Case-control study 1:Design and odds ratio

Preben Aavitsland

(partly based on Epiet 2004)

Contents

• Monday 1– Design: Case-control study as a smarter cohort study– The odds ratio

• Tuesday 2– Choosing cases and controls– Matching– Power calculation

• Wednesday– Case-control studies in outbreaks

• Thursday 3– Bias and confounding– Analysis

Why case-control study

• Best way to acquire knowledge about causes and protective factors of disease

• Both for outbreaks and endemic diseases

• Easy to perform and analyse

• Needs thorough planning

• Next step after surveillance and outbreak investigations

Source population

The cohort study

unexposed

exposed

The cohort study

unexposed

exposed

Occurrence amongexposed (I1 or R1)

Occurrence amongunexposed (I0 or R0)

a

b

The cohort study: calculation

Exposed I1 = a / Nt1 = 16 / 125 pyar

Unexposed I0 = b / Nt0 = 8 / 120 pyar

IRR = I1 = a / Nt1 = 16/125 pyar = 1.92

I0 b / Nt0 8/120 pyar

Problems of cohort

• Large sample size required– At least if disease is rare

• Latency period• Time consuming• Loss to follow up• Changing exposure over time• Only one exposure• Ethical considerations• Cost

That is whythe case-control study is smarter

• Gives the same measure of causal effect as the cohort study (risk ratio RR or incidence rate ratio IRR)

• It is called odds ratio (OR)

• Easier, quicker, cheaper, smarter

Exposed

Unexposed

Source population

The case-control study

CasesExposed

Unexposed

Source population

CasesExposed

Unexposed

Source population

Sample

Controls

CasesExposed

Unexposed

Source population

Sample

Controls

Cases = the same as in cohort study

Controls = sample of the source population, with representative distribution of exposed and unexposed persons (or person-time)

CasesExposed

Unexposed

Source population

Sample

Controls

a

d

c

b

CasesExposed

Unexposed

Source population

Sample

Controls

a

d

c

b

d / Nt0 = c / Nt1

because sampled independent of exposure

24 / 120 = 25 / 125

The case-control study: calculation

IRR = I1 = a / Nt1

I0 b / Nt0

= a . Nt0

b Nt1

= a . d b c

d = c

Nt0 Nt1

Nt0 = d

Nt1 c

= 16 . 24 = 1.9225 8

Saving resources with case-control study

• In stead of following a cohort of 245 people for one year to wait for the 24 cases

• We investigated the 24 cases in order to divide them between– exposed a = 16 and– unexposed b = 8

• We chose 49 controls and investigated them in order to divide them between– exposed c = 25 and– unexposed d = 24

• The result– exactly the same as cohort study, but much easier

The odds ratio (OR)

• OR = Incidence rate ratio (IRR)

• OR = Risk ratio (RR)

• Cross product ratio: ad / bc

Exposed Unexposed

Cases a b

Controls c d

Summary of the case-control study

• Imagine a source population– Consists of exposed and unexposed people– Gives rise to cases (same as if cohort study)

• Control group is a sample from this source population– Independent of exposure status– Same distribution of exposed persons (person-time) as

in source population• Determine exposure status of cases and controls• Calculate odds ratio

– = risk ratio or incidence rate ratio if a cohort had been done

Challenges in case control study

• No measure of disease occurrence– Not risk R or incidence rate IR

• Difficult to define source population

• Difficult to sample controls correctly– Independently from exposure

• Recall bias– Cases remember differently from controls