Limitations of Matching

1
Limitations of Matching
2
Why we do matching?
3
Confounding

• A distortion of an association between and
  exposure and disease brought about by an
  extraneous factor or factors.
• Occurs when the exposure is associated with the
  confounding factor and with the disease.

4
Strategies for control of confounding
1. Random allocation of exposure 2.
Restriction 3. Matching - Partial restriction
4. Stratification 5. Modeling
5
Strategies for control of confounding

• 1. Random allocation of exposure
• Ideal (adjusts for known as well as unknown
  confounders
• Rarely possible in observational studies of risk
  factors ethical constraints, time, and cost

6
Strategies for control of confounding

• 2. Restriction
• The effects of know or potential confounders can
  be eliminated by restriction of study subjects
• Should be considered for strong by uncommon risk
  factors
• Can simplify the analysis (fewer variables)
• Reduces the number of potential subject but
  increases precision of estimates number of
  subjects
• Loss of generalization of restricted factors

7
Strategies for control of confounding

• 3. Matching - Partial restriction
• Match on disease status
• Matching gains efficiency in case control studies
• Matching in design must be retained in the
  analysis
• Compare matched vs. unmatched estimates

8
Strategies for control of confounding

• 4. Stratification
• Use stratified analysis to evaluate interaction
  and control for confounding
• No assumptions and straightforward computational
  procedures
• Stratum specific estimates become imprecise with
  numbers in cells becomes small
• ALWAYS look at stratification before jumping into
  models (logistic, etc)

9
Strategies for control of confounding

• 5. Modeling
• After stratification - modeling may be employed
  to control confounding and test for interaction
• Modeling is attractive when number of variables
  is large or when continuous variables can not be
  / should not be categorized
• Disadvantage assumptions

10
Blood Pressure
Age
11
YS a S bXS
Blood Pressure
YNS a NS bXNS
Age
12
(No Transcript)
13
YS a S bXS
Blood Pressure
YNS a NS bXNS
Age
14
Blood Pressure
Age
15
aS - aNS
Blood Pressure
Age
16
b (XS - XNS )
Blood Pressure
Age
17
How Matching Can Reduce Confounding Bias?
18
Blood Pressure
Age
19
Blood Pressure
Age
20
Factors influencing efficiency of matching in
Bias Reduction
1. The difference of mean of matching factor
between groups.
21
Blood Pressure
Age
22
Blood Pressure
Age
23
Factors influencing efficiency of matching in
Bias Reduction
2. The ratio of the population variances.
24
Blood Pressure
Age
25
Blood Pressure
Age
26
Factors influencing efficiency of matching in
Bias Reduction
3. The size of the control sample from which the
investigator forms a comparison group.
27
Blood Pressure
Age
28
Blood Pressure
Age
29
Blood Pressure
Age
30
Blood Pressure
Age
31
YS a S b X2S
YNS a NS b X2NS
YS - YNS a S - a NS b (X2S - X2NS)
If XS XNS then b (X2S - X2NS ) may be
unequal to zero.
32
Hypotethical target population of 2 million people
Females
Males
Exposed
Exposed
Unexposed
Unexposed
No. cases in 1 year
4,500
50
100
90
Total
900,000
100,000
100,000
900,000
1-year risk
0.005
0.0005
0.001
0.0001
(4500100)/1,000,000
33
Crude risk ratio
(5090)/1,000,000
33
Expected results of a matched 1-year cohort study
of 200,000 subjects drawn from the target
population
Females
Males
Exposed
Exposed
Unexposed
Unexposed
No. cases in 1 year
450
45
10
1
Total
90,000
90,000
10,000
10,000
Relative Risk
10
10
(45010)/100,000
10
Crude risk ratio
(451)/100,000
34
Expected results of a case-control study matched
on sex when the source of subjects is the same
target population
Females
Males
Exposed
Exposed
Unexposed
Unexposed
4500
50
100
90
Cases (4740)
Controls (4740)
4095
455
19
171
Approximate expected OR
10
10
(4500100)(455171)
Approximate expected Crude OR
5

(409519)(5090)
35
Matching may induce selection bias in
case-control studies
36
Overmatching
Overmatching includes three forms

• Matching that harms statistical efficiency.
• - e.g case-control matching on a variable
  associated with exposure but not disease (not
  confounder).
• Matching that harms validity.
• - e.g matching on an intermediate variable
  between exposure and disease (causal pathway).
• Matching that harms cost efficiency.

37
Conclusion
Conventional matching is rarely the optimal
stratified design.