09/15/05William Wu / MS meeting1 Measurement error and measurement model with an example in dietary data

09/15/05 William Wu / MS meeting 1

Measurement error and measurement model

with an example in dietary data


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


Possible answers to the question

• Sample size and the power not enough,

• Measurement error,

• others


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.


Two distinguished variation

• Biological or natural variation (not measurement error),

• Variation in measurement process (systematic error and random error)


Potential causes of measurement error

• Misuse of tools,• Poor choice of measurement tool• Lack of training• Carelessness• Not possible to measure exactly


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.


Two other often seen terms

• Selection biassubjects recruited not representative of the target population

e.g.

• Information biasArising from errors in measuring exposure or disease

e.g. exaggerate risk estimate for case subjects.


Consequences of measurement error

• Effect size attenuatedmeasurement error dilutes the effects

(referred to as ‘regression dilution bias’)

• Significance biasedmeasurement error favors the null

hypothesis


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


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.


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


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*.


• 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.

Parallel of two indicators


Measurement model incorporated with structural model

• The general question thus can be depicted with path diagram as follows:

e1 e2

X1 X2 d

1.0 1.0

X* Y


Packages for the implementation of the equation

• SAS

proc calis

• AMOS

structural equation model


Study Setting

• Project: The Los Angeles Atherosclerosis Study

• Study design:Cohort study

• Study question:Association between dietary fiber intake and atherosclerosis progression.

• Study population:700 middle-aged man and women in a company.

• 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.


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.


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.


Building Measurement model

long-term fiber

fiber1

0

e1

fiber2

0

e211

1 1


Structural model

long-term fiber

fiber1

0

e1

fiber2

0

e211

1 1

IMT prgression

aIMT

0

e3

cIMT

0

e4

eIMT

0

e5

31

e5

1.5

v_e4v_e3

0

d1

1


Model of the example

AN057_d

CN057_d

0,

e41

0,

e51

0,

Pectin_F3

0

IMTg_F2aimta_1000

cimta_1000

eimta_1000

0, v_e1

e1

1

0, v_e2

e2

0, v_e3

e3

0,

d1

0

Initial_F1

0,

d2

1

1

1

1

1

3

1

1.5

age sex aC_SMOKE

01

1

1


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

Viscous fiber

Baseline -1.330.60 0.03

follow-up -0.900.62 0.15

Average of baseline and follow-up -1.570.62 0.03

Measurement error corrected -2.521.11 0.02

Pectin

Baseline -2.731.26 0.03

follow-up -1.951.31 0.12

Average of baseline and follow-up -2.221.05 0.04

Measurement error corrected -5.872.34 0.01

* Regression slope is the regression coefficient in the structural model.


Questions and Discussion

Documents

09/15/05William Wu / MS meeting1 Measurement error and measurement model with an example in dietary data