Case-control studies

• Overview of different types of studies

• Review of general procedures

• Sampling of controls– implications for measures of association– implications for bias

• Logistic regression modeling

Learning Objectives• To understand how the type of control

sampling relates to the measures of association that can be estimated

• To understand the differences between the nested case-control study and the case-cohort design and the advantages and disadvantages of these designs

• To understand the basic procedures for logistic regression modeling

Overview of types of case-control studies

No designated cohort,but should treat source population as cohort

Within a designated cohort

Nested case control Case-cohort

Cases only

Case-crossover

Cases and controls1) Type of sampling

- incidence density- cumulative “epidemic”

2) Source of controls- population-based- hospital - neighborhood- friends- family

Review of General Procedures

Obtaining cases1) Define target cases2) Identify potential cases3) Confirm diagnosis4) *Obtain physician’s consent5) Contact case6) Confirm case’s eligibility7) *Obtain case’s consent8) Obtain exposure data

*need to account for nonresponse

Obtaining controls1) Define target controls2) Define mechanism for identifying controls3) Contact control4) Confirm control’s eligibility5) *Obtain control’s consent6) Obtain exposure data

Pros/Cons of Different Methods

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Case cohort study

T0

Assemble cohort, samplesubcohort to beused in all future analyses

First case

Additional cases, compare all cases to the subcohort selectedat T0

Nested case-control Study

T0

Assemble cohort

First case;randomly select controlfrom remaining cohort

Likewise, select controlsagain at each separate time point; note: each of these cases was eligible to be a control for the first case

Crossover designs

Period the subject is exposed

Period the subject is unexposed

• Case-crossover: variation of crossover; case has a pre-disease period which is used as the control period

• Good method for control of confounding• May have limited applications• Assumes that neither exposure nor confounders

are changing over time in a systematic way

Source Population

• Think of all case-control studies as nested within a cohort, even when the cohort is not designated

• Source population is this underlying cohort• Source population describes the cohort giving

rise to the cases; controls are also from this source population

• Source population reflects the disease under study, difficulties in diagnosing disease, routine procedures for recording the disease occurrence, and the frequency of disease

Classic case-control

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S ou rce p op u la tion

Cases Controls

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Unexposed C D

Odds ratio = AD/BC

If sampling:OR = f1*A*f2*D = AD

f1*C*f2*B BC

Incidence Density Sampling

1) Collect information on each case

2) Collect control at the same time each case is observed; collect control from the underlying source population giving rise to the cases

3) Controls can be cases

Cumulative-based sampling1) Start after the event has happened

2) Ascertain cases

3) Collect controls from the noncases after event (e.g., epidemic)

Measures of Association

• Key concept, sampling fraction, independent of exposure

• Incidence density sampling/nested case-control studies– if exposure odds in controls(B/D)

approximates person-time ratio for source population, odds ratio will approximate rate ratio

– without rare disease assumption

Measures of Association• Case cohort

– if ratio B/D approximates overall prevalence of exposure in source population, odds ratio will approximate risk ratio

– without rare disease assumption• Cumulative “Epidemic” case-control studies

– odds ratio will approximate rate ratio if proportion diseased in each exposure group is low (< 20%) and remains steady during study period

When is the rare disease assumption needed?

• Cumulative-based sampling if want to approximate the relative risk

• Otherwise– nested case-control and incidence density

sampling will give an estimate of rate ratio without rare disease assumption

– case-cohort will give an estimate of risk ratio without rare disease assumption

• If disease is rare, all three measures will be very close

A closer lookRecall:

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If sampling does not lead to bias and the sample can approximate the person-years of distribution, a case-control study is a more efficient design (i.e. for same number of people, more precision). However not as precise as if you use the full cohort.

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Summary• Odds Ratio

approximates Rate Ratio– incidence density

sampling– nested case-control

studies– cumulative sampling

is proportion exposed is steady and relatively low

• Odds Ratio approximates Risk Ratio– case-cohort

design– cumulative

sampling if disease is rare

Source of Controlspopulation-based: not necessarily equal probability, control selection probability is proportional to the individual’s person time at riskneighborhood: need to think about referral patterns (e.g., not good for veteran’s hosp); also need to worry about overmatchinghospital: need to be especially concerned that sampling was independent of exposure; try to use a variety of diagnoses for controls.friends: main problem is with overmatching; cedes the control selection to the case rather than to the investigator family:may be worthwhile design to control for certain variable (e.g., spouse control, environment, twin control genetics and environment)

Review of control selection

• Select from source population• Select independent of exposure status• Probability of selection should be proportion

to amount s/he would have contributed to person-time in the denominator

• Not eligible to be a control, if during same time would not have been eligible to be a case

Ille-et-Vilaine study (epidat1.txt)

• conducted between January 1972 and April 1974

• French department of Ille-et-Vilaine (Brittany)

• Men diagnosed in regional hospitals

• Controls sampled from electoral lists in each commune of department

Other methodological points• exposure opportunity

– interest is in the fact of exposure– think about cohort design– make same exclusions to cases as to controls

• comparability of information– may not want comparability if errors are not

independent

• number of different types of control groups– may be appropriate in some situations (e.g., spouse,

siblings), but generally not recommended

• prior disease history

Regression ModelingRegression model- simpler function used to estimate the trueregression function

Benefit of Regression Modeling: overcome the numerical limitations of categorical analysis

Cost of Regression Modeling: assumptions of model; invalidinferences if model is misspecified

E(Y|X = x)

Y = dependent variable, outcome variable, regressandX = set of independent variables, predictors, covariates, regressors

Logistic Regression

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Likelihood in logistic regression

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Cases Controls

Interpreting Coefficients

If X is continuous, B represents the impact of a one-unit change in X to Y, the exponential of B will give you the OR for a one unit change Note: both modeling variables as either ordered categorical variables or continuous variables assumes the one unit change in X is the same irrespective of the level of X

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Logistic Modeling

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Logistic Model

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Assessing Linearity

• Create categories of continuous variable; categories should represent the same amount of units (e.g., 0-39 grams, 40-79 grams, 80-119, etc)

• Plot Beta coefficients; if pattern is approximately linear, keep variable as a continuous variable in model

Log ( Y ) (1-Y)

Logistic Model

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Creating Indicator VariablesAlso referred to as categorical regressors,dummy variables

Need to pick a reference level

Number of indicator variables created = # categories - 1

The intercept term picks of the effect of the left out category

Note: The precision of the estimate will depend on which category you pick as the referent

Things to keep in mind

Note: For some variables, nonusers/nonconsumersare different than users/consumers, therefore maywant to keep separate zero category

Last category may be too heterogeneous

Balance between homogeneity and parsimony

Changing units

One Unit Increase X unit increase (e.g., X=10)

Point esimate

Lower 95% CL

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Examining confounding and mediation

1) Run a model with exposure only

2) Run a model with exposure and potential confounder (and/or mediator)

3) Examine the changes in the estimate with exposurebetween model 1 and 2

- if different keep in confounder- many use a 10% change in estimate - if estimate is different but B is still associated with outcome -- partial confounder- data cannot distinguish b/w confounder and mediator

Comparing Models

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If model B is no worse than model A, we want touse model B. Always favor parsimony if we don’t have to give up anything

One way of comparing models is using the log likelihood ratio test

Likelihood Ratio Tests

model)(smaller B''for likelihood

model)(larger A''for likelihoodlog2log2 LR

~ Chi Square with df = (total number of parameters in larger model - total number of parameters in smaller model)

Comparing models:

Subtract the log likelihoods (part of SAS output)

Can use following code or look up in a Chi Square table:

data;p = (1-probchi(diff, df));put p;run;

diff = difference in -2 *log likelihoods df = degrees of freedom see above