1
病例对照研究
Case-Control Study
吕筠
北京大学公共卫生学院
流行病与卫生统计学系
2011-09-15 预防医学本科07级 2
Case-Control Study
Rationale
Selection of Cases and Controls
Matching
Data Analysis
Sample Size & Power Calculation
Bias
2011-09-15 预防医学本科07级 3
Rationale
Design of a case-control study
Exposed NotExposed Exposed
Not
Exposed
Disease NoDisease
CASES CONTROLS
4
Database Format (Independent)
ID Disease Exposure
Case
Group
1 1 1
2 1 0
3 1 1
4 1 1
…… 1 1
100 1 0
Control
Group
101 0 0
102 0 0
103 0 1
104 0 0
…… 0 1
200 0 0
2011-09-15 预防医学本科07级
Disease
1=Yes
0=No
Exposure
1=Yes
0=No
2011-09-15 预防医学本科07级 5
Proportions
exposed
2×2 Table
(1) First Select
Case Controls
(2) Then Measure
Past Exposure
Exposed a b
Not exposed c d
Totals a+c b+d
Calculation of Proportion Exposed in a Case-Control Study
2011-09-15 预防医学本科07级 6
Recall: Cohort Study
Defined
Population
Exposed Non-Exposed
Disease No Disease
NON-RANDOMIZED
Disease No Disease
Design of a cohort study
2
2011-09-15 预防医学本科07级 7
Incidence
Proportion
of Disease
Recall: Cohort Study
Analysis of Cohort Study
(2) Then Follow
to See Whether TotalsDisease
Develops
Disease Does
Not Develop
(1) First
Select
Exposed a b a+b
Not exposed c d c+d
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2×2 Table
(1) First Select
Case Controls
(2) Then Measure
Past Exposure
Exposed a b
Not exposed c d
Totals a+c b+d
Proportions
exposed
Calculation of Proportion Exposed in a Case-Control Study
COMPARE
Sampling Error Statistical Significance Testing
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Chi-Square Test
Question 1: Is there a relationship
(association) between exposure and
disease?
Or: Is there statistical significant difference
between cases and controls regarding the
proportion of exposed people?
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Chi-Square Test
Result
No Association: STOP HERE
Have Association: GO ON ……
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Strength of Association
Question 2: How strong is the relationship
(association) between exposure and
disease?
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Recall: Cohort Study
Risk Calculation in a Cohort Study
(2) Then Follow
to See Whether Totals
Incidence
Proportion
of DiseaseDiseaseDevelops
Disease Does
Not Develop
(1) First
Select
Exposed a b a+b
Not exposed c d c+d
预防医学本科07级
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2011-09-15 预防医学本科07级 13
Recall: Cohort Study
The meaning of RR
Exposed people is ?? times more likely to
develop a disease than non-exposed
people
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Traditional Case-Control Design
Cannot calculate the RR directly
Can obtain a very good approximation of
the RR from a case-control study using
the odds ratio
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Odds
Probability that the event will occur divided
by the probability that the event will not
occur
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Odds
(1) First Select
Case Controls
(2) Then Measure
Past Exposure
Exposed a b
Not exposed c d
Calculation of Proportion Exposed in a Case-Control Study
What are the odds that a case was exposed?
What are the odds that a control was exposed?
2011-09-15 预防医学本科07级
Odds
(1) First Select
Case Controls
(2) Then Measure
Past Exposure
Exposed a b
Not exposed c d
Calculation of Proportion Exposed in a Case-Control Study
What are the odds that a case was exposed?
What are the odds that a control was exposed?
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Odds Ratio, OR
The ratio of the odds that the cases were
exposed to the odds that the controls were
exposed
4
19
Odds Ratio, OR
(1) First Select
Case Controls
(2) Then Measure
Past Exposure
Exposed a b
Not exposed c d
Analysis of Case-Control Study
Cross-products ratio
OR=
Support hypothesis of an association: a, d – diseased people
who were exposed and non-diseased people who were not
exposed
Negate hypothesis of an association: b, c – non-diseased
people who were exposed and diseased people who were not
exposed
2011-09-15 预防医学本科07级 2011-09-15 预防医学本科07级 20
Confidence Interval, C.I.
Woolf’s method
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Odds Ratio, OR
Question 3: What is the direction of the
association and how to interpret it?
OR = 1
OR > 1
OR < 1
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OR vs. RR
Question 4: How well the OR approximates
the RR? When is the OR a good estimate of
the RR?
Answer: When the disease being studied
does not occur frequently
2011-09-15 预防医学本科07级 23
Database Format (Matched)
Pair No ExposureCase Control
1 1 0
2 1 1
3 1 1
4 0 0
5 0 1
6 1 0
7 1 0
8 1 0
……
Disease
1=Yes
0=No
Exposure
1=Yes
0=No
Pair No Disease Exposure
1 1 1
1 0 0
2 1 1
2 0 1
3 1 1
3 0 1
4 1 0
4 0 0
……
2011-09-15 24
Chi-Square Test
Control
Exposed Not Exposed
Case Exposed a bNot Exposed c d
Analysis of Matched Case-Control Study
Step 1: Chi-Square Test
预防医学本科07级
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2011-09-15 预防医学本科07级 25
Pairs Contribute to our knowledge
4 possible combination of exposure status
for each pair
+ -
0 1
0 1
Exposure
Case
Control
+ -
1 0
1 0
+ -
0 1
1 0
+ -
1 0
0 1
26
Pairs Contribute to our knowledge
Control
Exposed Not Exposed
Case Exposed a bNot Exposed c d
Analysis of Matched Case-Control Study
Concordant
pairs
1. Pairs in which both the case and the control were
exposed a
2. Pairs in which neither the case nor the control
was exposed d
Discordant
pairs
3. Pairs in which the case was exposed but the
control was not b
4. Pairs in which the control was exposed and the
case was not c
2011-09-15 预防医学本科07级
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Odds Ratio, OR
Control
Exposed Not Exposed
Case Exposed a bNot Exposed c d
Analysis of Matched Case-Control Study
Step 2: Calculating OR
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Odds Ratio, OR
Control
Exposed Not Exposed
Case Exposed a bNot Exposed c d
Analysis of Matched Case-Control Study
OR=
Support hypothesis of an association: b – the number of
pairs in which the case was exposed and the control was
not
Negate hypothesis of an association: c – the number of
pairs in which the control was exposed and the case was
not
2011-09-15 预防医学本科07级 29
Confidence Interval, C.I.
Control
Exposed Not Exposed
Case Exposed a bNot Exposed c d
Analysis of Matched Case-Control Study
Step 3: 95% C.I.
2011-09-15 预防医学本科07级 30
Dose Response: Test for Trend
When exposure is categorized into multiple
ordinal categories, it may be of interest to
assess whether the observed relation
between increasing (or decreasing) levels of
exposure and the risk (or odds) of disease
follows a linear dose-response pattern.
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2011-09-15 预防医学本科07级 31
Dose Response: Test for Trend
Stratum
(i)
No. of Cases
(ai)
No. of controls
(bi)
Total
(ni) ORi
1 a1 b1 n1 1.0
2 a2 b2 n2
. . . .
. . . .
k ak bk nk
Total A B N
2011-09-15 预防医学本科07级 32
Dose Response: Test for Trend
Step 1: 2 by k chi-square independence test
Step 2: calculating stratum-specific OR and their
95% C.I.
Step 3: chi-square test for linear trend
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Recall: Cohort Study
ARexp
Unexposed Exposed
Attributable risk in the exposed
Inc
ide
nce
(p
er
10
00
)
预防医学本科07级 2011-09-15 预防医学本科07级 34
Recall: Cohort Study
Population attributable risk and its dependence on the
population prevalence of the exposure
ARexp
Unexposed Exposed
Inc
ide
nce
(p
er
10
00
)
Population
A
Exposure is
rare
Pop AR
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Recall: Cohort Study
Exposure is
common
ARexp
Unexposed Exposed
Inc
ide
nce
(p
er
10
00
)
Population
B Pop AR
预防医学本科07级 2011-09-15 预防医学本科07级 36
AR% in Case-Control Studies
When the odds ratio is a reasonable
estimate of the RR, then
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2011-09-15 预防医学本科07级 37
Case-Control Study
Rationale
Selection of Cases and Controls
Matching
Data Analysis
Sample Size & Power Calculation
Bias
2011-09-15 预防医学本科07级 38
Sample Size
Proportion of controls with exposure
0.0 – 1.0
Expected RR / OR
Power (% chance of detecting)
Usually 80%
Significance level (alpha)
Usually 0.05
Ratio of sample size
Controls / Cases
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Power or Beta
Power
The probability of rejecting a false null
hypothesis
= 1 – Beta
Beta
The probability of a type-II error, which occurs
when a false null hypothesis is not rejected
In other words, a type-II error occurs when you
fail to reject the null hypothesis of equal
proportions when in fact they are different
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2011-09-15 43
OR=2.0
p0=0.30
alpha=0.05
Ncase=85
2011-09-15 预防医学本科07级 44
Case-Control Study
Rationale
Selection of Cases and Controls
Matching
Data Analysis
Sample Size & Power Calculation
Bias
2011-09-15 预防医学本科07级 45
Bias, Systematic Error
Why considering bias?
That results in a mistaken estimate of an
exposure’s effect on the risk of disease
When considering bias?
Before a study: avoid and control
After a study: control and explain
2011-09-15 预防医学本科07级 46
Bias, Systematic Error
Selection bias
Information bias
Confounding bias
2011-09-15 预防医学本科07级 47
Selection Bias
Selection bias in case-control study is caused
when individuals have different probabilities
of being included in the study according to
the exposure of interest.
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Unbiased
Biased
Selection Bias
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2011-09-15 预防医学本科07级 49
Berkson Bias
E.g.,
Exposure: Uses of tobacco, alcohol, tea,
and coffee
Disease: Cancer of the pancreas
2011-09-15 预防医学本科07级 50
Berkson Bias
Case-control study
Cases: Patients with histologically proved cancer
of the pancreas
Controls: Other patients under the care of the
same physician of the cases with pancreatic cancer
Exclusion: Patients with diseases known to be
associated with smoking or alcohol
consumption
2011-09-15 预防医学本科07级 51
Berkson Bias
Cases Controls
Coffee 1
cup/day 207 275
No coffee 9 32
OR= (207/9) / (275/32) = 2.7 (95% C.I., 1.2-6.5)
2011-09-15 预防医学本科07级 52
Berkson Bias
There are many reasons to believe that this oddsratio is biased
Controls who were examined were:
Other patients under the care of the samephysician at the time of an interview with apatient with pancreatic cancer
Most of the MDs were gastroenterologistswhose other patients were likely advised tostop using coffee
2011-09-15 预防医学本科07级 53
Berkson Bias
Controls who were examined were:
Patients with diseases known to be associatedwith smoking or alcohol consumption wereexcluded
Smoking and alcohol use are correlated withcoffee use; therefore, sample is relativelydepleted of coffee users
2011-09-15 预防医学本科07级 54
Berkson Bias
10
2011-09-15 预防医学本科07级 55
Berkson Bias
When hospitalization rates differ for different
exposure groups, the relation between exposure and
disease in the hospital will not reflect the relation in
the population that serves as the source of
hospitalized cases.
Hospital
controls
2011-09-15 预防医学本科07级 56
Neyman Bias
2011-09-15 预防医学本科07级 57
Neyman Bias
2011-09-15 预防医学本科07级 58
Information Bias
Information bias, also known as observation,
classification, or measurement bias, results
from incorrect determination of exposure or
outcome, or both
2011-09-15 预防医学本科07级 59
Information Bias
Exposure suspicion bias
Knowledge of disease status may influence the
intensity and outcome of a search for exposure
to the putative cause
Cases may be questioned more intensively than
controls
Recall bias
Recall of cases and controls may differ both in
amount and in accuracy (selective recall)
2011-09-15 预防医学本科07级 60
Information Bias
E.g., Studying the possible relationship of congenital
malformations to prenatal infections
Cases (with
congenital
malformations)
Controls (without
congenital
malformations)
Assume that:
True incidence of infection (%) 15.0 15.0
Infections recalled (%) 60 10
Result will be:
Infection rate as ascertained by
interview (%)
9.0 1.5
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2011-09-15 61
Confounding Bias
E.g., Smoking, Matches, and Lung Cancer
A tobacco company researcher believes that
exposure to matches is the cause of lung
cancer
He conducts a large case-control study to test
this hypothesis
预防医学本科07级 2011-09-15 预防医学本科07级 62
Confounding Bias
Lung
Cancer
No Lung
Cancer
Matches 820 340
No Matches 180 660
2=472.91, P<0.01
OR = (820/180) / (340/660) = 8.8
95% C.I. (7.2, 10.9)
Confounding Bias LungCancer No LungCancer
Matches 820 340
No Matches 180 660
Lung
Cancer
No Lung
Cancer
Matches 810 270
No Matches 90 30
Lung
Cancer
No Lung
Cancer
Matches 10 70
No Matches 90 630
Crude
Stratified
Smoker Non-Smoker
2=0.00, P=1.00
ORs = (810/90) / (270/30) = 1.0
95% C.I. (0.65, 1.55)
2=0.00, P=1.00
ORns = (10/90) / (70/630) = 1.0
95% C.I. (0.50, 2.01)
2=472.91, P<0.01
OR = (820/180) / (340/660) = 8.8
95% C.I. (7.2, 10.9)
2011-09-15 63预防医学本科07级 2011-09-15 预防医学本科07级 64
Confounding Bias
Test of Homogeneity
Null hypothesis: The individual stratum-specific
estimates of the measure of association differ
only by random variation
i.e., the strength of association is
homogeneous across all strata
2011-09-15 预防医学本科07级 65
Confounding Bias
Assuming homogeneity is present
Form a summary of the unconfounded stratum-
specific estimates
Mantel-Haenszel hypothesis testing and
confidence interval
2011-09-15 预防医学本科07级 66
Confounding Bias
Compare “adjusted” estimate to crude
estimate
If “adjusted” measure differs meaningfully from
crude estimate, then confounding is present
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2011-09-15 67
Confounding Bias
This example illustrates:
How confounding can create an apparent effect
even when there is no actual true effect
In the relationship between matches and lung
cancer, smoking is a confounding factor or a
confounder
Smoking confounds the relationship between
matches and lung cancer
预防医学本科07级 2011-09-15 预防医学本科07级 68
Confounding Bias
How to examine the relationship between
smoking and lung cancer independent from
the use of matches?
Stratified Analysis LungCancer No LungCancer
Smoking 900 300
No Smoking 100 700
Lung
Cancer
No Lung
Cancer
Smoking 810 270
No Smoking 10 70
Lung
Cancer
No Lung
Cancer
Smoking 90 30
No Smoking 90 630
Crude
Stratified
Matches Present
2=140.42, P<0.01
ORm = (810/10) / (270/70) = 21.0
95% C.I. (10.67, 41.32)
2=238.64, P<0.01
ORnm = (90/90) / (30/630) = 21.0
95% C.I. (13.14, 33.55)
2=750.00, P<0.01
OR = (900/100) / (300/700) = 21.0
95% C.I. (16.4, 26.9)
Matches Absent
2011-09-15 69预防医学本科07级 2011-09-15 预防医学本科07级 70
Confounding Bias
What is the effect of matches on the
relationship between smoking and lung
cancer?
Smoking
Lung
Cancer
Matches
Matches
Lung
Cancer
?Smoking
2011-09-15 预防医学本科07级 71
Confounder
A true confounder (C) must be associated
with:
the exposure (E) in question
the disease (D) under study
A variable that is an intermediate step in
the causal path between the exposure in
question and disease under study is not a
confounding variable. E
D
Factor
2011-09-15 预防医学本科07级 72
Before a study
Randomization
Restriction
Matching (+ stratification analysis)
After a study
Stratification analysis
Multivariate techniques
Control for Confounding
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Summary
以现在确诊的患有某特定疾病的病人作为病例,
以不患有该病但具有可比性的个体作为对照,通过
询问、实验室检查或复查病史,搜集各种可能的危
险因素的暴露史,测量并比较病例组与对照组中各
因素的暴露比例,经统计学检验,若两组差别有意
义,则可认为暴露因素与疾病之间存在着统计学上
的关联。在评估了各种偏倚对研究结果的影响后,
再借助病因推断技术,推断出某个或某些暴露因素
是疾病的危险因素,从而达到探索和检验病因假说
的目的。
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