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)