gerstman case-control studies 1 epidemiology kept simple section 11.5 case-control studies

GerstmanGerstman Case-Control StudiesCase-Control Studies 11

Epidemiology Kept SimpleEpidemiology Kept Simple

Section 11.5 Section 11.5

Case-Control StudiesCase-Control Studies


IntroductionIntroduction The goal of analytic epidemiologic studies The goal of analytic epidemiologic studies

is to elucidate exposure – disease is to elucidate exposure – disease relationsrelations

For rare diseases, cohort studies require For rare diseases, cohort studies require large sample sizeslarge sample sizes

Case-control methods were developed to Case-control methods were developed to overcome the statistical efficiency of overcome the statistical efficiency of cohort samplingcohort sampling


Case-Control SamplingCase-Control Sampling Study all casesStudy all cases Select a random sample of non-cases from source Select a random sample of non-cases from source

populationpopulation Compare exposure status in cases and controlsCompare exposure status in cases and controls

Source Population

Identify m1

casesSelect m0 noncases

Determine % exposed

Determine % exposed


Historical Example: Levin (1950) Historical Example: Levin (1950) Identify 236 individuals with lung cancer casesIdentify 236 individuals with lung cancer cases Identify 481 individuals with other non-cancerous Identify 481 individuals with other non-cancerous

conditions conditions 156 of the 236 cases (66%) smoked156 of the 236 cases (66%) smoked 212 of the 481 non-cases (44%) smoked212 of the 481 non-cases (44%) smoked Because smoking was more common is cases, we Because smoking was more common is cases, we

can infer that there was a positive association can infer that there was a positive association between suggesting that smoking and lung cancerbetween suggesting that smoking and lung cancer

Note: Incidence and prevalence can Note: Incidence and prevalence can NOT NOT be calculated be calculated from case-control samples because sizes of the from case-control samples because sizes of the

populations at risk are populations at risk are notnot known. known.


Notation Notation

Disease +Disease + Disease -Disease - TotalTotal

Exposed +Exposed + AA11 BB11 NN11

Exposed -Exposed - AA00 BB00 NN00

TotalTotal MM11 MM00 NN

Disease status indicated by lettersDisease status indicated by letters A (cases) A (cases) B (controls)B (controls)

Exposure status indicated by subscriptExposure status indicated by subscript [subscript] [subscript] 11 = exposed = exposed

[subscript] [subscript] 00 = nonexposed = nonexposed


Calculation of Odds Ratio (Calculation of Odds Ratio ())

Disease +Disease + Disease Disease −− TotalTotal

Exposed +Exposed + AA11 BB11 NN11

Exposed Exposed −− AA00 BB00 NN00

TotalTotal MM11 MM00 NN

01

01Ratio OddsAB

BA

The odds ratio (denoted The odds ratio (denoted ψψ) is simply the cross-) is simply the cross-product ratio of the counts in the 2-by-2 tableproduct ratio of the counts in the 2-by-2 table

Use the Odds Ratio as an estimate of the Risk Ratio


Illustrative Example: Illustrative Example: Tampon Use and Toxic Tampon Use and Toxic Shock, Wisconsin Data (p. 215)Shock, Wisconsin Data (p. 215)

Exposure = tampon useExposure = tampon use Disease = toxic shock syndromeDisease = toxic shock syndrome

D+D+ D-D-

E+E+ 30 71

E-E- 1 22

TotalTotal 31 93

3.9)1)(71(

)22)(30(ˆ

01

01 AB

BA Tampon-exposed individuals have

9.3× risk


Small Sample Size Formula For the Odds Ratio Small Sample Size Formula For the Odds Ratio (Optional)(Optional)

Some statisticians recommend adding ½ to each cell before Some statisticians recommend adding ½ to each cell before calculating the odds ratio, esp. when some cells have very few calculating the odds ratio, esp. when some cells have very few counts (This is known as the “small sample odds ratio formula”)counts (This is known as the “small sample odds ratio formula”)

))((

))((ˆ

21

021

1

21

021

1

AB

BAeSmallSampl

For the illustrative data:

4.6)1)(7(

)22)(30(ˆ

21

21

21

21

Sample Small


Why the OR is used as an estimate of Why the OR is used as an estimate of the RRthe RR

We use the OR as an estimate of the RRWe use the OR as an estimate of the RR There are two justifications for thisThere are two justifications for this The classical justification described in The classical justification described in

Cornfield, J. (1951). A method of estimating comparative rates from clinical data. Application to cancer of the lung, breast, and cervix. Journal of the National Cancer Institute, 11, 1269-1275.

The modern justification described in The modern justification described in Miettinen, O. (1976). Estimability and estimation in case-referent

studies. American Journal of Epidemiology, 103, 226-235.


Miettinen’s (1976)Miettinen’s (1976) Justification of the ORJustification of the OR

Time

5

4

3

2

1

t1 t2

DD

Imagine 5 people followed for occurrence of disease D. At time t1, D occurs in person 1. At t1 (shaded), select at random a non-cases to serve as a control. (Note: person #2 becomes a case later on, but can still as a control at time t1).Justification (optional): Let A no. of cases in population and T

person-time in population. The ratio of rates in the exposed (1) and nonexposed (0) populations can be estimated as the ratio of (A1/A0) to (T1/T0). (A1/A0) is available in the case series and (T1/T0) is stochastically equivalent to B1/B0 in the control series if the controls are a random sample of the population.

01

01

00

11

0

1

/

/

/

/

rate

rate Ratio Rate

TT

AA

TA

TA


Multiple Levels of ExposureMultiple Levels of ExposureEExample: Wynder & Graham (1950)xample: Wynder & Graham (1950)

SmokingSmoking CasesCases ControlsControls

ChainChain 123123 6464

ExcessiveExcessive 186186 9898

HeavyHeavy 213213 274274

ModerateModerate 6161 147147

LightLight 1414 8282

NoneNone 88 115115

TotalTotal 605605 115115

Break-up data into separate 2-Break-up data into separate 2-by-2 tables using the least by-2 tables using the least exposed group as referenceexposed group as reference

e.g., Compare chain-smokers e.g., Compare chain-smokers vs. non-smokersvs. non-smokers

SmokingSmoking CasesCases ControlsControls

ChainChain 123 64

NoneNone 8 115

63.27)64)(8(

)115)(123(ˆ

10

01 BA

BA


Multiple Levels of Exposure (cont)Multiple Levels of Exposure (cont)

Smoking levelSmoking level CasesCases ControlsControls

Chain smokersChain smokers 123123 6464 OROR55 = (123)(115)/(64)(8) = 27.6 = (123)(115)/(64)(8) = 27.6

Excessive smokersExcessive smokers 186186 9898 OROR44 = (186)(115)/(98)(8) = 27.3 = (186)(115)/(98)(8) = 27.3

Heavy smokersHeavy smokers 213213 274274 OROR33 = = (213)(115)/(274)(8) = 11.2(213)(115)/(274)(8) = 11.2

Mod. heavy smokersMod. heavy smokers 6161 147147 OROR22 = (61)(115)/(147)(8) = 6.0 = (61)(115)/(147)(8) = 6.0

Light smokersLight smokers 1414 8282 OROR11 = (14)(115)/(82)(8) = 2.5 = (14)(115)/(82)(8) = 2.5

Non-smokersNon-smokers 88 115115 reference groupreference group

TotalTotal 605605 115115

Notice increasing risk with increasing exposure: dose-response relationship (biological gradient)


Matched-PairsMatched-Pairs

Matching is employed to Matching is employed to help adjust for help adjust for confounding confounding

e.g., matching on age e.g., matching on age and sex will adjust for and sex will adjust for these factors these factors

Each Each pairpair now represents now represents a single observationa single observation

Cross-tabulate pairs to Cross-tabulate pairs to determine odds ratiodetermine odds ratio

ControlControl E+ E+ ControlControl E− E−

Case E+Case E+ t u

Case Case E−E− v w

v

u

Odds ratio formula Odds ratio formula for matched pairsfor matched pairs


Example (Matched Pairs)Example (Matched Pairs)

Control E+Control E+ Control E−Control E−Case E+Case E+ 5 30

Case E−Case E− 10 5

00.310

30ˆ Exposure triples

risk


Comparison of Sampling MethodsComparison of Sampling Methods

Although sampling methods differ, all have the same of goal: to elucidate exposure – disease relationships


Comparisons Study DesignsComparisons Study Designs

Randomized Randomized TrialsTrials

CohortCohort Case-ControlCase-Control

ExperimentalExperimental ObservationalObservational ObservationalObservational

Randomly assign Randomly assign exposureexposure

Select fixed number Select fixed number of exposed and non-of exposed and non-exposed individualsexposed individuals

Select fixed number Select fixed number of cases and non-of cases and non-cases (efficient cases (efficient sampling design)sampling design)

Can calculate RDs Can calculate RDs and RRsand RRs

Can calculate RDs Can calculate RDs and RRsand RRs

Can calculate ORs Can calculate ORs only only

Convenient for Convenient for studying multiple studying multiple outcomesoutcomes

Convenient for Convenient for studying multiple studying multiple outcomesoutcomes

Convenient for Convenient for studying multiple studying multiple exposuresexposures

Must be prospectiveMust be prospective Can be prospective Can be prospective or retrospectiveor retrospective

Exposure must be Exposure must be retrospectiveretrospective

gerstman case-control studies 1 epidemiology kept simple section 11.5 case-control studies

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