Download HOUR 1 Case control studies

Case-Control Studies
Lecture 5
June 14, 2006
K. Schwartzman MD
Case Control Studies
Readings
• Fletcher, chapter 6
• Walker, chapter 6 [Case-Control Studies] from
Observation and Inference, 1991 [course pack]
Case-Control Studies - Slide 1
Objectives
Students will be able to:
1.
Define the term “case-control study”
2.
Explain the relationship between case-control
and cohort studies
3.
Understand the difference between
cumulative incidence and incidence density designs
Case-Control Studies - Slide 2
Objectives
4.
Calculate parameters which may be validly obtained
from case-control studies, namely:
a. Odds parameters:
- odds of exposure in cases
- odds of exposure in controls
- odds ratio
b. Risk parameters:
- approximation of relative risk
- attributable fraction
c. Incidence rate parameters:
- incidence rate ratio
- attributable fraction among the exposed
- attributable fraction for the population
Case-Control Studies - Slide 3
Objectives
5.
Indicate situations in which case-control studies
permit estimation of rate differences between
exposure groups
6.
Highlight advantages and disadvantages of
case-control studies, including key biases
7.
List possible sources of controls in
case-control studies
8.
Identify biases which may result from
different types of control selection
Case Control Studies - Slide 4
Case-Control Studies
Fletcher, p. 92:
“Two samples are selected: patients who have developed the
disease in question, and otherwise similar people who do not
have not developed this disease. The researchers then look
backward in time to measure the frequency of exposure to a
possible risk factor in the two groups.”
In other words, a study population is first assembled
based on a determination as to whether subjects
have or have not developed an outcome of interest.
Subjects (or person-time) are then classified as to
whether an exposure of interest took place.
Data on other variables (e.g. potential confounders)
are also obtained.
Case-Control Studies - Slide 5
Walker, 1991:
“Case-control studies constitute the
major advance in epidemiologic methods
of our time”
Classic example:
Doll & Hill, relationship between lung cancer
and cigarette smoking (1950)
Case-Control Studies - Slide 6
Advantages
Useful for study of conditions that are rare
and/or characterized by a long latency
between exposure(s) and outcomes of interest.
May be useful in evaluating the impact of
multiple types of exposure.
Disadvantages
May be particularly vulnerable to biases arising from
selection of subjects (most often of the control group),
and measurement (estimation) of exposure
Case-Control Studies - Slide 7
In case-control studies, data about exposure status is
calculated after first determining outcome status.
However, subjects may be recruited “prospectively”
(concurrently), e.g.:
-
All persons aged 30-50 who are diagnosed with
hypertension on the island of Montreal during 2006,
within 2 weeks of diagnosis.
-
Controls recruited among persons of the same age
who are newly diagnosed with appendicitis in
Montreal during the same time period.
Case Control Studies - Slide 8
Often, outcome status is already available for all subjects
(“historical”) at the time of initiation, e.g.:
-
During 2006, a researcher identifies all women
aged 40-50 who were diagnosed with breast cancer
on the island of Montreal in 2004.
-
In 2006, she recruits a control group among
women of the same age who had negative
screening mammograms in Montreal in 2004.
Case-Control Studies - Slide 9
Note that the terms
“prospective” and “retrospective”
are not very useful
with respect to case-control studies,
since data about exposure status
is always retrospective (by definition).
Case-Control Studies - Slide 10
Cohort and Case-Control Studies
Every case control study corresponds to an underlying cohort study,
which is (ordinarily) hypothetical.
Example (from Doll & Hill, 1950):
_____________________________________________________
Women diagnosed with lung cancer vs other diseases
at 20 London hospitals
Smokers
Non-Smokers
Total
Lung cancer cases
41
19
60
No lung cancer (controls)
28
32
60
Total
69
51
120
_________________________________________________________
Crude odds ratio = odds of exposure in cases/odds of exposure in controls
= (a/b)/(c/d)
= ad/bc = (41x32) / (19x28) = 2.5
Case-Control Studies - Slide 11
In the corresponding cohort study,
women from the same geographic area
would be recruited and classified as to
smoking status, then followed for the
development vs non-development of lung cancer.
Case-Control Studies - Slide 12
Assuming all cases of lung cancer during the period of interest
were detected,
one possible 2x2 table
would be
Lung cancer
No lung cancer
Total
OR = 2.5
but it could also be:
Lung cancer
No lung cancer
Total
OR = 2.5
Smokers
41
859
Non-Smokers
19
981
Total
60
1,840
900
1000
1,900
Smokers
41
70
Non-Smokers
19
81
Total
60
151
111
100
211
Case-Control Studies - Slide 13
•
The cases diagnosed and included, and the
controls sampled, relate to the exposure experience
of an underlying source population.
•
In each scenario, the estimated odds of cigarette
smoking among women with lung cancer are 2.5 times
those among women without lung cancer.
•
In each scenario, all cases of lung cancer were
included. The size of the source population
(and hence the number of non-cases) was varied.
Case-Control Studies - Slide 14
Cumulative incidence case-control studies
Goal is to
derive estimate of relative risks
(relative cumulative incidences)
of outcomes among
exposed vs. unexposed
Design:
-
Cases are ascertained during a defined
observation period
-
Controls are persons who did not become cases
during the period of observation.
-
The underlying cohort is a fixed one
(not open or dynamic).
Case-Control Studies - Slide 15
Doll and Hill, 1950
Assume that the source population was as follows:
900 smokers & 1000 non smokers - followed 5 years
Then the 2x2 table would be:
Smokers
Non-Smokers
Total
Cancer +
Cancer -
41
859
19
981
60
1,840
Total
900
1,000
2,000
________________________________________________
Risk of cancer in smokers:
41/900 = 0.046
Risk of cancer in non smokers:
Risk ratio:
19/1000 = 0.019
0.046/0.019 = 2.4
Odds of smoking in women with cancer:
Odds of smoking in women without cancer:
Odds ratio
41/19 = 2.2
859/981 = 0.88
= 2.5
Case-Control Studies - Slide 16
In the corresponding case control study we take 100% of cases, but
sample the controls (60/1840 or 3.3% of all potential controls - those
who happened to be admitted to hospital for some other reason).
Hence the new table is:
Cancer +
Cancer -
Smokers
Non smokers
100% x 41 = 41
3.3% x 859 = 28
100% x 19 = 19
3.3% x 981 = 32
Total
60
60
Total
69
51
120
_________________________________________________________
“Risk” of cancer in smokers:
“Risk” of cancer in non smokers:
41/69 = 0.59 INVALID
19/51 = 0.37 INVALID
The “risk ratio” from this 2x2 table is also invalid
Odds of smoking among cases:
Odds of smoking among controls:
Odds ratio:
41/19 = 2.2 (as before)
28/32 = 0.88 (as before)
2.2/0.88 = 2.5 (as before)
Case-Control Studies - Slide 17
General Form: Cumulative incidence case-control studies
outcome +
outcome -
exposure +
a
c
___________
exposure b
d
_____________
|
||
total cases
total controls
total exposed
total unexposed
|
total subjects
Odds of exposure in cases = a/b
Odds of exposure in controls = c/d
Odds ratio =
odds
of exposure in cases
______________________
odds of exposure in controls
= a/b
___
c/d
= ad
__
bc
but:
Odds of disease among exposed = a/c
Odds of disease among unexposed = b/d
Odds ratio =
odds
of disease among exposed
= a/c
___________________________
___
odds of disease among unexposed
b/d
= ad
__
bc
Case-Control Studies - Slide 18
Risk parameter estimation
in cumulative incidence case-control studies:
Recall that relative risk =
risk
of disease in exposed
______________________
risk of disease in unexposed
 From our 2x2 table, this is:
a/(a+c)
_______ =
b/(b+d)
a(b+d)
______
b(a+c)
 If the disease is rare,
then
a<<c and b<<d among the source population
then
a+c ~ c
then
a(b+d)
______ ~ ad
__
b(a+c)
bc
and
b+d ~ d
Case-Control Studies - Slide 19
In a case-control study, it is then possible to estimate
the attributable risk (fraction) among the exposed,
even if the risk for the population is unknown.
In a cohort study, the attributable risk fraction is:
R
exp - Runexp
__________
Rexp
=
(R
exp/Runexp) - (Runexp/Runexp)
_______________________
Rexp/Runexp
=
RR-1
_____
RR
In a case-control study, this is estimated by (OR-1)/OR
This is the proportion of disease among exposed persons,
which is attributable to the exposure
Case-Control Studies - Slide 20
Hence, from Doll and Hill (1950),
the estimated fraction of
lung cancer among female smokers
which is attributable to smoking is:
2.5 -1
______
2.5
= 0.6 or 60%
In other words, there would have been
60% fewer lung cancers among those
women, had they never smoked
Case-Control Studies - Slide 21
Incidence Density Case-Control Studies
The incidence density case-control study involves the
implicit comparison of the person-time experience
of cases and controls with respect to the exposure(s)
of interest.
The absolute quantity of person-time sampled - and
hence the sampling fraction - is unknown. This is
analogous to the situation with respect to persons in a
cumulative incidence case-control study.
Case-Control Studies - Slide 22
Hence the underlying (hypothetical) cohort is an open
or dynamic one.
Persons considered controls at one point in time
may then become cases; they can then appear twice
in the 2x2 table.
For this cohort, the general form of the 2x2 table is:
exposure +
a
Pe
outcome +
person-time
Where
Pe = person-time among exposed
Po = person-time among unexposed
IRe = a/Pe
IRR =
exposure b
Po
aPo
____
bPe
and
IRo = b/Po
Case-Control Studies - Slide 23
Suppose that all cases are counted, but the
controls are sampled with respect to person-time,
with sampling fraction ”f” generating the incidence
density case-control study.
Then the 2x2 table is:
outcome +
outcome -
exposure +
a
c = fPe
Then OR = ad = afPo
___
_____
bc
bfPe
exposure b
d = fPo
= aPo
____
bPe
which is equivalent to the IRR above.
Case-Control Studies - Slide 24
Note that this formulation does not involve any
assumptions about disease rarity.
It requires that the likelihood of being sampled from the
source “population” of person-time varies as
a proportion of the person-time potentially “contributed”
by each individual.
For example:
A potential control subject who was absent from
the geographic area of interest during most of the
accrual period should have less chance of being selected
than a potential subject who was present throughout.
As with the cumulative incidence design, validity hinges
on the assumption that f (the sampling fraction)
does not vary with exposure status.
Case-Control Studies - Slide 25
Relationship between “open” cohort and incidence
density case-control studies
•
A researcher wishes to evaluate the association
between the use of nonsteroidal anti-inflammatory
drugs (NSAIDS) and ventricular tachycardia (VT)
•
In an open cohort study lasting 2 years,
subjects are recruited and classified as to
exposure status (NSAID use), then followed for
development of VT
•
In principle, it is possible to document periods
of exposure and non-exposure for individuals,
e.g. months on/off medication, as long as
exposure is somehow reassessed
Case-Control Studies - Slide 26
Then for the cohort,
incidence rates and an incidence rate ratio can be calculated for
the exposed vs unexposed person-time experience, e.g.
VT, cases
Person-years
Incidence
NSAID
No NSAID
Total
80
800
0.1/p-y
40
1200
0.033/p-y
120
2000
0.06/p-y
The estimated incidence rate ratio is:
80/800
_______
40/1200
=3
So, assuming no confounding, we estimate that the
incidence of ventricular tachycardia among NSAID users
is 3 times that among non-users
Case-Control Studies - Slide 27
Suppose we instead devise a case-control study.
Here, cases will be defined by a first diagnosis
of VT at Montreal hospitals, and
controls will be recruited among persons who
visit the eye clinics of the same hospitals:
both over a 2-year accrual period.
They will be compared with respect to use of
NSAIDS within the last 24 hours prior to presentation.

If sampling is done correctly (e.g. the probability
of selection is unrelated to NSAID use) then
the controls should represent the
person-time experience of the source population
Case-Control Studies - Slide 28
•
If a possible control spent half the accrual period
on NSAIDS, and half off, he has a 50% chance
of contributing to the “exposed” group and a
50% chance of contributing to the “unexposed” group
•
This individual will contribute one or the other,
depending on the date of the visit chosen as control;
but in a larger group of people,
the control days sampled will reflect the proportion
of exposed person-time
•
A person can be a control early in the accrual period
and a case later
•
In principle, a single person can also be sampled
repeatedly as a control if the time window for
exposure definition is short (more complicated in
terms of analysis)
Case-Control Studies - Slide 29
Suppose that the case-control study includes all cases which
would have been detected with the open cohort design.
Two controls are recruited per case. This (unbeknownst
to the researchers) corresponds to a sampling fraction
for controls of 0.12 person-day sampled per person-year
of follow-up that would have occurred in the open cohort.
Then the 2x2 table is:
NSAID
No NSAID
Total
VT, cases
No VT(controls)
80
40
120
800*0.12
1200*0.12
2000*0.12
= 96
= 144
= 240
_____________________________________________
Total
176
OR = (80x144)/(40x96) = 3.0
184

360
same as earlier IRR
Case-Control Studies - Slide 30
Another example of an incidence density design:
•
Bronchodilators are used for the treatment of asthma
•
There is concern that overuse may be associated with
an increased risk of adverse events, including death
•
Side effects can include arrhythmias, which may lead
to sudden death
•
Suissa et al conducted a case-control study using
the Saskatchewan health insurance database
•
They identified 30 persons prescribed anti-asthma
medications who died of cardiovascular events,
rather than of asthma; the date of death was
termed the index date
Case-Control Studies - Slide 31
•
4080 control days were then sampled randomly
from the 574,103 person-months of follow-up
for the entire asthmatic group; each such day
was also an index date
•
Cases and controls were then compared as to
use of theophylline and beta-agonists during the
3 months preceding the index date
•
These were the main exposures of concern
Case-Control Studies - Slide 32
Questions for discussion:
•
Why do you think the researchers chose
this study design?
•
What would have been the corresponding
cohort study?
Case-Control Studies - Slide 33
With respect to the relationship between theophylline use and
sudden cardiac death, the authors found the following:
Theophylline in last 3 months
Cardiac Death
Yes
No
Yes
17
956
No
13
3124
|
|
|
Total
30
4080
Note that numbers in table refer to
person-days (not to persons)
OR (crude)
= ad
__ =
bc
17
x 3124
________
13 x 956
IRR (crude)
= 4.3 (2.1 - 8.8)
=
4.3 (2.1 - 8.8)
Case-Control Studies - Slide 34
The odds of recent theophylline use among persons
aged 5-54 years prescribed anti-asthma drugs
who died of cardiovascular events were
4.3 times those among other persons in the same age
range who were also prescribed anti-asthma drugs,
but did not die.
“Asthmatics” aged 5-54 who are prescribed theophylline
have an estimated 4.3 fold increase in incidence of
fatal cardiovascular events, compared with
“asthmatics” who are not prescribed theophylline.
Case-Control Studies - Slide 35
As with the cumulative incidence design, an attributable rate
fraction can be estimated for exposed persons:
It is:
I____
e-Io,
Ie
where
= IRR
-1 =
______
IRR
Ie = incidence among exposed and
Io = incidence among the unexposed
OR
-1
_____
OR
For the Saskatchewan study, the estimated attributable
rate fraction among “asthmatics” who were prescribed
theophylline is:
4.3
- 1 = 0.77
______
4.3
Among “asthmatics” aged 5-54 prescribed theophylline,
an estimated 77% of fatal cardiovascular events
were related to its prescription.
Case-Control Studies - Slide 36
It is also possible to estimate the attributable rate fraction
for the entire population (PAR%)
In a cohort study, this is simply
I_____
t - Io,
It
where
It = incidence among the total population
Io = incidence among the unexposed
For the corresponding incidence density case-control study,
the population attributable rate fraction is
IRR
____- 1 x proportion of cases who were exposed,
IRR
estimated as
OR
-1 x
_____
OR
a
____
a+b
Similar parameters involving risk can be generated for
the cumulative incidence design
Case-Control Studies - Slide 37
For the Saskatchewan study, recall the 2 x 2 table
Theophylline in last 3 months
Cardiac death
Yes
No
Yes
17
956
No
13
3124
|
|
|
Total
30
4080
OR = 4.3
Pexp |case = 17/30 = 0.57
then PAR fraction = OR -1 x Pexp |case
_____
OR
=
4.3
- 1 x 0.57 = 0.44
______
4.3
Among Saskatchewan “asthmatics” aged 5-54, an estimated
44% of cardiovascular deaths relate to theophylline prescriptions.
Alternatively, had theophylline never been prescribed, 44% fewer deaths
would have occurred among “asthmatics.”
Case-Control Studies - Slide 38
Attributable rates (rate difference)
The absolute rate difference (i.e., the absolute
rate of disease attributable to exposure) is Ie - Io
Data from a standard case-control study alone
cannot validly be used to estimate
absolute rates of disease.
Even if case ascertainment is complete,
the controls represent an unknown and
arbitrary fraction of the true person-time at risk.
Hence the rate difference cannot be estimated.
Case-Control Studies - Slide 39
However, incidence rates can be estimated if there is
additional knowledge about the amount of person-time at risk
Exposure
Disease (+)
Disease (-)
(+)
(-)
a
c = f x  x Pt
b
d = f x (1- ) x Pt
Then Ie
=
a
= ___________
a
_____
 x Pt
[c/(c+d)] x Pt
Then Io
=
b
=___________
b
_________
(1- ) x Pt [d/(c+d)] x Pt
and the rate difference is Ie-Io
where  = proportion of person-time which is exposed
Case-Control Studies - Slide 40
Example:
In this nested case-control study,
the researchers knew that in the source cohort
(Saskatchewan “asthmatics” aged 5-54), there were
47,842 person-years at risk during the study period
The 2x2 table was:
Cardiac death
Yes
No
Theophylline in last 3 months
Yes
17
956
No
13
3124
|
|
|
Total
30
4080
Case-Control Studies - Slide 41
Then the estimated incidence of cardiac death in “asthmatics”
prescribed theophylline (Ie) is:
a
___________
[c/(c+d)] x Pt
= ________________
17
956/4080 x 47,842
= 0.0015 per person-year
And in “asthmatics” who were not prescribed theophylline the
estimated incidence (Io) is:
b
=
___________
[d/(c+d)] x Pt
13
= 0.00035 per person-year
_________________
3124/4080 x 47,842
The estimated rate difference is therefore
0.0015-0.00035 = 0.00115 per person-year.
Note that the IRR computed as Ie/Io remains 4.3
Case-Control Studies - Slide 42
Ie and Io may also be estimated if It is known for the source population
Recall that It = (Ie x ) + [Io x (1- )]
But Ie = Io x OR
Then It = Io [(OR x ) + (1- )]
So Io =
It
=
It
______________
________________________
(OR x ) + (1- )
{OR x [c/(c+d)]} + [d/(c+d)]
Then use Ie = Io x OR
Then RD = Ie - Io as usual [= Io (OR-1)]
Case-Control Studies - Slide 43
Example:
The total incidence (It) of cardiovascular death
in the Saskatchewan cohort was
30 deaths/47,842 person-years
= 0.00063 per person-year.
Then Io =
0.00063
___________________________
[4.3 x (956/4080)] + (3124/4080)
and Ie = 0.00036 x 4.3 = 0.0015
RD = 0.0015 - 0.00035 = 0.00115
= 0.00035
Case-Control Studies - Slide 44
Additional points

Corresponding estimates of attributable risks and
risk differences can be made for cumulative incidence
case-control studies, if the corresponding additional data
is available

Estimates of absolute risks/incidence rates and
risk/rate differences can be made only if the
total amount of persons/person-time at risk is known,
or at least one absolute risk/incidence rate is known
(i.e. for the total population, the exposed, or
the unexposed)

Nested case-control studies are a special type of study
where cases and controls are explicitly drawn from
a defined larger cohort (as in the Saskatchewan
asthma study)
Case-Control Studies - Slide 45
Case-Control Studies: Strengths and Limitations
Advantages of case-control studies:

Efficiency - much less expensive/intensive
than cohort studies.

Very useful for outcomes that are rare
or occur after a long latency period.

Most outcomes are relatively rare over
short-term follow-up.

Permit evaluation of multiple exposures.

Can rapidly “accrue” person-time experience.

Avoid losses to follow-up inherent in cohort studies.
Case-Control Studies - Slide 46
Disadvantages
• Not useful/efficient for very rare exposures
(may not be present in either cases or controls).
• Cannot directly compute incidence rates.
• Cannot usually evaluate more than one outcome.
• Temporality may be lost or distorted.
• Potential for considerable bias, i.e. loss of validity.
Bias relates to:
-
Measurement of exposure status
-
Selection of subjects (usually controls)
Case-Control Studies - Slide 47
With respect to measurement,
exposure ascertainment must be consistent
for cases and controls.
There may be potential for misclassification of
exposure in relation to disease status
Case-Control Studies - Slide 48
Example 1
Differential recall of exposures among cases
vs controls
e.g. medication use and congenital malformations
- particularly if mothers “attuned” to
study hypothesis.
If cases more likely to recall exposure,
results will be biased toward a
positive association between exposure and outcome.
The more objective the source of exposure data,
the better.
Case-Control Studies - Slide 49
Example 2
Different sources of information about exposure
e.g. family members asked about
alcohol consumption of persons
who died of gastric cancer,
vs direct questioning of control subjects.
If family members tend to underestimate cases’
alcohol consumption, results will be biased
against finding a positive association between
alcohol and gastric cancer.
Case-Control Studies - Slide 50
Example 3
Exposure status changes as a consequence of
the outcome
e.g. patients with symptoms of lung cancer
stop smoking
If patients with newly diagnosed lung cancer are
compared to controls with respect to current
or recent smoking, results may be biased, i.e.,
the association between smoking and lung cancer
will be underestimated.
Data collection must reflect relevant person-time
experience and temporality of exposure and outcome.
Case-Control Studies - Slide 51
Association may also be missed
if the exposure of interest is poorly documented
(an example of non-differential misclassification)
Example: mesothelioma
It can be caused by brief, intense exposures
to asbestos, with a very long latency period
(>30 years).
In a case control study,
both cases and controls may recall such exposures
very poorly, thereby leading to an underestimate
of the true association.
Case-Control Studies - Slide 52
Control selection in case-control studies
Recall that the validity of case-control studies
hinges on the assumption that the
sampling fraction for cases (which may be 100%)
and that for controls (usually unknown)
does not vary by exposure status.
In other words, controls should represent the
source population from which the cases arose,
with respect to exposure experience.
Case-Control Studies - Slide 53
Example 1
A researcher wishes to test the hypothesis that
use of nonsteroidal anti-inflammatory drugs (NSAIDs)
is associated with development of gastric cancer.
She plans a case-control study comparing gastric cancer
patients (cases) with patients seen at the same hospital
for peptic ulcer disease (controls).
- NSAID use is a known risk factor for ulcers.
What will be the effect on her findings:
a) if NSAID use is truly a risk factor for gastric cancer?
b) if NSAID use is truly unassociated with gastric cancer?
Case-Control Studies - Slide 54
Hence, controls should not differ systematically
from the population of interest
with respect to exposure experience.
Sometimes the bias may be less obvious,
i.e. unrelated to explicit criteria for
control selection.
Case-Control Studies - Slide 55
Example 2
A researcher wishes to evaluate the association between
cell phone use and brain tumours using a case-control design.

Cases are recruited from the brain tumour clinic at the
Royal General Hospital, a neurosurgery referral centre.

Controls are recruited from the family medicine clinic
at the same hospital. This clinic primarily serves a
low-income population from the area adjacent to
the hospital.

This control group is less likely than the general population
to own cell phones.
Result:
The study will be biased toward detecting an
association between brain tumours and cell phone use.
Case-Control Studies - Slide 56
Controls should be at risk for developing the outcome of interest
- otherwise they do not contribute useful data to the study
(inefficient)
- inclusion of individuals not at risk may
also distort the results if the reason they are not at risk
relates to the exposure under study. This may not be obvious.
Example:
Sleep apnea (exposure)
Cases:
and
risk of traffic accidents (outcome)
Drivers involved in car accidents.
Including non-drivers in the control group would be
a waste of time
- it could bias the results if
persons with severe apnea have chosen not to drive
and are over-represented in the control group.
Case-Control Studies - Slide 57
Controls should be persons who,
had they developed the outcome of interest,
would have had the same opportunity as
the actual cases to be included as such.
Similarly, cases should have
had the same opportunity as actual controls
to be included, had they
not developed the outcome of interest.
If this is not the case, controls may not properly
represent the source population.
e.g., study of brain tumours and cell phone use
discussed above
Case-Control Studies - Slide 58
Types of controls in case-control studies
1.
Population Controls

Suitable if cases are a representative sample
(or all cases) arising from a well-defined
source population.

Controls are then randomly sampled
from the same population.

With the incidence-density design,
the probability of being sampled should
vary with an individual’s person-time at risk.

Often, it is not easy to define the
precise source population.
Case-Control Studies - Slide 59
2.
Neighbourhood Controls

May match controls to individual cases
with respect to neighbourhood of residence.

If cases are from a hospital, their neighbours
may or may not be equally likely to be
treated at the same hospital should
they develop the disease in question.
Example:
A hospital which caters to a particular group
within society.
Case-Control Studies - Slide 60
3.
Family members or friends as controls

May share exposure characteristics with cases
as opposed to broader source population
(e.g. tobacco and alcohol use, dietary intake,
use of household products).
This can obscure relevant associations.

Depends on information provided by cases;
investigator loses control over factors leading
to selection.

Cases’ friends may overlap, leading to
disproportionate probabilities of selection
of certain individuals as controls.
Case-Control Studies - Slide 61
4.
Hospital/clinic based controls

Often used when cases accrued at specific
hospital(s)/clinic(s).

Controls are recruited among persons seen
at the same hospitals/clinics for
other reasons or conditions.

To avoid bias, the basis for control selection
cannot be related to the exposure under study.

The incidence of the “control” condition(s)
determines the sampling fraction.
Case-Control Studies - Slide 62
Example:
A researcher wishes to examine the relationship
between anti-hypertensive medication use
and car accidents.
What will happen if controls are recruited
in the cardiology clinic?
Case-Control Studies - Slide 63
The best hospital controls are
persons with acute conditions that
consistently require hospital care but
are not related to the exposure of interest.
Example:
In a case control study of smoking as a
risk factor for colon cancer, a researcher
recruits controls who undergo appendectomy,
prostatectomy, or hysterectomy at
the same hospital as the cases.
Supplemental Material - Slide 1
Derivation of formula - Part 1
For the cohort study, the 2 x2 table is:
Cases
Person-time
IRR
= Ie
___
Io
=
exposed
a
Pe
unexposed
b
Po
a/Pe
aPo
_____
b/Po
= a(P
t - Pe)
_______
bPe
= a
_ x
b
=
=
____
total
a+b
Pe + Po = Pt
bPe
a
(1 - Pe/Pt)
_________
b (Pe/Pt)
(1-)
____

Where  = Pe/Pt =
the proportion of person-years with
exposure among total person-years
in the source population
Supplemental Material - Slide 2
Furthermore,
a
_ =
b
a/(a+b)
_______
b/(a+b)
=
=
P
exp|case
__________
1- Pexp|case
where Pexp|case = proportion of cases exposed
Then IRR
=
P
exp|case (1- )
_____________
 (1-Pexp|case)
Equation 1
Supplemental Material - Slide 3
Derivation of formula - Part 2
if
 = proportion of person-years with exposure
then 1- = proportion of person-years without exposure
and
It = Ie  + Io (1- )
i.e. a weighted average of incidence rates
among exposed and unexposed persons
Supplemental Material - Slide 4
Then the PAR fraction is:
I_____
t - Io
It
=
=
(I
e ) + [(Io (1- )] - Io
____________________
(Ie ) + [Io (1- )]
 (Ie/Io) + (1- ) (Io/Io) - Io/Io
______________________________________
 (Ie/Io) + (Io/Io) (1- )
=

(IRR) + 1 -  - 1
________________
 (IRR) + 1 - 
=
 (IRR - 1)
____________
 (IRR - 1) + 1
Supplemental Material - Slide 5
Derivation - Part 3
= IRR
-1
_____________
IRR + (1/ ) - 1
= IRR
-1
____________
IRR + (______
1-  )

= IRR
-1
______________
IRR + IRR
(1- )
_________
IRR ()
Supplemental Material - Slide 6
Substituting equation 1 for IRR, this is
IRR
-1
____________________________
IRR + _______________________
IRR (1- ) () (1 - Pexp |case)
() (Pexp |case) (1- )
=
IRR
-1
__________________
IRR + _____________
IRR (1-Pexp |case)
Pexp case
=
IRR
-1
______________________________
IRR
(Pexp |case) + IRR - IRR (Pexp |case)
______________________________
Pexp case
=
IRR
-1 x
______
IRR
Pexp |case
= OR
-1 x Pexp |case
____
OR