# Case-control study 1: Design and odds ratio Preben Aavitsland (partly based on Epiet 2004)

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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 among exposed (I 1 or R 1 ) Occurrence among unexposed (I 0 or R 0 ) a b

The cohort study: calculation Exposed I 1 = a / Nt 1 = 16 / 125 pyar UnexposedI 0 = b / Nt 0 = 8 / 120 pyar IRR = I 1 =a / Nt 1 = 16/125 pyar = 1.92 I 0 b / Nt 0 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 why the 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

Cases Exposed Unexposed Source population

Cases Exposed Unexposed Source population Sample Controls

Cases Exposed 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)

Cases Exposed Unexposed Source population Sample Controls a d c b

Cases Exposed Unexposed Source population Sample Controls a d c b d / Nt 0 = c / Nt 1 because sampled independent of exposure 24 / 120 = 25 / 125

The case-control study: calculation IRR = I 1 = a / Nt 1 I 0 b / Nt 0 = a. Nt 0 b Nt 1 = a. d b c d= c Nt 0 Nt 1 Nt 0 = d Nt 1 c = 16. 24 = 1.92 25 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

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

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