1. Chapter 19 Stratified 2-by-2 Tables
4/15/2017
Chapter 19 Stratified 2-by-2 Tables
April 17
Basic Biostat 1

2. In Chapter 19: 19.1 Preventing Confounding
19.2 Simpson’s Paradox (Severe Confounding)
19.3 Mantel-Haenszel Methods
19.4 Interaction

3. §19.1 Confounding
Confounding ≡ a distortion in an association brought about by extraneous variables
Variables E = exposure variable D = disease variable C = confounding variable
Confounder word origin: “to mix together,” the effects of the confounder gets mixed up with the effects of the exposure

4. Properties of confounding variables
Associated with exposure
Independent risk factor
Not in causal pathway

5. Mitigating Confounding
Randomization balances groups with respect to measured and unmeasured confounders
Restriction of the study base imposes uniformity within groups
. St. Thomas Aquinas Confounding Averroлs

6. Mitigating confounding (cont.)
3. Matching – balances confounders
4. Regression models – mathematically adjusts for confounders
5. Stratification – subdivide data into homogenous groups (THIS CHAPTER)

7. §19.2 Simpson’s 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

8. Can we conclude that helicopter evacuation is 35% riskier?
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?

9. Confounder = Severity of Accident
Died
Survived
Total
Helicopter 64
136
200
Road
260
840
1100
Serious Accidents
Died
Survived
Total
Helicopter 48 52
100
Road 60 40
Stratify by the confounding variable:
Minor Accidents
Died
Survived
Total
Helicopter 16 84
100
Road
200
800
1000

10. Accident Evacuation Serious Accidents
Died
Survived
Total
Helicopter 48 52
100
Road 60 40
Among serious accidents, the risk of death was decreased by 20% with helicopter evacuation.

11. Accident Evacuation 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%.

12. Accident Evacuation Properties of Confounding
Seriousness of accident
Evacuation method
Death

13. 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

14. Summary Relative Risk
In practice, the strata-specific results won’t 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 > Compare2 for data analysis
William Haenszel
Nathan Mantel

15. Summary Estimates with WinPEPI > Compare2 >A.
Input
Output
RR-hatM-H = 0.80 (95% CI for RR: 0.63 – 1.02)

16. Summary Hypothesis Test with WinPEPI > Compare2 >A.
Null hypothesis H0: no association in population (e.g., RRM-H = 1)
Test statistics: WinPEPI > Compare2 > A. > Stratified  see prior slide for data input
Interpretation: the usual, i.e., P value as measure of evidence
χ2 = 3.46, df = 1, P = .063
 pretty good evidence for difference in survival rates

17. 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
I’m back
I’m back

18. 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

19. Example: Case-Cntl Data E= Asbestos D = Lung CA C = Smoking
Too heterogeneous to summarize with a single OR

20. Test for Interaction Hypothesis Statements
H0: no interaction vs. Ha: interaction
For case-control study with two strata H0:OR1 = OR2 vs. Ha:OR1 ≠ OR2

21. Test for Interaction Test Statistics
Use WinPEPI > Compare2 > A. > Stratified  …
OR-hat1 = 60
OR-hat2 = 2
Output:

22. Test for Interaction Interpretation
The test of H0:OR1 = OR2 vs. Ha:OR1 ≠ OR2
χ2 = 21.38, df = 1, P =
 Conclude: Good evidence for interaction
Report strata-specific results:
OR is smokers is 60
OR in nonsmokers is 2

23. Strategy
Let MA ≡ Measure of Association (RR, OR, etc.)