unmatched case control studies

UNMATCHED

CASE-

CONTROL

STUDIES

MRINMOY PRATIM BHARADWAZIIPS, MUMBAI

TYPES OF STUDY

Experimental Observational

RCT Non RCT Analytical Descriptive

Ecological Cross-sectional Case-control Cohort

Case Control StudyO It is an observational study in which subjects are

sampled based upon presence or absence of disease and then their prior exposure status is determined.

O DISTINCT FEATURE: 1. Both exposure and outcome (disease) have occurred

before the start of the study. 2. The study proceeds backwards from effect to cause. 3. It uses a control or comparison group to support or

refute an inference.

Need of case-control

O In CASE-CONTROL study, it is more efficient in terms of study operation, time and cost w.r.to COHORT study.

OSuitable for rare diseases.OFor 1 particular disease it can be used.OSample size relatively small.

Steps In Study Design

OSTEP-1: Determine and select cases of your research interest.

OSTEP-2: Selection of appropriate controls.

OSTEP-3: Determine exposure status in both cases and controls.

Cases SelectionO Study begins with cases, i.e. the patients in whom the

disease has already occurred. O Patients with the disease in question (cases) were enquired

for all the details of their exposure to the suspected cause.O The new cases, which are similar clinically, histologically,

pathologically and in their duration of exposure (stage) will be chosen to avoid any error and for better comparison.

Sources of Cases Hospitals. General population

Who will be controls?O Control ≠ non-caseO Controls are also at risk of the disease in his(her)

future.O “Controls” are expected to be a representative sample

of the catchment population from which the case arise.O For e.g. in a case-control study of gastric cancer, a

person who has received the Gastrectomy cannot be a control since he never develop gastric cancer .

Sources of controls: Hospital controls General population Relatives/Neighborhood

Basic Design

*

RISK FACTORS

CASES(Disease Present)

CONTROLS

(Disease Absent)

PRESENT a bABSENT c d

Total a+c b+d a/(a + b) - Incidence of disease in exposed

c/( c + d)- Incidence of disease in non exposed if a/(a + b )> c/ (c + d) It would suggest that the disease and suspected causes are associated.

Statistical analysis “Matched” vs. “Unmatched” studies

The procedures for analyzing the results of case-control studies differ depending on whether the cases and controls are matched or unmatched.

Matched Unmatched・ McNemar’s test ・ Chi-square test・ Conditional logistic ・ Unconditional logistic　 regression analysis regression analysis

ANALYSISO EXPOSURE RATE among cases and controls to

suspected factors.Cases = a/(a + c) Controls = b/(b + d)

O Estimation of the Disease risk associated with exposure (ODDS RATIO).

The odds ratio is also known as the cross-products ratio.

Odds ratio is a Key Parameter in the analysis of case control studies = (a*d)/(b*c)

It interprets that odds of cases being exposed are so many times higher compared to the odds of controls being exposed.

INTERPRETATION OF ODDS RATIO(OR) If OR =1 (exposure is not related to disease) >1 (+ly related) <1 (- ly related).

O OR is a good approximation of RR when:cases studied are representative of those with

the disease.controls studied are representative of those

without the disease.disease being studied does not occur frequently.

TWO MAIN COMPLICATIONS OF ANALYSIS OF SINGLE EXPOSURE EFFECT

(1) Effect modifier

(2) Confounding factor

- useful

information - bias

EFFECT MODIFIER• Variation in the magnitude of measure of effect across levels of a third variable.

• Effect modification is not a bias but useful information.

Happens when RR or OR is different between strata (subgroups of population)

Continue….• To study interaction between risk

factors.• To identify a subgroup with a lower or

higher risk.• To target public health action.• Better understand of the disease:

biological mechanism.

To identify a subgroup with a lower or higher

risk• Example 1 : Influenza :

O Important complications for old people, for person with cardiac and pulmonary disease or diabetes…

O The risk of complication is more higher for these categories of people.

O Age and comorbidity are effect modifiers for influenza.

To target public health action

• Example 1 : Influenza

• Vaccination is recommanded for :

Old person,

Person with cardiac and pulmonary disease .

Diabetes …

EFFECT MODIFICATION : EXAMPLE

CONFOUNDINGExposure Outcome

Third variable

Be associated with exposure - without being the consequence of exposure.Be associated with outcome - independently of exposure.

OShould be prevented or Needs to be controlled for.

ODistortion of measure of effect because of a third factor.

OStratification and Multivariate modeling are the analytic tools used to control for confounding.

OStratification allows for assessment of confounding and effect modification.

OMultivariate analyses are used to carry out statistical adjustment.

Continue….

ASSUMPTIONSStratification

O Strata must be meaningfully and properly defined.

O Strata must be homogenous within stratum.Adjustment

O Simple techniques such as direct and indirect adjustment and Mantel-Haenszel assume that the association are homogenous across strata and there is not interaction

O Multivariate regression techniques are more mathematically complex models and each has it’s own set of assumptions

• Positive confounding - positively or negatively related to both the disease and exposure

• Negative confounding - positively related to disease but is negatively related to exposure or the reverse

Confounding: example

Drinker

Non-drinker

100 200

Lung cancer

No lung cancer

50 50

50 150

50% of cases are drinkers, but only 25% of controls are drinkers.Therefore, it appears that drinking is strongly associated with lung cancer.

CONFOUNDING: EXAMPLE

Drinker

Non-drinker

Lung cancer

No lung cancer

45 15

30 10

Drinker

Non-drinker

Lung cancer

No lung cancer

5 35

20 140

Smoker

Non-smoker

Among smokers, 45/75=60% of lung cancer cases drink and 15/25=60% of controls drink.

Among non-smokers 5/25=20% of lung cancer cases drink and 35/175=20% of controls drink.

75

25

25

175

HOW TO PREVENT/CONTROL CONFOUNDING?

Prevention (Design Stage)O Restriction to one stratumO Matching

Control (Analysis Stage)O Stratified analysisO Multivariate analysis

STRATIFICATION AND MULTIVARIATE MODELING

OStratification and Multivariate modeling are the analytic tools used to control for confounding

OStratification allows for assessment of confounding and effect modification

OMultivariate analyses are used to carry out statistical adjustment

GENERAL FRAMEWORK FOR STRATIFICATION

In the study design phase:• Decide which variables to control for

In the implementation phase:• Measure the confounders or other variables

needed to block path

In the analytical phase: • Assess clinical, statistical and practical

consideration

STRATIFICATION: Principle Principle :

O Create strata according to categories of the third variable

O Perfom analysis inside these strataO Conclude about the studied relation

inside the strataO Forming «adjusted summary

estimate»: concept of weighted averageO Assumption: weak variability in the strata

TO PERFORM A STRATIFIED ANALYSIS,WE HAVE 6 STEPS:

1. Carry out simple analysis to test the association between the exposure and the disease and to Identify potential confounder

2. Categorize the confounder and divide the sample in strata, according to the number of categories of the confounder

3. Carry out simple analysis to test the association between the exposure and the disease in each stratum

4. Test the presence or absence of effect modification between the variables

5. If appropriate, check for confounding and calculate a point estimate of overall effect (weighted average measure)

6. If appropriate, carry out and interpret an overall test for association

STRATIFICATION: CONCLUSIONStratification is useful tool to assess the real effect of exposure on the disease

But, its have some limits:

• Possibility of insufficient data when we have several strata

• Tool developped only for categorical variable

• Precision of the adjusted summary measure could be affected with overcontrolled

• Only possible to adjust for a limited number of confounders simultaneously

Necessity of other tools

MULTIVARIATE ANALYSISDefinition: A technique that takes into

account a number of variables simultaneously.

• Involves construction of a mathematical model that efficiently describes the association between exposure and disease, as well as other variables that may confound or modify the effect of exposure.Examples:

Multiple linear regression model Logistic regression model

MULTIPLE LINEAR REGRESSION MODEL:

Y = a + b1X1 + b2X2 + …bnXn

Where:

n = the number of independent variables (IVs) (e.g. Exposure(s) and confounders)

X1 … Xn = individual’s set of values for the Ivs

b1 … bn = respective coefficients for the IVs

LOGISTIC REGRESSION MODEL:

ln [Y / (1-Y)] = a + b1X1 + b2X2 + …bnXn

Where:Y = probability of disease

n = the number of independent variables (IVs)

(e.g. exposure(s) and confounders)

X1 … Xn = individual’s set of values for the IVs

b1 … bn = respective coefficients for the IVs

EPI 809/Spring 2008 31

Cochran Mantel Haenszel Methods

Assess association between disease and exposure after controlling for one or more confounding variables.

ai

ci

bi

di

(ai + ci) (bi + di)

(ai + bi)

(ci + di)

ni

D

D

E E

where i = 1,2,…,K is the number of strata

Mantel Haenszel Methods-Notations

(1) Correlation Statistic (Mantel-Haenszel statistic) has 1 df and assumes that either exposure or disease are measured on an ordinal (or interval) scale, when you have more than 2 levels.

(2) ANOVA (Row Mean Scores) Statistic has k-1 df and disease lies on an ordinal (or interval) scale when you have more than 2 levels.

(3)General Association Statistic has k-1 df and all scales accepted

CMH Chi-square tests

(1) The Mantel-Haenszel estimate of the odds ratio assumes there is a common odds ratio:

ORpool = OR1 = OR2 = … = ORK

To estimate the common odds ratio we take a weighted average of the stratum-specific odds ratios:

MH estimate: 1

1

ˆ

K

i i iiK

i i ii

a d nOR

bc n

CMH common odds ratio

(2) Test of common odds ratioHo: common OR is 1.0 vs. Ha: common OR 1.0

- A standard error is available for the MH common odds- Standard CI intervals and test statistics are based on the standard normal distribution.

(3) Test of effect modification (heterogeneity, interaction)Ho: OR1 = OR2 = … = ORK

Ha: not all stratum-specific OR’s are equal

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Computing Cochran-Mantel-Haenszel Statistics for a Stratified Table

OThe data set Migraine contains hypothetical data for a clinical trial of migraine treatment. Subjects of both genders receive either a new drug therapy or a placebo. Assess the effect of new drug adjusting for gender.

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Example - Migraine Response

Treatment Better Same Total Active 28 27 55 Placebo 12 39 51

Total 40 66 106

Pearson Chi-squares test p = 0.0037

But after stratify by sex, it will be different for male vs female.

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Male Response

Treatment Better Same Total Active 12 16 28 p = 0.2205Placebo 7 19 26

Total 19 35 54

Female Response

Treatment Better Same Total Active 16 11 27 p = 0.0039Placebo 5 20 25

Total 21 31 52

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CommentsO The significant p-value (0.004) indicates that the

association between treatment and response remains strong after adjusting for gender

O The probability of migraine improvement with the new drug is just over two times the probability of improvement with the placebo.

O The large p-value for the Breslow-Day test (0.2218) indicates no significant gender difference in the odds ratios.