19: Stratified 2-by-2 Tables

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Chapter 19Stratified 2-by-2 Tables
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In Chapter 19

• 19.1 Preventing Confounding
• 19.2 Simpsons Paradox (Severe Confounding)
• 19.3 Mantel-Haenszel Methods
• 19.4 Interaction

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19.1 Confounding

• Confounding a distortion in an association
  brought about by extraneous variables
• Variables E exposure variableD disease
  variableC confounding variable
• Confounder word origin to mix together, the
  effects of the confounder gets mixed up with the
  effects of the exposure

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Properties of confounding variables

• Associated with exposure
• Independent risk factor
• Not in causal pathway

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Mitigating Confounding

1. Randomization balances groups with respect to
   measured and unmeasured confounders
2. Restriction of the study base imposes uniformity
   within groups

. St. Thomas Aquinas Confounding Averro?s
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Mitigating confounding (cont.)

• 3. Matching balances confounders
• 4. Regression models mathematically adjusts for
  confounders
• 5. Stratification subdivide data into
  homogenous groups (THIS CHAPTER)

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19.2 Simpsons Paradox
An extreme form of confounding in which in which
the confounding variable reverses the direction
the association
Any statistical relationship between two
variables may be reversed by including additional
factors in the analysis. Application Which
factors should be included in the analysis?
Wrong Simpson
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Example
Does helicopter evaluations (exposure) decrease
the risk of death (disease) following accidents?
Crude comparison head-to-head comparison
without consideration of extraneous factors.
Died Survived Total
Helicopter 64 136 200
Road 260 840 1100
Can we conclude that helicopter evacuation is 35
riskier?
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Confounder Severity of Accident
Died Survived Total
Helicopter 64 136 200
Road 260 840 1100
Serious Accidents Serious Accidents
Died Survived Total
Helicopter 48 52 100
Road 60 40 100
Stratify by the confounding variable
Minor Accidents Minor Accidents
Died Survived Total
Helicopter 16 84 100
Road 200 800 1000
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Accident Evacuation Serious Accidents
Serious Accidents Serious Accidents
Died Survived Total
Helicopter 48 52 100
Road 60 40 100
Among serious accidents, the risk of death was
decreased by 20 with helicopter evacuation.
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Accident Evacuation Minor Accidents
Minor Accidents Minor Accidents
Died Survived Total
Helicopter 16 84 100
Road 200 800 1000
Among minor accidents, the risk of death was also
decreased by 20.
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Accident EvacuationProperties of Confounding
Seriousness of accident
Death
Evacuation method
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Summary Relative Risk

• Since the RRs were the same in the both subgroups
  (RR1 RR2 0.8), combine the strata-specific RR
  to derive a single summary measure of
  association, i.e., the summary RR for helicopter
  evacuation is 0.80, since it decreases the risk
  of death by 20 in both circumstances

This summary RR has adjusted for severity of
accident
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Summary Relative Risk

• In practice, the strata-specific results wont be
  so easily summarized
• Most common method for summarizing multiple
  2-by-2 tables is the Mantel-Haenszel method
• Formulas in text
• Use SPSS or WinPEPI gt Compare2 for data analysis

William Haenszel
Nathan Mantel
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Summary Estimates with WinPEPI gt Compare2 gtA.
Input
Output
RR-hatM-H 0.80 (95 CI for RR 0.63 1.02)
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Summary Hypothesis Test with WinPEPI gt Compare2
gtA.

• Null hypothesisH0 no association in population
  (e.g., RRM-H 1)
• Test statistics WinPEPI gt Compare2 gt A. gt
  Stratified ? see prior slide for data input
• Interpretation the usual, i.e., P value as
  measure of evidence

?2 3.46, df 1, P .063 ? pretty good
evidence for difference in survival rates
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M-H Methods for Other Measures of Association

• Mantel-Haenszel methods are available for odds
  ratio, rate ratios, and risk difference
• Same principles of confounder analysis and
  stratification apply
• Covered in text, but not in this presentation

Im back
Im back
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Interaction (Effect Measure Modification)

• When we see different effects within subgroups, a
  statistical interaction is said to exist
• Interaction Heterogeneity of the effect
  measures
• Do not use M-H summaries with heterogeneity ?
  would hide the non-uniformity

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Example Case-Cntl Data E Asbestos D Lung CA
C Smoking
Too heterogeneous to summarize with a single OR
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Test for InteractionHypothesis Statements

• H0 no interaction vs. Ha interaction
• For case-control study with two strataH0OR1
  OR2 vs. HaOR1 ? OR2

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Test for InteractionTest Statistics
Use WinPEPI gt Compare2 gt A. gt Stratified ?
OR-hat2 2
OR-hat1 60
Output
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Test for InteractionInterpretation

The test of H0OR1 OR2 vs. HaOR1 ? OR2 ?2
21.38, df 1, P 0.0000038.
? Conclude Good evidence for interaction
Report strata-specific results OR is smokers is
60 OR in nonsmokers is 2
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Strategy
Let MA Measure of Association (RR, OR, etc.)