unmatched case control studies

MRINMOY PRATIM BHARADWAZ
IIPS, MUMBAI

TYPES OF STUDY
Experimental Observational
RCT Non RCT
Analytical Descriptive
Ecological Cross-sectional Case-control Cohort

Case Control Study
O 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
OIn 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 Selection
O 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-case
O 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)
CONTRO
LS
(Disease
Absent)
PRESENT a b
ABSENT 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

ANALYSIS
O 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

CONFOUNDING
Exposure 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….

ASSUMPTIONS
Stratification
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 stratum
O Matching
Control (Analysis Stage)
O Stratified analysis
O 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 strata
O Conclude about the studied relation
inside the strata
O Forming «adjusted summary
estimate»: concept of weighted average
O 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: CONCLUSION
Stratification 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 ANALYSIS
Definition: 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 i
i
K
i i i
i
a d n
OR
b c n





CMH common odds ratio

(2) Test of common odds ratio
Ho: 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

36
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.

37
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.

38
Male Response
Active 12 16 28
p = 0.2205
Placebo 7 19 26
Total 19 35 54
Female Response
Active 16 11 27
p = 0.0039
Placebo 5 20 25
Total 21 31 52

39
Comments
O 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.

unmatched case control studies

unmatched case control studies

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