1. Acknowledgment: Kostas Danis
Confounding,
Effect modification, and Stratification Tunisia, 30th October 2014
Acknowledgment: Kostas Danis
Takis Panagiotopoulos
National Schoool of Public Health, Athens, Greece

2. Main points The concept of confounding and of effect modification
How to check if confounding and if effect modification is present: stratification
How to show results if confounding or if effect modification is present
How to prevent confounding

3. Galaxy, Vol 11, Issue 2, Feb 1871 . . . . . . Mark Twain
Source:

4. Lying in bed Confounding Disease
The real player
Lying in bed
Disease
(a “third variable”),
associated with the outcome,
and also with the exposure (independently of the outcome)
Exposure
Outcome
Is there a third variable–risk factor for the Outcome– which may be hidden behind the Exposure?
Q. 1
Confounding
The lying-in-bed association: a fallacy  unmask the “real player”

5. Driving fast Effect modification
The co-player
Driving fast
Exposure
Outcome
I s there a third variable–risk factor for the Outcome–
which may be acting in combination with the Exposure?
Q. 2
Effect modification
The driving-fast association: a half-truth  disentangle effects of “co-players”

6. Exposure Outcome Third variable Confounding: To eliminate (bias)
Effect modification: To analyse (useful info)
fallacy vs half-truth

7. Cohort studies marching towards outcomes

8. Cohort study Non cases Risk % Total Cases Exposed 100 50 50 50 %%
Not exposed
100 %
Risk ratio: 50% / 10% = 5

9. Case-control studies

10. Cases Controls Source population Exposed Sample Unexposed Controls:
Sample of the source population
Representative with regard to exposure
Controls

11. Case-control study a/c b/d Cases Controls a b Exposed Not exposed c d
Total
b+d
% exposed
a/(a+c)
b/(b+d)
d/(b+d)
Odds Ratio:
= (a/c) / (b/d)
= ad / bc
% unexposed
c/(a+c)
Odds of
exposure
a/c
b/d

12. Cross-sectional (prevalence) studies

13. Cross-sectional study: Sampling
Sample
Sampling
Population
Target Population

14. Cross-sectional study
Non
cases Prevalence %
Total
Cases
Exposed
1000 %
Not exposed
1000 %
Prevalence ratio (PR) % / 10% = 5

15. Should I believe my measurement?
Exposure Outcome
RR = 4
Chance?
Bias?
Confounding?
True association
- Causal?
- Non-causal?

16. Exposure Outcome Third variable Confounding: To eliminate (bias)
Effect modification: To analyse (useful info)
fallacy vs half-truth

17. What should you do? 1. Check for effect modification  Analyse it.
In practice, we deal with:
effect modification FIRST; confounding SECOND
1. Check for effect modification  Analyse it.
2. Check for confounding  Eliminate it.
How? 1. Stratification
2. Stratified analysis
Create strata
according to levels of exposure to the third variable

18. Effect modification

19. Effect modification
Variation in the magnitude of measure of effect across levels of a third variable
Happens when RR or OR is different between strata (subgroups of population)

20. Why study effect modification
To sort out (quantitatively) effect of the exposure under study and of a “third variable” (a potential effect modifier)
To identify a subgroup with a lower or higher risk ratio
To target public health action
To study interaction between risk factors

21. Effect modification Disease Factor A (lung cancer) (asbestos) Factor B
(smoking)
Effect modifier / Interaction
Effect modification: epi term. Interaction: statistical term (vs. biological)

22. Asbestos (As) and lung cancer (Ca)
Case-control study, unstratified data
As Ca Controls OR
Yes
No Ref.
Total

23. Asbestos Lung cancer
Smoking?

24. Are stratum-specific RRs/ORs different between them?

25. Asbestos (As), smoking and lung cancer (Ca)
Smoking As Cases Controls OR
Yes Yes
Yes No
No Yes
No No Ref.
(Reference group is the same for all ORs)

26. Asbestos, smoking and lung cancer: interpretation
In smokers, exposure to asbestos is 6 times higher among lung cancer cases than among controls
In non-smokers, exposure to asbestos is 3 times higher among lung cancer cases than among controls
Therefore, exposure to smoking modifies (increases by a factor of 2) the effect of exposure to asbestos
Present data by stratum
Public health implications?

27. Physical activity and myocardial infarction (MI)

28. Physical Infarction
activity
Gender?

29. Are stratum-specific RRs/ORs different between them?

30. Interpretation Different effects (RR) in different strata (men-women)
Therefore, effect of physical activity is modified by gender (more protective for men)
Present data by stratum (gender)

31. Vaccine efficacy ARU – ARV VE = ---------------- ARU VE = 1 – RR
VE: vaccine efficacy
ARU: Attack rate in unvaccinated
ARV: Attack rate in vaccinated
RR: risk ratio

32. Vaccine efficacy (VE)
VE = RR =
VE = 72%

33. Vaccine Disease
Age?

34. Vaccine efficacy by age group
Are stratum-specific RRs/ORs different between them?

35. Interpretation Different effects (RR) in different strata (age groups)
Therefore, VE is modified by age
Present data by age-stratum
Public health implications?

36. Any statistical test to help us?
Breslow-Day
Woolf test
Test for trends: Chi square
Homogeneity ?
(i.e. are they similar?)

37. Comparison of strata-specific RRs/ORs
Question:
Are stratum-specific RRs/ORs different between them?
Answer:
Do stratum-specific estimates look different?
95% CI of OR/RR do NOT overlap?
Is the Test of Homogeneity significant?

38. Death from diarrhoea according to breast feeding, Brazil, 1980s (crude analysis)
Diarrhoea Controls OR (95% CI)
No breast feeding ( )
Breast feeding Ref

39. No breast Diarrhoea
feeding
Age?

40. Death from diarrhoea according to breast feeding, Brazil, 1980s
Infants < 1 month of age
Cases Controls OR (95% CI)
No breast feeding (6-203)
Breast feeding Ref
Infants ≥ 1 month of age
Cases Controls OR (95% CI)
No breast feeding ( )
Breast feeding Ref
Woolf test (test of homogeneity): p=0.03
Are stratum-specific RRs/ORs different between them?

41. Interpretation Different effects (OR) in different strata (age groups)
Therefore, protective effect of breast feeding is modified by age (more protective in neonates <1 mo of age compared to infants ≥1 mo by a factor of 12)
Present data by age-stratum
Public health implications?

42. Risk of gastroenteritis by exposure, outbreak X, place Y, time Z (crude analysis)
Exposed
Exposure
Yes No
RR†
(95% CI‡) n
AR (%)*
AR(%)*
pasta 94 77 7
4.2
18.0
(8.8-38)
tuna 49 68 24
2.9
( )
* AR = Attack Rate
† RR = Risk Ratio
‡ 95% CI = 95% confidence interval of the RR

43. Tuna Gastroenteritis
Pasta?

44. Risk of gastroenteritis by exposure, Outbreak X, Place, time X
Pasta Yes
Cases Total AR (%) RR (95% CI)
Tuna ( )
No tuna Ref
Pasta No
Cases Total AR (%) RR (95% CI)
Tuna (2.6-46)
No tuna Ref
Woolf’s test (test of homogeneity): p=0.0007
Are stratum-specific RRs/ORs different between them?

45. Negative modification of effect
Interpretation
Different effects (RR) in different strata
Therefore, effect of exposure to tuna is modified by exposure to pasta
Exposure to pasta reduces the effect of exposure to tuna (by a factor of 10)
Present data by stratum
Negative modification of effect
is also possible

46. How to check for effect modification in stratified analysis
Perform crude analysis
Measure the strength of association (RR/OR with CIs)
List potential effect modifiers
Stratify data by level of exposure to potential modifier(s)
Check for effect modification
Are stratum-specific RRs/ORs different between them?
Observe RRs/ORs
CIs: overlapping?
Woolf’s test: statistical significance?
If YES effect modification  Show data by stratum
If NO effect modification  Check for confounding
[Yes = EM]

47. Crazy findings!! Why??
A trial compared two treatments for kidney stones, Treatment A (surgery) and Treatment B (percutaneous nephrolithotomy). Successful outcome was defined as stones reduced to <2 mm in size. 350 patients were included in each treatment branch of the study. It was found that:
Successful outcome, crude results
Treatment A Treatment B
273/350 (78%) 289/350 (83%)
Therefore, Treatment B is better (83% vs 78%).
Successful outcome, stratified results by size of stones
Treatment A Treatment B
Small stones (<2 cm) 81/87 (93%) 234/270 (87%)
Large stones (≥2 cm) 192/263 (73%) 55/80 (69%)
TOTAL 273/ /350
Therefore, Treatment A is better (93% vs 87% and 73% vs 69%).
Show without any explanation  5-10 min break
Source: Charig CR et al, BMJ 29/03/1986.

48. Crazy findings!! Why??
A trial compared two treatments for kidney stones, Treatment A (surgery) and Treatment B (percutaneous nephrolithotomy). Successful outcome was defined as stones reduced to <2 mm in size. 350 patients were included in each treatment branch of the study. It was found that:
Successful outcome, stratified results by size of stones
Treatment A Treatment B
Small stones (<2 cm) 81/87 (93%) 234/270 (87%)
Large stones (≥2 cm) 192/263 (73%) 55/80 (69%)
TOTAL 273/350 (78%) 289/350 (83%)
First systematic description by Edward Simpson in Also called “amalgamation paradox”
Distortion of effect by confounding to the extent of reversal of the apparent effect.
Solution: calculate adjusted proportions by applying stone-size-and-treatment-specific rates to treatment groups with strata of equal size (equivalent to direct standardization).
Treatment A dominated by large stones: 263/350 (75%)
Treatment B dominated by small stones: 270/350 (77%)
AND
Less successful outcome for large stone
“Simpson’s paradox” or “reversal paradox”
SOS: crude rates can be misleading in some circumstances!!
Source: Charig CR et al, BMJ 29/03/1986.

49. Confounding

50. (potential confounding factor)
Exposure
Outcome
Third factor
(potential confounding factor)
Distortion of measure of effect because of a third (confounding) factor, which
must be related to the exposure
must be a risk factor itself
must not be in the causal chain of exposure-outcome
Confounding should be prevented or controlled for

51. Example: third factor in the causal chain
Heart
attack
Smoking + NO
Atherosclerosis
NOT a confounding

52. Example 1 Skate- boarding Chlamydia infections Age?
Age not evenly distributed between the two exposure groups: 90% of Skate-boarders are young 20% of Non skate-boarders are young
In conclusion (1) Age is a possible CF (2) Thus, the effect of skateboarding on chlamydia infections likely close to 1

53. Example 2 Lung Coffee cancer drinking Smoking?
NOTE: New study says that coffee drinkers are more likely to get lung cancer”
Smoking?
Smoking not evenly distributed between coffee drinkers/non-drinkers: - Drinkers: 70% smokers - Non-drinkers: 10% smokers
In conclusion (1) Effect of coffee drinking on lung cancer likely confounded by smoking. Smoking is a likely CF (2) Effect of coffee drinking on lung cancer likely close to 1

54. Example 3
Birth
order
Down
syndrome
Age of
mother?

55. Example 3 (ii)
Incidence of Down syndrome by birth order

56. Example 3 (iii)
Incidence of Down syndrome babies by mothers‘ age group

57. XXXXXXXXXXXXXXXXXXXXX
Incidence of Down syndrome
babies by birth order AND age of mother
XXXXXXXXXXXXXXXXXXXXX

58. Example 3 (v) Birth Down order syndrome Age of mother?
In conclusion (1) Effect of birth order on Down syndrome babies confounded by age of mothers (possible CF). (2) Effect of birth order on down syndrome will be likely close to 1

59. So, remember ! A confounding factor always…..
Confounding factors must met the two following conditions:
Exposure
Outcome
Third variable
Be associated with outcome
- independently of exposure
Be associated with exposure
- without being the consequence of exposure

60. The distortion introduced by confounding factors
May simulate an association
May hide an association that does exist

61. How to prevent/control confounding?
Prevention of confounding (in study design)
Randomization (experiment)
Restriction to one stratum
Matching
Control of confounding (in analysis)
Stratified analysis
Multivariable analysis

62. Example: Are Mercedes more dangerous than Porsche?
A paper looking at 1000 Mercedes and 1000 Porsche drivers who were followed for one year (cohort study)
95% CI =

63. Distribution by age of driver
Proportion of < 25 yo among Porsche drivers: %
among Mercedes drivers: 30 %

64. Car type=Porsche Accidents
Confounding factor:
Age of driver?

65. Is adjusted RR/OR different from crude?
Crude RR = 1.5
Adjusted RR = 1.1 ( )

66. Incidence of malaria according to the presence of a radio set, Kahinbhi Pradesh
Crude data
Malaria Total AR% RR
Radio set
No radio Ref
95% CI =

67. Radio Malaria
Confounding factor:
Mosquito net?

68. Is adjusted RR/OR different from crude?
Crude RR = 0.7
Adjusted RR = 1.01
Is adjusted RR/OR different from crude?

69. To identify confounding
Compare crude measure of effect (RR or OR) to
adjusted (weighted) measure of effect
 Mantel-Haenszel RR or OR

70. Any statistical test to help us?
When is ORMH different from crude OR ?
Adjusted – Crude
Crude
> 10-20%

71. Mantel-Haenszel summary measure
Adjusted or weighted RR or OR
Advantages of MH
Zeroes allowed
S (ai di) / ni
ORMH =
S (bi ci) / ni

72. Mantel-Haenszel summary measure
For each stratum
Mantel-Haenszel (adjusted or weighted) OR a1 b1 c1 d1
Cases
Controls
Exp+
Exp-
OR MH =
SUM (ai di / ni)
SUM (bi ci / ni) n1
Cases
Controls
(a1 x d1) / n1 +
ORMH =
Exp+
(a2 x d2) / n a2 b2
(b1 x c1) / n1 +
(b2 x c2) / n
Exp- d2 c2 n2

73. How to check for confounding in stratified analysis
Perform crude analysis
Measure the strength of association (RR/OR with CIs)
List potential confounders
Stratify data by level of exposure to potential confounder(s)
Check for effect modification
If NO effect modification  Check for confounding
Is adjusted RR/OR different from crude? [Yes = CF]
adjusted RR/OR: Mantel-Haenszel
(Adjusted-Crude)/Crude > 10–20% ?
If YES confounding  Show adjusted data
If NO confounding  Show crude data

74. How to define the strata?
Strata defined according to third variable:
‘Usual’ confounders (e.g. age, sex, socio-economic status)
Any other suspected confounder, effect modifier or additional risk factor
Strata of public health interest
For two risk factors:
stratify on one to study the effect of the second on outcome
Two or more exposure categories:
each is a stratum
Residual confounding ?

75. How to deal with multiple risk factors
Logical order of data analysis
Crude analysis
Stratified analysis
Multivariate analysis (mathematical model)
- linear regression
- logistic regression
- Simultaneous adjustment for multiple risk factors/confounders
- Can address effect modification

76. Stratified Analysis: an example
. csinter case pesto, by(pasta)
Pasta = Exposed
Pesto Total Cases Risk %
Exposed
Unexposed
Risk difference [-0.17–0.13]
Risk Ratio [0.81–1.19]
Attrib.risk.exp [-0.19–0.19]
Attrib.risk.pop [.–.]
Pasta = Unexposed
Pesto Total Cases Risk %
Exposed
Unexposed
Risk difference [-0.09–0.11]
Risk Ratio [0.15–9.53]
Attrib.risk.exp [-5.52–0.90]
Attrib.risk.pop [.–.]
Test of Homogeneity (M-H) : pvalue :
Crude RR for pesto : [1.56–2.79]
MH RR for pesto adjusted for pasta : [0.81–1.20]
Adjusted/crude relative change : %
> 10-20%

77. Examples of stratified analysis
1-EM, 2-CF, 3-EM, 4-CF, 5-no EM, no CF
1) Are RRs/ORs different between strata?  EM
2) Is adjusted RR/OR different from crude?  CF

78. Summary: effect modification and confounding
Belongs to nature
Modifies effect of “exposure” under study
Need to disentangle effect of risk factors
Useful: increases knowledge of biological mechanism
Allows targeting of public health action
Confounding
Belongs to study
Distorts effect of “exposure” under study
Need to unmask effect of “third variable”
Prevent (study design)
Control (analysis)

79. Effect modification The co-player
Exposure
Outcome
The driving-fast association: a half-truth  disentangle effects of “co-players”

80. The lying-in-bed association: a fallacy  unmask the “real player”
Confounding
The real player
Exposure
Outcome
The lying-in-bed association: a fallacy  unmask the “real player”

81. Summary: how to conduct a stratified analysis
Perform crude analysis
Measure the strength of association (RR/OR with CIs)
List potential effect modifiers and/or confounders
Stratify data by level of exposure to potential modifiers or confounders
Check for effect modification (Are stratum-specific RRs/ORs different between them? CIs / Woolf’s test)
If YES effect modification  Show data by stratum
If NO effect modification  Check for confounding
(Is adjusted RR/OR different from crude? >10-20%)
If YES confounding  Show adjusted data
If NO confounding  Show crude data

82. A variable can mask another variable!
A train can mask a second train
A variable can mask another variable!

83. Takis Panagiotopoulos
Thank you
Takis Panagiotopoulos
National Schoool of Public Health, Athens, Greece