Measurement error and measurement model with an example

Measurement error and measurement model with an example in dietary data 09/15/05 William Wu / MS meeting 1

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 09/15/05 William Wu / MS meeting 2

Possible answers to the question • Sample size and the power not enough, • Measurement error, • others 09/15/05 William Wu / MS meeting 3

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. 09/15/05 William Wu / MS meeting 4

Two distinguished variation • Biological or natural variation (not measurement error), • Variation in measurement process (systematic error and random error) 09/15/05 William Wu / MS meeting 5

Potential causes of measurement error • • • Misuse of tools, Poor choice of measurement tool Lack of training Carelessness Not possible to measure exactly 09/15/05 William Wu / MS meeting 6

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. 09/15/05 William Wu / MS meeting 7

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. 09/15/05 William Wu / MS meeting 8

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 09/15/05 William Wu / MS meeting 9

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 09/15/05 William Wu / MS meeting 10

Measurement model with two indicators Our general question: Y= a + b. X* + e where X* is the true score. In reality the X* is not available, instead, we have two rough measurements of X*, say, X 1 and X 2. 09/15/05 William Wu / MS meeting 11

Solutions to the regression There are three ways to address this question: Y = a + b. X 1 + e Y = a + b. X 2 + e Y = a + b[(X 1+X 2)/2] + e Y = a + b 1 X 1 + b 2 X 2 + e 09/15/05 William Wu / MS meeting 12

Measurement model • The question can also be addressed with a better way by building a measurement model which is specified as follows: X 1 = X* + e 1 X 2 = X* + e 2 Where X 1 and X 2 are the two indictors of X* which is unobserved and thus called latent variable. Two assumptions: e 1 and e 2 are symmetrically distributed about the true scores, and are uncorrelated with each other and X*. 09/15/05 William Wu / MS meeting 13

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. 09/15/05 William Wu / MS meeting 14

Measurement model incorporated with structural model • The general question thus can be depicted with path diagram as follows: e 1 e 2 X 1 1. 0 X 2 1. 0 X* 09/15/05 d Y William Wu / MS meeting 15

Packages for the implementation of the equation • SAS proc calis • AMOS structural equation model 09/15/05 William Wu / MS meeting 16

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. 09/15/05 William Wu / MS meeting 17

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. 09/15/05 William Wu / MS meeting 18

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. 09/15/05 William Wu / MS meeting 19

Building Measurement model 09/15/05 William Wu / MS meeting 20

Structural model 09/15/05 William Wu / MS meeting 21

Model of the example 09/15/05 William Wu / MS meeting 22

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. 09/15/05 William Wu / MS meeting 23

Questions and Discussion 09/15/05 William Wu / MS meeting 24