests controlling for this factor in the analysis. Do you agree? Explain. (1 pt).
Answer: In this case CHD is a collider because it is a common effect of the exposure and outcome. Conditioning on
a collider will induce a spurious association between the two factors for which arrows lead into the collider (cause
the collider). This factor therefore should not be controlled for in the analysis.




Epi Methods: Problem Set 9                          18                   Confounding and Interaction I
11. Consider the Grosso et al. article on oral bisphosphonates and atrial fibrillation that was
discussed in Journal Club a few weeks ago. The DAG below shows the system under study.
The boxes shown are encompassing two major factors or type of factors leading to confounding.
One box indicates that the node was dealt with by adjustment and the other by the study design
per se. Fill in what you believe these nodes within the boxes are. (1 pt extra credit)




                                      Oral bisphosphonates




                                                                     (managed
                                                      ?            by adjustment)

        (managed by study design)



                                             Atrial fibrillation




Answer: Age was measured and directly adjusted for. The authors controlled for age using ten, five-year, age bands (45–
49 years, 50–54, 55–59 etc.). IRR’s were calculated within each age stratum of the exposed period compared to baseline periods.
There is, however, the potential for other confounding factors, but the within-person nature of the self-controlled cases series
approach precludes confounding by these factors because each person is compared to him/herself. Hence, at least the time-
invariant “other factors” cannot result in confounding. Indeed, accommodation for these factors without having to measure them
is a key advantage of the study design.




                                      Oral bisphosphonates




                                                                      Age
        Other unmeasured factors                                     (managed
                                                      ?            by adjustment)

(managed by within-person study design)



                                             Atrial fibrillation




Epi Methods: Problem Set 9                                19                  Confounding and Interaction I

				
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