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Confounding, Effect Modification, Confounding, Effect Modification, and Stratification and Stratification HRP 261 1/27/03 10 HRP 261 1/27/03 10 - - 10:50 am 10:50 am
Confounding, Effect Modification, Confounding, Effect Modification, and Stratificationand Stratification
HRP 261 1/27/03 10HRP 261 1/27/03 10--10:50 am10:50 am
Adding a Third Dimension to Adding a Third Dimension to the the RxCRxC picturepicture
Exposure Disease?
Mediator
Confounder
Effect modifier
Some TermsSome Terms1. What Agresti calls, “Marginally associated but
conditionally independent”…epidemiologists call “confounding.”
2. What Agresti calls, “partial tables,”…epidemiologists call, “stratification.”
3. What epidemiologists call, “effect modification”…statisticians call, “interaction.”
1. Confounding1. Confounding
A confounding variable is associated with the exposure and it affects the outcome, but it is not an intermediate link in the chain of causation between exposure and outcome.
Examples of ConfoundingExamples of Confounding
Oral contraceptive use?
Cervical cancer
Infection with humanpapillomavirus (HPV)
Oral contraceptive use?
Breast cancer
Late age at first birth/ low parity
More ConfoundingMore Confounding
Poor nutrition?
Menstrual irregularity
Low weight
Menstrual irregularity?
Low bone strength
Late menarche
Confusion over Confusion over postmenopausal hormones: postmenopausal hormones:
?Heart attacks (MI)Postmenopausal HRT
High SES, high education, other confounders?
Mixture May Rival Estrogen in Preventing Heart Disease
August 15, 1996, Thursday
“Widely prescribed hormone pills that combine estrogen and progestin appear to be just as effective as estrogen alone in preventing heart disease in women after menopause, a study has concluded.” “Many women take hormones … to reduce the risk of heart disease and broken bones.”“More than 30 studies have found that estrogen after menopause is good for the heart.”
Example: Nurse’s Health Study Example: Nurse’s Health Study
protective relative risks
Nurse’s Health StudyNurse’s Health Study
No apparent Confounding…No apparent Confounding…
e.g., the effect is the same among smokers and non-smokers, so the
association couldn’t be due to confounding by smokers (who may take less hormones and certainly get
more heart disease).
RCT: Women’s Health RCT: Women’s Health Initiative (2002)Initiative (2002)
On hormones
On placebo
Controlling for confounders in Controlling for confounders in medical studiesmedical studies
1. Confounders can be controlled for in the design phase of a study (randomization or restriction or matching).2. Confounders can be controlled for in the analysis phase of a study (stratification or multivariate regression).
Analytical identification of Analytical identification of confounders through confounders through
stratificationstratification
MantelMantel--HaenszelHaenszel Procedure:Procedure:NonNon--regression technique used to regression technique used to
identify confounders and to control identify confounders and to control for confounding in the for confounding in the statistical statistical
analysisanalysis phase rather than the phase rather than the designdesignphase of a study.phase of a study.
From From AgrestiAgresti……
“It is more informative to estimate the strength of association than simply to test a hypothesis about it.”
“When the association seems stable across partial tables, we can estimate an assumed common value of the k true odds ratios.”
Controlling for confounding by Controlling for confounding by stratificationstratification
Example: Let’s revisit the Berkeley study
Crude RR = (1276/1835)/(1486/2681) =1.25
(1.20 – 1.32)
Denied
Admitted
1835 2681
Female Male
1276 1486
559 1195
Program AProgram A
Stratum 1 = only those who applied to program A
Stratum-specific RR = .90 (.87-.94)
Denied
Admitted
108 825
Female Male
19 314
89 511
Program BProgram B
Stratum 2 = only those who applied to program B
Stratum-specific RR = .99 (.96-1.03)
Denied
Admitted
25 560
Female Male
8 208
17 352
Program CProgram C
Stratum 3 = only those who applied to program C
Stratum-specific RR = 1.08 (.91-1.30)
Denied
Admitted
593 325
Female Male
391 205
202 120
Program DProgram D
Stratum 4 = only those who applied to program D
Stratum-specific RR = 1.02 (.89-1.18)
Denied
Admitted
375 407
Female Male
248 265
127 142
Program EProgram E
Stratum 5 = only those who applied to program E
Stratum-specific RR = .88 (.67-1.17)
Denied
Admitted
393 191
Female Male
289 147
104 44
Program FProgram F
Stratum 6 = only those who applied to program F
Stratum-specific RR = 1.09 (.84-1.42)
Denied
Admitted
341 373
Female Male
321 347
20 26
SummarySummaryCrude RR = 1.25 (1.20 – 1.32)
Stratum specific RR’s:.90 (.87-.94).99 (.96-1.03)1.08 (.91-1.30) 1.02 (.89-1.18).88 (.67-1.17)1.09 (.84-1.42)
Maentel-Haenszel Summary RR: .97
Recall: Cochran-Manetl-Haenszel Test is NS. Gender and denial of admissions are conditionally independent given program.The apparent association (RR=1.25) was due to confounding.
∑
∑
=
=
+
+
k
i i
iii
k
i i
iii
Tbac
Tdca
1
1
)(
)(k strata
The MantelThe Mantel--HaenszelHaenszelSummary Risk RatioSummary Risk Ratio
Disease
Not Disease
Exposure Not Exposed
a c
b d
E.g., for Berkeley…E.g., for Berkeley…
97.
714)341(347
584)393(147
782)375(265
918)593(205
585)25(208
933)108(314
714)373(321
584)191(289
782)407(248
918)325(391
585)560(8
933)825(19
=+++++
+++++
∑
∑
=
=k
i i
ii
k
i i
ii
Tcb
Tda
1
1
The MantelThe Mantel--HaenszelHaenszelSummary Odds RatioSummary Odds Ratio
Exposed
Not Exposed
Case Control
a b
c d
Country
OR = 1.32 Spouse smokes
Spouse does not smoke
137 363
71 249US
Spouse smokes
Spouse does not smoke
19 38
5 16
Great
BritainOR = 1.6
Spouse smokes
Spouse does not smoke
Lung Cancer Control
73 188
21 82Japan OR = 1.52
Source: Blot and Fraumeni, J. Nat. Cancer Inst., 77: 993-1000 (1986).
From Problem 3.9 in Agresti…
Summary ORSummary OR
38.1
820363*71
785*38
36421*188
820137*249
7816*19
36482*73
=++
++
Not Surprising!
MH assumptionsMH assumptions
OR or RR doesn’t vary across strata. (Homogeneity!)If exposure/disease association does vary for different subgroups, then the summary OR or RR is not appropriate…
advantages and limitationsadvantages and limitationsadvantages…• Mantel-Haenszel summary statistic is easy to
interpret and calculate• Gives you a hands-on feel for the datadisadvantages…• Requires categorical confounders or continuous
confounders that have been divided into intervals
• Cumbersome if more than a single confounder To control for ≥ 1 and/or continuous confounders, a multivariate technique (such as logistic regression) is preferable.
2. Effect Modification2. Effect Modification
Effect modification occurs when the effect of an exposure is different among different subgroups.
Years of Life Lost Due to Obesity Years of Life Lost Due to Obesity ((JAMA.JAMA. Jan 8 2003;289:187Jan 8 2003;289:187--193)193)
Data from US Life Tables and the National Health and Nutrition Examination Surveys (I, II, III).
ConclusionConclusion
Race and gender modify the effect of obesity on years-of-life-lost.
Among white women, stage of breast cancer at detection is associated with education.
However, no clear pattern among black women.
Colon cancer and obesity in preColon cancer and obesity in pre--and postand post--menopausal womenmenopausal women
Obesity appears to be a risk
factor in pre-menopausal
womenBut appears to be
protective or unrelated in post-menopausal
women
Hypothetical Example: Effect Hypothetical Example: Effect ModificationModification
Feelings of Elation on 1/26
No change or depression
Watched the super-bowl
1250 2500
Did not watch the super-bowl
250 500
OR = 1.0
Conclusion: Watching the super-bowl doesn’t affect anyone’s mood?…
Football-team preference
OR = 1.5 Watched
Did not
450 300
375 375
Other/none
Tampa BayFans
Watched
Did not
1240 10
125 125OR = 124.0
Watched
Did not
Mood + Mood -
10 1240
125 125OR = .008Oakland
Fans
Should have highly significant Breslow-Day statistic!
