Transcript Measurement error, and measurement model

Measurement error and measurement model
with an example in dietary data
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Why the established association was not found in my study,
or
why the findings on the association from similar studies
were inconsistent?
When we say established association, it means it was well studied,
generally acknowledged, and widely cited.
Examples:
Physical activity and the occurrence of CVDs.
NSAID intake and colon cancer
Dietary fiber
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Possible answers to the question
• Sample size and the power not enough,
• Measurement error,
• others
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Measurement Error
• The error that arises when a recorded
value is not exactly the same as the true
value due to a flaw in the measurement
process.
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Two distinguished variation
• Biological or natural variation (not measurement
error),
• Variation in measurement process (systematic
error and random error)
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Potential causes of measurement error
•
•
•
•
•
Misuse of tools,
Poor choice of measurement tool
Lack of training
Carelessness
Not possible to measure exactly
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Causes of measurement error in dietary record
• Underreporting
Subjects generally report eating less than they actually do eat.
• Differential recall
Subjects are more likely to recall eating foods that they perceive as
healthy than those considered unhealthy.
• Regression dilution
When the object of interest is long-term diet, a measurement on a
short-term record of diet measures this with error.
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Two other often seen terms
• Selection bias
subjects recruited not representative of the target
population
e.g.
• Information bias
Arising from errors in measuring exposure or disease
e.g. exaggerate risk estimate for case subjects.
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Consequences of measurement error
•
Effect size attenuated
measurement error dilutes the effects
(referred to as ‘regression dilution bias’)
•
Significance biased
measurement error favors the null
hypothesis
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Approaches to reducing measurement error
•
Study design stage
Conduct pilot study
improve Instrument
re-design the questionnaire
validate the equipment
standardize measurement protocols
reproducibility
reliability
train study personnel,
Analytical stage
statistical approaches
average the repeated measurements
measurement model
others
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Measurement model
with two indicators
Our general question:
Y= a + bX* + e
where X* is the true score.
In reality the X* is not available, instead, we have two
rough measurements of X*, say, X1 and X2.
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Solutions to the regression
There are three ways to address this question:
Y = a + bX1 + e
Y = a + bX2 + e
Y = a + b[(X1+X2)/2] + e
Y = a + b1X1 + b2X2 + e
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Measurement model
• The question can also be addressed with a better way by
building a measurement model which is specified as
follows:
X1 = X* + e1
X2 = X* + e2
Where X1 and X2 are the two indictors of X* which is unobserved
and thus called latent variable.
Two assumptions:
e1 and e2 are symmetrically distributed about the true scores, and
are uncorrelated with each other and X*.
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Parallel of two indicators
• Parallelism of the two indicators is specified
when repeated measurements with the same
method is involved. It is the most restrictive
constrain to a measurement model.
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Measurement model
incorporated with structural model
• The general question thus can be depicted with path
diagram as follows:
e1
e2
X1
1.0
X2
1.0
X*
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Packages for the implementation of the equation
• SAS
proc calis
• AMOS
structural equation model
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Study Setting
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Project:
The Los Angeles Atherosclerosis Study
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Study design:
Cohort study
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Study question:
Association between dietary fiber intake and atherosclerosis progression.
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Study population:
700 middle-aged man and women in a company.
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Outcome:
Atherosclerosis progression =
yearly enlargement rate of common carotid intima-media thickness (IMT), which was derived from
a baseline measurement, and two follow-up measurements with 1.5 years apart.
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Measurement of dietary intake
• Dietary data interested:
Daily intake of viscous dietary fiber (also classified as water-soluble
fiber) and its major component, pectin.
• Data collection instrument:
three days 24-hours recall
• Measurements:
Two measurements, one in baseline and one in 1.5 years follow-up.
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In this study, we try to
• estimates the slope of the dependent variable (IMT progression)
regressed on the long-term average intake of viscous dietary fiber or
pectin which was unobserved,
• assume that the errors of measurement at each examination were
random.
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Building Measurement model
0
0
e1
e2
1
1
fiber1
1
fiber2
1
long-term fiber
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Structural model
0
0
e1
e2
1
1
0
fiber1
1
fiber2
d1
1
1
long-term fiber
IMT prgression
1
aIMT
1.5
cIMT
v_e4
v_e3
0
e3
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e4
3
eIMT
e5
0
e5
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Model of the example
0,
e4
0,
e5
1
AN057_d
1
0,
1
CN057_d
1
Pectin_F3
sex
age
0
1
Initial_F1
1
aC_SMOKE
aimta_1000
1
0
0, v_e1
1.5
e1
0,
d2
cimta_1000
1
0, v_e2
IMTg_F2
1
1
1
0
3
0,
d1
e2
eimta_1000
1
0, v_e3
e3
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RESULT: Influence of measurement error on the estimates of regression slope relating
IMT progression to dietary fiber. The LAAS (1995-1999)
Model
Regression slope*
P value
Baseline
-1.330.60
0.03
follow-up
-0.900.62
0.15
Average of baseline and follow-up
-1.570.62
0.03
Measurement error corrected
-2.521.11
0.02
Baseline
-2.731.26
0.03
follow-up
-1.951.31
0.12
Average of baseline and follow-up
-2.221.05
0.04
Measurement error corrected
-5.872.34
0.01
Viscous fiber
Pectin
* Regression slope is the regression coefficient in the structural model.
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Questions and Discussion
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