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Transcript of Please take an i>clicker from the box in front of the room.
Please take an i>clicker from the box in front of the room
Classification Schemes for Error
• Szklo and Nieto– Bias (Systematic error)
• Selection Bias• Information/Measurement Bias
– Confounding– Chance (Random error)
• Other Common Approach– Bias (Systematic error)
• Selection Bias• Information/Measurement Bias• Confounding Bias
– Chance (Random error)
Think of the “BIG 4” in all of your work
• Descriptive studies– Objective: Estimate measures of disease occurrence
(e.g., prevalence or incidence)
• Analytic studies– Objective: Estimate measures of association between
exposure (predictors) and outcome (e.g., disease)
Bias in Clinical Research: Measurement Bias
• In descriptive studies
• In analytic studies
– Misclassification of dichotomous exposure & outcome variables
• non-differential misclassification
• differential misclassification
• magnitude and direction of bias
– Mis-measurement of interval scale variables
– Advanced topics (mention only)
• misclassification of multi-level categorical variables
• misclassification of confounding variables
• back-calculating to the truth
Measurement Bias
• Definition– bias that is caused when any measurement collected about or
from subjects is not completely reproducible or valid (accurate)• any type of variable: exposure, outcome, or confounder
– aka: misclassification bias; information bias (S&N text); identification bias
• misclassification is what happens when there is error in measurement of a categorical variable, for which everyone is “classified”
Misclassification of Dichotomous Variables
What does d/(b+d) refer to?
Sensit
ivity
- A
Positiv
e pr
edict
ive va
lue -
C
Specif
icity
- B
Negat
ive p
redic
tive
value
- D
Characterizing the Measurement of a Dichotomous Variable (e.g., present vs absent)
What does d/(b+d) refer to?
Sensit
ivity
- A
Positiv
e pr
edict
ive va
lue -
C
Specif
icity
- B
Negat
ive p
redic
tive
value
- D
Characterizing the Measurement of a Dichotomous Variable (Present vs Absent)
Terms Used to Characterize Measurement/Classification of Dichotomous Variables (Terms for Validity)
• Sensitivity
– the ability of a measurement to identify correctly those who
HAVE the characteristic (disease or exposure) of interest.
• Specificity
– the ability of a measurement to identify correctly those who
do NOT have the characteristic of interest
• Applies to any dichotomous variable, not just diagnoses
Gold Standard Present Absent
Your Present a b Measurement Absent c d
Sensitivity = a/(a+c) Specificity = d/(b+d)
Positive predictive value = a/(a+b)
Negative predictive value = d/(c+d)
Causes for Misclassification• Questionnaire problems
– inaccurate recall– socially desirable responses– ambiguous questions– under or overzealous interviewers
• Biological specimen collection– problems in specimen collection or processing or storage
• Biological specimen testing– inherent limits of detection– faulty instruments
• Data management problems in coding• Study design or analytic problems (See Problem Set)
– incorrect time period assessed, particularly for exposure– lumping of outcome variables (composite variables)
SOURCE POPULATION = CALIFORNIA
STUDY SAMPLE = PRE-ELECTION POLL(Field Poll)
Descriptive Study: Measurement Bias
Deukmejian
Bradley +7%
1982 California Governor Election
SOURCE POPULATION = CALIFORNIA
STUDY SAMPLE = PRE-ELECTION POLL(Field Poll, one of the largest pre-election surveys)
Descriptive Study: Measurement Bias
“Bradley Effect” = Respondents who favored Deukmejian sought to avoid
appearing racist and hence did not state true choice in pre-election survey
Deukmejian
Deukmejian 49% Bradley +7%
Bradley 48%
1982 California Governor Election
SOURCE POPULATION
STUDY SAMPLE
Contrast with Selection Bias
Uneven dispersion of arrows
e.g., Dewey backers were
over-represented
Descriptive Biomedical Studies: Measurement Bias
• e.g., Prevalence of:– Flossing– Condom use– Exercise– Etc.
• “Social desirability bias”– Humans tend to give socially desirable responses
Bias in Clinical Research: Measurement Bias
• Measurement bias in descriptive studies
• Measurement bias in analytic studies
– Misclassification of dichotomous exposure & outcome variables
• non-differential misclassification
• differential misclassification
• magnitude and direction of bias
– Mismeasurement of interval scale variables
– Advanced topics (mention only)
• misclassification of multi-level categorical variables
• misclassification of confounding variables
• back-calculating to the truth
Diseased
Exposed
+ -
+
-
SOURCE POPULATION
STUDY SAMPLE
Non-Differential Misclassification of Exposure: Imperfect Sensitivity
Problems with sensitivity in measurement of exposure - independent of disease status
e.g., case-control study
exposure = alcohol abuse
Evenly weighted arrows =
non-differential
Non-differential Misclassification of Exposure
Truth: No misclassification (100% sensitivity/specificity)
Exposure Cases ControlsYes 50 20No 50 80
OR= (50/50)/(20/80) = 4.0
Presence of 70% sensitivity in exposure classification
Exposure Cases ControlsYes 50-15=35 20-6=14No 50+15=65 80+6=86
OR= (35/65)/(14/86) = 3.3
Effect of non-differential misclassification of dichotomous exposures: Bias “toward the null” value of 1.0
Diseased
Exposed
+ -
+
-
SOURCE POPULATION
STUDY SAMPLE
Non-Differential Misclassification of Exposure: Imperfect Specificity
Problems with specificity of exposure measurement - independent of disease status
e.g., exposure = self-reported second-hand smoke exposure
Non-differential Misclassification of Exposure
Truth: No misclassification (100% sensitivity/specificity)
Exposure Cases ControlsYes 50 20No 50 80
OR= (50/50)/(20/80) = 4.0
Presence of 70% specificity in exposure classification
Exposure Cases ControlsYes 50+15=65 20+24=44No 50-15=35 80-24=56
OR= (65/35)/(44/56) = 2.4
Effect of non-differential misclassification of dichotomous exposures: Bias toward the null value of 1.0
Diseased
Exposed
+ -
+
-
SOURCE POPULATION
STUDY SAMPLE
No misclassification
e.g., exposure = self-reported second-hand smoke exposure
50
50
20
80 OR = 4.0
Diseased
Exposed
+ -
+
-
SOURCE POPULATION
STUDY SAMPLE
Non-Differential Misclassification of Exposure: Imperfect Specificity
e.g., exposure = self-reported second-hand smoke exposure
OR = 2.4
65
50 35
44
80 56
differences become blurred
Diseased
Exposed
+ -
+
-
SOURCE POPULATION
STUDY SAMPLE
Non-Differential Misclassification of Exposure: Imperfect Specificity and Sensitivity
Problems with sensitivity - independent of disease status
Problems with specificity - independent of disease status
Assuming no sampling error, what will the observed OR be?
OR = 3
.1 -
A
OR = 2
.4
- C
OR = 2
.8
- B
OR = 1
.6
- D
Exposure Cases ControlsYes 50 20No 50 80
True OR = (50/50) / (20/80) = 4.0
But, now assume non-differential exposure misclassification problemswith both sensitivity and specificity
Sensitivity = 70%Specificity = 70%
OR = 1
.2
- E
Assuming no sampling error, what will the observed OR be?
OR = 3
.1 -
A
OR = 2
.4
- C
OR = 2
.8
- B
OR = 1
.6
- D
Exposure Cases ControlsYes 50 20No 50 80
True OR = (50/50) / (20/80) = 4.0
But, now assume non-differential exposure misclassification problemswith both sensitivity and specificity
Sensitivity = 70%Specificity = 70%
OR = 1
.2
- E
Exposure Cases ControlsYes 50 20No 50 80 True OR = (50/50) / (20/80) = 4.0
True Cases Controls Distribution exp unexp exp unexp (gold standard) 50 50 20 80
Study distribution: Cases ControlsExposed 35 15 50 14 24 38Unexposed 15 35 50 6 56 62
sensitivity 0.70 0.70 0.70 0.70 or specificity
Exposure Cases ControlsYes 50 38No 50 62 Observed OR = (50/50) / (38/62) = 1.6
Non-Differential Misclassification of Exposure: Imperfect Sensitivity and Specificity
SOURCE POPULATION
STUDYSAMPLE
Sensitivity = 0.7
Specificity = 0.7
Assuming no sampling error, what will the observed OR be?
OR = 3
.5 -
A
OR = 3
.0
- C
OR = 3
.2
- B
OR = 2
.8
- D
Exposure Cases ControlsYes 50 20No 50 80
True OR = (50/50) / (20/80) = 4.0
But, now assume non-differential exposure misclassification problemswith both sensitivity and specificity
Sensitivity = 90%Specificity = 80%
OR = 2
.4
- E
Assuming no sampling error, what will the observed OR be?
OR = 3
.5 -
A
OR = 3
.0
- C
OR = 3
.2
- B
OR = 2
.8
- D
Exposure Cases ControlsYes 50 20No 50 80
True OR = (50/50) / (20/80) = 4.0
But, now assume exposure misclassification problemswith both sensitivity and specificity
Sensitivity = 90%Specificity = 80%
OR = 2
.4
- E
Non-Differential Misclassification of Exposure: Imperfect Sensitivity and Specificity
Exposure Cases ControlsYes 50 20No 50 80 True OR = (50/50) / (20/80) = 4.0
True Cases Controls Distribution exp unexp exp unexp (gold standard) 50 50 20 80
Study distribution: Cases ControlsExposed 45 10 55 18 16 34Unexposed 5 40 45 2 64 66
sensitivity 0.90 0.80 0.90 0.80 or specificity
Exposure Cases ControlsYes 55 34No 45 66 Observed OR = (55/45) / (34/66) = 2.4
SOURCE POPULATION
STUDYSAMPLE
Sensitivity = 0.9
Specificity = 0.8
Seemingly respectable Sn and Sp result in
substantial bias
Non-Differential Misclassification of Exposure: Imperfect Sensitivity & Specificity and Uncommon Exposure
Exposure Cases ControlsYes 50 20No 500 800 True OR = (50/500) / (20/800) = 4.0
True Cases Controls Distribution exp unexp exp unexp (gold standard) 50 500 20 800
Study distribution: Cases ControlsExposed 45 100 145 18 160 178Unexposed 5 400 405 2 640 642
sensitivity 0.90 0.80 0.90 0.80 or specificity
Exposure Cases ControlsYes 145 178No 405 642 Observed OR = (145/405) / (178/642) = 1.3
SOURCE POPULATION
STUDYSAMPLE
e.g., radon exposure
Sensitivity = 0.9
Specificity = 0.8
Higher exposure prevalence is more balanced and more resilient to misclassification
Non-differential Misclassification of Exposure: Magnitude of Bias on the Odds Ratio
True OR=4.0
2.20.080.900.90
2.80.200.900.90
3.00.370.900.90
1.90.200.600.90
3.20.200.950.90
1.90.200.850.60
2.60.200.850.90
Observed ORPrev of Exp in controls
SpecificitySensitivity
Bias as a function of non-differential imperfect sensitivity and specificity of exposure measurement
0.9
0.7
0.5
Sensitivity of exposure measurement
Specificity of exposure measurement
Copeland et al. AJE 1977
True OR = 2.67
Case-control study
Prevalence of exposure in controls = 0.2
Ap
par
ent
Od
ds
Rat
io
2.8
2.5
2.2
1.9
1.6
1.3
1.0
.50 .55 .60 .65 .70 .75 .80 .85 .90 .95 1.00
Bias as a function of non-differential imperfect sensitivity and specificity of exposure measurement
0.9
0.7
0.5
Sensitivity of exposure measurement
Specificity of exposure measurement
Copeland et al. AJE 1977
True OR = 2.67
Prevalence of exposure in controls = 0.2
Ap
par
ent
Od
ds
Rat
io
2.8
2.5
2.2
1.9
1.6
1.3
1.0
.50 .55 .60 .65 .70 .75 .80 .85 .90 .95 1.00
When does OR fall
below 2?
Non-Differential Misclassification of Exposure in a Cohort Study: Effect of Sensitivity, Specificity and Prevalence of Exposure
Flegal et al. AJE 1986
True Risk Ratio = 10
App
aren
t Ris
k R
atio
U = sensitivity; V = specificity
All RR < 8
If Pe >.25, ↑ Sn. influ.
Dependence upon Prev.
Sn Sn Sn Sn Sn
Sp Sp Sp Sp Sp
Sn Sp
Sn and Sp
In the presence of non-differential misclassification of exposure (e.g., sensitivity and specificity of 80%), what can we say in our Discussion section about any measures of association derived from the exposure?
Are a
n un
dere
stim
ate
of tr
uth
- A
Tend
to u
nder
estim
ate
truth
- C
Will,
on
aver
age,
unde
resti
mat
e tru
th -
B
Are a
n ov
eres
timat
e of
trut
h -
D
Need
mor
e inf
orm
ation
- E
Are a
n un
dere
stim
ate
of tr
uth
- A
Tend
to u
nder
estim
ate
truth
- C
Will,
on
aver
age,
unde
resti
mat
e tru
th -
B
Are a
n ov
eres
timat
e of
trut
h -
D
Need
mor
e inf
orm
ation
- E
In the presence of non-differential misclassification of exposure (e.g., sensitivity and specificity of 80%), what can we say in our Discussion section about any measures of association derived from the exposure?
Non-differential misclassification of exposure and “Bias towards the null”
• In any single study, non-differentiality by itself does not guarantee that the observed measure of association is falsely low
• Reason: in any single study, the observed results are a function of bias plus CHANCE– Only if a study is repeated many times over and the findings averaged, can we
say that the observed measure of association is biased towards the null
• Don’t say: “Because we had non-differential misclassification of exposure, our findings are an underestimate of the true measure of association.” (i.e., do not be definitive)
• Instead, say: “Because imperfect sensitivity and specificity of <the exposure measurement> was generally the same irrespective of outcome, our findings tend to be (or, “on average are likely to be) an underestimate of the true association.”
Jurek et al. IJE 2005
Non-Differential Misclassification of Exposure: Rules of Thumb Regarding Sensitivity & Specificity
Exposure Cases ControlsYes 50 100No 50 300 True OR = (50/50) / (100/300) = 3.0
SOURCE POPULATION
Sens + Spec = 1 gives OR = 1 (no effect)
Sensitivity Specificity Observed OR
0.8 1.0 2.6
0.8 0.8 1.9
0.4 0.6 1.0
0.4 0.4 0.82
0 0 0.33
Sens + Spec >1 but <2 gives attenuated effect
Sens + Spec < 1 gives reversal of effect
Coding error
Diseased
Exposed
+ -
+
-
SOURCE POPULATION
STUDY SAMPLE
Non-Differential Misclassification of Outcome
Problems with outcome sensitivity -independent of exposure status
Problems with outcome specificity - independent of
exposure status
Evenly weighted arrows =
non-differential
Bias as a function of non-differential imperfect sensitivity and specificity of outcome measurement in a cohort study
Sensitivity of outcome measurement0.9
0.7
0.5
Specificity of outcome measurementCopeland et al. AJE 1977
True risk ratio = 2.0
Cumulative incidence in unexposed = 0.05
Steep bias with change in
specificity
Relatively less influence
from sensitivity
App
aren
t Ris
k R
atio
Non-Differential Misclassification of Outcome: Effect of Incidence of Outcome
Copeland et al. AJE 1977
Specificity of outcome measurement
0.2 0.1
0.1 0.05
0.05 0.025
Cumulative incidence of outcome
Exposed Unexposed
True risk ratio = 2.0
Sensitivity of outcome measurement held fixed = 0.9
App
aren
t Ris
k R
atio
Special Situation In a Cohort or Cross-sectional Study
Misclassification of outcome• If specificity of outcome measurement is 100%• Any degree of imperfect sensitivity, if non-differential, will not
bias the risk ratio or prevalence ratio• e.g.,
• Risk difference, however, is changed by a factor of (1 minus sensitivity), in this example, 30% (truth=0.1; biased = 0.07)
DiseaseNoDisease
Exposed 20 80 100Unexposed 10 90 100
2.0
1001010020
ratio )prevalence (or Risk
DiseaseNoDisease
Exposed 20-6=14 80+6=86100Unexposed 10-3=7 90+3=93100
2.0
1007
10014
ratio )prevalence (or Risk
Truth
70% sensitivity
When specificity of outcome is 100% in a cohort or cross-sectional study
Sensitivity of outcome measurement0.9
0.7
0.5
Specificity of outcome measurementCopeland et al. AJE 1977
True risk ratio = 2.0
Cumulative incidence in unexposed = 0.05
App
aren
t Ris
k R
atio
When specificity of outcome measurement is 100% in a cohort or cross sectional study
• Worth knowing about when defining outcomes, such as choosing cutoffs for continuous variables on ROC curves
• Choosing most specific cutoff (or 100% cutoff) will lead to least biased ratio measures of association
0.0 0.1 0.2 0.3 0.4 0.5
0.5
0.6
0.7
0.8
0.9
1.0
1.0 0.9 0.8 0.7 0.6 0.5
Sen
sit
ivit
y
1 - Specificity
00.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
OD: 0.06 Specificity: 84 % Sensitivity: 100 %
OD: 0.19 Specificity: 95 % Sensitivity: 94 %
OD: 0.49 Specificity: 100 % Sensitivity: 74 %
0.0 0.1 0.2 0.3 0.4 0.5
0.5
0.6
0.7
0.8
0.9
1.0
1.0 0.9 0.8 0.7 0.6 0.5
Sen
sit
ivit
y
1 - Specificity
00.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
OD: 0.06 Specificity: 84 % Sensitivity: 100 %
OD: 0.19 Specificity: 95 % Sensitivity: 94 %
OD: 0.49 Specificity: 100 % Sensitivity: 74 %
OD: 0.06 Sensitivity = 100%OD: 0.06 Specificity = 84%
OD: 0.19 Sensitivity = 94%OD: 0.19 Specificity = 95%
OD: 0.49 Sensitivity = 74%OD: 0.49 Specificity = 100%
1.0 0.9 0.8 0.7 0.6 0.5
Specificity
Example of ROC curve
What should you choose as your primary outcome variable?
>5 da
ys o
f cou
gh -
A
Abnor
mal
ches
t x-ra
y - C
Micr
obiol
ogic
diagn
osis
of
pertu
ssis
- B
>5 da
ys o
f cou
gh +
micr
obiol
ogic
diagn
osis
of p
ertu
ssis
- D
Efficacy of a pertussis (whooping cough) vaccine in adults
• RCT of: Approved (in kids) pertussis vaccine vs. control vaccine for the prevention of pertussis in adults
Group No. of subjects Person-years Pertussis vaccine 1391 2421 Control 1390 2444
Ward et al. NEJM 2005
What should you choose as your primary outcome variable?
>5 da
ys o
f cou
gh -
A
Abnor
mal
ches
t x-ra
y - C
Micr
obiol
ogic
diagn
osis
of
pertu
ssis
- B
>5 da
ys o
f cou
gh +
micr
obiol
ogic
diagn
osis
of p
ertu
ssis
- D
Efficacy of a pertussis (whooping cough) vaccine in adults
• RCT of: Approved (in kids) pertussis vaccine vs. control vaccine for the prevention of pertussis in adults
Group No. of subjects Person-years Pertussis vaccine 1391 2421 Control 1390 2444
Ward et al. NEJM 2005
Efficacy of a pertussis (whooping cough) vaccine in adults
• Outcome: Cough > 5 days– No. of events: 2672 (and lots of statistical power)– Result: No significant difference between groups
• Outcome: Cough + microbiologic pertussis confirmation– No. of events: 10– Result: rate ratio = 0.08 (92% vaccine efficacy) (95% CI = 0.01 to 0.68)
• Acellular vaccine vs. control vaccine for the prevention of pertussis in adults (Ward et al. NEJM 2005)
Group No. of subjects Person-years Pertussis vaccine 1391 2421 Control 1390 2444
Pervasiveness of Non-Differential Misclassification
• Direction of this bias is typically towards the null
• Therefore, called a “conservative” bias
• Goal, however, is to get the truth
• Consider how much underestimation of effects must be occurring in research
• How many “negative” studies are truly “positive”?
Differential Misclassification of ExposureWeinstock et al. AJE 1991• Nested case-control study in Nurses Health Study cohort
• Cases: women with new melanoma diagnoses
• Controls: women w/out melanoma - by incidence density sampling
• Measurement of exposure: questionnaire about self-reported
“tanning ability”; administered shortly after melanoma development
Melanoma
No Melanoma
No tan to light tan 15 77 Medium to dark tan 19 157
1.6
157771915
OR
• Question asked after diagnosis
• Question asked before diagnosis (NHS baseline)
MelanomaNoMelanoma
No tan to light tan 9 79Med to dark tan 25 155
0.7
15579259
OR
MelanomaNoMelanoma
No tan to light tan 15 77Med to dark tan 19 157
1.6
157771915
OR
Virtually unchanged
Substantially changed
Melanoma
Tanningability
+ -
No
Yes
SOURCE POPULATION
STUDY SAMPLE
“Tanning Ability” and Melanoma:
Differential Misclassification of Exposure
Imperfect specificity of exposure measurement - mostly in cases
Bias away from the null
leading to spurious
association
Congenital Malformation
Exposed
+ -
+
-
SOURCE POPULATION
STUDY SAMPLE
Differential Misclassification of Exposure:
Exposures During Pregnancy and Congenital Malformations
Cases more likely than controls to remember a variety of exposures
Cases might be more likely than controls to falsely state a
variety of exposures
Uneven weighting of
arrows = differential
Differential Misclassification of Exposure: Magnitude of Bias on the Odds Ratio
True OR=3.9
Exposure Classification
Sensitivity Specificity
Cases Controls Cases Controls OR
0.90 0.60 1.0 1.0 5.79
0.60 0.90 1.0 1.0 2.22
1.0 1.0 0.9 0.70 1.00
1.0 1.0 0.7 0.90 4.43
Prevalence of Exposure in Controls = 0.1
Misclassification of Dichotomous Exposure or Outcome: Summary of Bias
Misclassification Bias on Ratio Measure of Association
Non-differential Exposure Towards null Outcome Towards null*
Differential
Exposure Away or towards null Outcome Away or towards null
*Exception: When specificity is 100%, no effect on risk ratio or prevalence ratio regardless of sensitivity
Relating Last Week to This Week:Relating Validity / Reproducibility of Individual
Dichotomous Measurements to Measurement Bias in Inferences in Analytic Studies
• Validity– How sensitivity and specificity of a measurement results
in measurement bias covered in prior slides
• Reproducibility– Recall that a measurement with imperfect reproducibility
will typically lack perfect validity when used in practice -- (unless it is repeated many many times)
Reproducibility and Validity of a Measurement
With only one shot at the measurement, most of the time you
will be off the center of the target
GoodB-Ball
PoorB-Ball
>6 ft 10 30 40 +1 10 +3 30<6 ft 10 50 60 10 +1 50 +5
20 80 100 20 80
P
GoodB-Ball
PoorB-Ball
>6 ft 10 32 42<6 ft 10 48 58
20 80 100
Truth = Prevalence Ratio= (10/40) / (10/60) = 1.5
Observed = Prevalence Ratio = (10/42) / (10/58) = 1.38
10% Misclassification
Imperfect reproducibility leads
to 90% sensitivity and 90% specificity of
height measurement –non-differential with respect to outcome
Reproducibility
of Measurement
Validity of
Measurement in Practice
Validity of
Analytic Inferences
Derived from Measurement
“Measurement Bias”Systematic
Error of
Measurement
Bias in Clinical Research: Measurement Bias
• Measurement bias in descriptive studies
• Measurement bias in analytic studies
– Misclassification of dichotomous exposure & outcome variables
• non-differential misclassification
• differential misclassification
• magnitude and direction of bias
– Mismeasurement of interval scale variables
– Advanced topics (mention only)
• misclassification of multi-level categorical variables
• misclassification of confounding variables
• back-calculating to the truth
Effect of Lack of Validity and Reproducibility in Interval Scale Measurements
• Lack of Validity (Systematic Error)– Measurements systematically off truth by some multiplicative factor or absolute difference
x xtruth observed
xxx x x x xtruth observedobserved
• Lack of Reproducibility– Measurements off truth by some random factor or difference
Relating the Validity and Reproducibility of Measurements to Measurement Bias in Analytic Studies – Interval Scale Variables
Validity (Systematic error)• Result moves systematically up or down scale by given factor or absolute
difference• e.g., systematic error in an interval scale outcome variableMean Ratio of Means Difference in Means
Truth Exposed 100
Unexposed 50 2 50
Measurement off by factor of 10 Exposed 1000
Unexposed 500 2 500
Measurement off by difference of 10 Exposed 110
Unexposed 60 1.83 50
Bias depending
upon measure of association
Relating the Reproducibility and Validity of Measurements to Measurement Bias in Analytic Studies – Interval Scale Variables
Reproducibility (Random error)
e.g., random error in an exposure variableAssuming:
• Exposure is normally distributed with variance, 2True
• Random error is normally distributed with variance, 2E
• Then, the observed regression coefficient is equal to the true regression coefficient times:
• i.e., the greater the measurement error, the greater the attenuation (bias) towards the
null (e.g., if ICC is 0.5, the measure of association is halved)
22
2
ETrue
True
(i.e. reproducibility, the intraclass correlation coefficient)
Truth and Error
Truth
Regression Dilution Bias
Relating the Reproducibility and Validity of Measurements to Measurement Bias in Analytic Studies – Interval Scale Variables
• See Extra Slides for Additional Examples
Advanced Topics• Misclassification of multi-level categorical exposure variables
– some of the rules change regarding direction of bias– See Extra Slides for examples
• Mis-measurement of confounding variables– When confounding variables are mis-measured, the net result is failure
to fully control (adjust) for that variable• You are left with “residual confounding”• You have not fully adjusted for the variable• “Adjusted” measures of association may be over or under-estimated
– Very common problem• Researchers focus mainly on optimal measurement of exposure & outcome• By the time confounders surface, everyone is too exhausted
– e.g., when controlling for smoking, does classification of people into smokers and non-smokers based on current smoking capture the essence of the exposure?
Advanced Topics
• Back-calculating to unbiased results– thus far, truth about measurement quality and the relationships
between exposure/outcome variables have been assumed • We have then predicted what the bias will be in observed results
– In practice, we have observed results and sometimes a guess about the measurement quality
– when extent of classification errors (e.g., PPV, NPV, sensitivity & specificity, ICC) are known, it is possible to back-calculate to truth
– if exact classification errors are not known, it is possible to perform sensitivity analyses to estimate a range of study results given a range of possible classification errors
– “Quantitative bias analysis”
Poor Reproducibility
Poor Validity
Good Reproducibility
Good Validity
Managing Measurement Bias• Prevention and avoidance are critical
– study design phase is critical – use state-of-the-art techniques, blinding, SOPs, and replicates
• Little to be done after study (but back-correction may be possible)
• Become an expert in the measurement of your primary variables
• For the other variables, seek out the advice of experts (teams)
• Optimize the reproducibility/validity of your measurements!
Extra slides
Mismeasurement of Interval Scale Variables: Summary of Bias When Relating to Perfectly Measured Variables
Issue Bias on Measure of Association
Imperfect validity (systematic error)
Exposure Depends upon characterization of exposure (per unit or per factor change)
Outcome Depends upon measure (ratio or difference) Imperfect reproducibility (random error)
Exposure Towards null (“regression dilution”)* Outcome No effect*
*Also affects precision
• Correlating one interval scale measurement to another
– e.g., weight and cholesterol
• Correlation is attenuated directly proportional to ICC of measurements (r = correlation coefficient)
– e.g., If ICC of both weight and cholesterol is 0.80
– 20% attenuation
yxtrueyxobservedyx ICCICCrr ;, ;,
Relating the Reproducibility of Measurements to Measurement Bias in Analytic Studies – Interval Scale Variables
)8.0)(8.0( ; , ; , truelcholesteroweightobservedlcholesteroweight rr
)8.0( ; , ; , truelcholesteroweightobservedlcholesteroweight rr
Non-differential Misclassification of Multi-level Exposure
Cases ControlsOddsRatio
None 100 100 1.0
Low 200 100 2.0
High 600 100 6.0
Exposure
Cases ControlsOddsRatio
None 100 100 1.0
Low 440 140 3.1
High 360 60 6.0
Misclassification between adjacent exposure categoriesTruth
Bias away from the nullDosemeci et al. AJE 1990
Misclassification of Multi-level Exposure
Cases ControlsOddsRatio
None 100 100 1.0
Low 200 100 2.0
High 600 100 6.0
Exposure
Cases ControlsOddsRatio
None 420 180 1.0
Low 120 60 0.86
High 360 60 2.57
Misclassification between adjacent and non-adjacent exposure categories
Truth
Appearance of J-shaped relationshipDosemeci et al. AJE 1990