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Leicester Warwick Medical School
Health and Disease in Populations
Case-Control Studies
Paul Burton
Lecture Objectives
You should be able to:1. Describe the principles underlying case-control
studies2. Describe the differences and similarities
between case-control studies and other epidemiological designs
3. Outline the factors which suggest that a case-control design might be suitable for a particular epidemiological question
Lecture Objectives
4. Describe the limitations and assumptions inherent to case-control designs
5. Estimate the strength of an association from the result of a simple case-control study, and calculate and interpret the error factor and 95% confidence interval for this estimate
Recommended reading from Prescribed book: Farmer and Miller, Ch 6, pp56-67
A hierarchy of study designs
Cohort Studies
Exposed
Unexposed
Time
Count events and pyrs
Count events and pyrs
Cohort and case-control studies
• Cohort study (bladder cancer and cigarette smoking)• Exposed: 100 cases in 100,000 people followed over 10
years = 1,000,000 pyrs• Unexposed: 10 cases in 200,000 people followed over 10
years = 2,000,000 pyrs• IRR = (100/1,000,000) (10/2,000,000) = 20
Cohort and case-control studies• Now ask question the other way around
• What are the odds of having been a smoker if you are a case?
• 100:10 = 100/10 = 10• What are the odds of having been a smoker if you are not
a case?• 99,900:199,990 = 99,900/199,990 = 0.4995
• What is the ratio of the odds (OR=odds ratio)?• 10/0.4995 = 20.02• NB (100/99,900) (10/199,900) = (100/10)
(99,900/199,900) = 20.02
• Very similar result to cohort analysis
Cohort and case-control studies
• What if we only have a 10% sample of the non-cases?• What are the odds of being a smoker if you are a case?
• 100:10 = 100/10 = 10• What are the odds of being a smoker if you are not a case?
• 9,990:19,999 = 9,990/19,999 = 0.4995• What is the ratio of the odds (OR=odds ratio)?
• OR=10/0.4995 = 20.02
• Exactly the same result!!
Cohort and case-control studies• What if we only have a 50% sample of the cases and
a 20% sample of the non-cases?:• What are the odds of being a smoker if you are a case?
• 50:5 = 50/5 = 10• What are the odds of being a smoker if you are not a
case?• 19,980:39,998 = 19,980/39,998 = 0.4995
• What is the ratio of the odds (OR=odds ratio)?• OR=10/0.4995 = 20.02
• Exactly the same result again!!
The general case (full population data)
CASES
NON-CASES
EXPOSED
a
b
UNEXPOSED
c
d
d
c
b
a
bc
ad
d
b
c
aOR
Sampling fractions: 0.637 in cases,0.02 in non-cases
CASES
NON-CASES
EXPOSED
a0.637
b0.02
UNEXPOSED
c0.637
d0.02
bc
ad
d
b
c
a
0.02d
0.02b
0.637c
0.637aOR
Sampling fractions
• Regardless what proportion of all possible cases are collected (the sampling fraction in cases) and what proportion of all possible non-cases (the sampling fraction in non-cases) the two sampling fractions always cancel in calculating the odds ratio (OR)
• If we now call the non-cases “controls” this is a “case-control study”
Case-control studies
• We compare the odds of having been exposed in cases with the odds of having been exposed in the controls
• This gives us an odds ratio (OR) which is unaffected by the potentially different sampling fractions in cases and controls
Case-control Studies
Case
Non-Case(Control)
Exposed?
Exposed?
Time
Conducting a case-control study
• Identify a group of cases• Identify a suitable group of non-cases• Ascertain exposure status of everyone• Compare level of exposure in cases and controls
Why use a case-control approach?
• Quick• Fundamentally retrospective: no need to wait for a
follow-up period
Why use a case-control approach? • Cheap
• With a rare disease, most people in a cohort study will not develop disease and so most of the follow-up will be of people who contribute little information
• By using a low sampling fraction in controls in a case-control study you avoid having to collect information on a large number of non-cases
e.f. for IRR =
dd
112exp
Expected yield of cohort studies:
Disease P-y observation needed to yield 100 cases
CHD (cases) 10,000 CHD (deaths) 20,000 Lung cancer 50,000 Stomach cancer 200,000 Bladder cancer 1,000,000 Leukaemia 2,000,000
The OR and the IRR• Original example: IRR=20, OR=20.02• “The rare disease assumption”
• The approximation gets better and better as a disease gets rarer and rarer in the general population
• There is a special form of case-control study based on what is called “incidence density sampling” for which the approximation is always perfect – you don’t need to know about this for the HaDPop course
• Even when the IRR and OR are different (e.g. IRR=5.1, OR=6.3) both are still measures of some sort of ‘risk ratio’ and both are therefore useful. It is not that one is ‘right’ and one is ‘wrong’: they express the same thing in a slightly different way.
Benefits of case-control studies
• Good for rare outcomes• Possible to look at a lot of different exposures in
detail• Often no practicable alternative
Limitations of case-control studies• No estimate of population incidence, only of relative
risk• The differing sampling fractions always cancel out in
calculating ad/bc, but not in trying to calculating e.g. c/d (the odds of someone in the general population being a case if they are unexposed).
• Unless you know the sampling fractions• More prone to bias:
• Information bias• Selection bias
• It can be impossible to determine whether the disease causes the exposure or vice versa
• Not suitable for rare exposures
Information bias• Does cigarette smoking cause ischaemic heart
disease?• Cases: average 5 cigarettes/day• Controls: average 5 cigarettes/day
• Looks as if the exposure is not associated with the disease. But:• True exposure in cases: 10 / day• True exposure in controls: 5 / day
• Here, cases tend to understate their intake• In addition
• Random errors push OR towards 1.0 (shrinkage)
Selection bias• Case-control study of lung cancer and smoking• Get cases of lung cancer from the respiratory
medicine wards.• Get controls as a random sample of patients
from the same wards who do not have lung cancer
• But, smoking causes lots of other respiratory diseases as well as lung cancer so the patients on the ward are not a representative sample of the general population. Will underestimate OR.
Analysis
CASES
CONTROLS
EXPOSED
w
x
UNEXPOSED
y
z
xy
wz
z
x
y
wOR
z
1
y
1
x
1
w
12expe.f.
95%CI: OR e.f., OR e.f.
How many controls?
• Unlike an IRR, the precision of an OR is affected by the number of healthy people (x and z):
•
• So, it is worth increasing the number of controls - up to a point (typically up to 4-6 times as many controls as there are cases)
z
1
y
1
x
1
w
12expe.f.
Creutzfeld Jacob Disease (CJD) and occupation
• Odds ratio = (9×104)/(3×13) = 24
•
• 95% CI: 24÷4.29, 24×4.29 = (5.59, 103.0)
CJD Cases
Non CJD Controls
Farmer/meat worker
9 3
Other occupation
13 104
29.4104
1
13
1
3
1
9
12expe.f.
Multiple levels of exposureCigarettes
/day Cases Controls OR
(95% CI) 35+ 123
w 59 x
29.7 (13.4-65.9)
21-34 186 w
91 x
29.1 (13.4-63.3)
16-20 213 w
278 x
11.0 (5.2-23.3)
10-15 61 w
148 x
5.9 (2.7-13.0)
1-9 14 w
90 x
2.2 (0.9-5.6)
0 8 y
114 z
[1]
605 780
Retrospective v prospective?• Confusing terminology: two different issues• (1) Does the analysis look forwards or backwards?• (2) Are the data collected as and when they occur (i.e.
prospectively) or from historical review - questionnaire, case-notes or other health records – (i.e. retrospectively).
• Cohort analysis always looks forwards in time:• Given exposure status at baseline, how many events
occurred over time in how many person years and what is the incidence rate ratio?
• Simple case-control analysis is usually expressed as being backwards in time:• Given case-control status now, what is the ratio of the odds of
exposure at baseline?
Retrospective v prospective?• Confusing terminology: two different issues• (1) Does the analysis look forwards or backwards?• (2) Are the data collected as and when they occur (i.e.
prospectively) or from historical review - questionnaire, case-notes or other health records – (i.e. retrospectively).
• Conventional cohort study: prospective• Historical cohort study: retrospective• Conventional case-control study: retrospective
Comparison of cohort andcase-control studies
Cohort Studies Case-control studies Compare groups based on exposure status
Compare groups based on disease status
Large and time-consuming, therefore expensive
Quick, relatively inexpensive
Not good for rare diseases Not good for rare exposures Wish to study a range of outcomes Wish to study a range of
exposures for one disease Minimises bias in the ascertainment of exposure, but prone to losses to follow-up.
Prone to information bias (e.g. recall bias) and to selection bias (choice of controls important)
Can establish that the exposure precedes the disease
Can directly measure incidence
Rooms for mid-module assessment9.30-10.30 14th March 2002
• Warwick Students• Use their normal small group session rooms
• Leicester Students• MSB room LT1 (candidate numbers 1-63)• MSB room 206 (candidate numbers 64-114)• MSB room 320 (candidate numbers 115 onwards)
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