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

09/15/05William Wu / MS meeting2 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

09/15/05William Wu / MS meeting3 Possible answers to the question Sample size and the power not enough, Measurement error, others

09/15/05William Wu / MS meeting4 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.

09/15/05William Wu / MS meeting5 Two distinguished variation Biological or natural variation (not measurement error), Variation in measurement process (systematic error and random error)

09/15/05William Wu / MS meeting6 Potential causes of measurement error Misuse of tools, Poor choice of measurement tool Lack of training Carelessness Not possible to measure exactly

09/15/05William Wu / MS meeting7 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.

09/15/05William Wu / MS meeting8 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.

09/15/05William Wu / MS meeting9 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

09/15/05William Wu / MS meeting10 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

09/15/05William Wu / MS meeting11 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.

09/15/05William Wu / MS meeting12 Solutions to the regression T here 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

09/15/05William Wu / MS meeting13 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*.

09/15/05William Wu / MS meeting14 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

09/15/05William Wu / MS meeting15 Measurement model incorporated with structural model The general question thus can be depicted with path diagram as follows: e1e2 X1X2d X* Y

09/15/05William Wu / MS meeting16 Packages for the implementation of the equation SAS proc calis AMOS structural equation model

09/15/05William Wu / MS meeting17 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.

09/15/05William Wu / MS meeting18 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.

09/15/05William Wu / MS meeting19 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.

09/15/05William Wu / MS meeting20 Building Measurement model

09/15/05William Wu / MS meeting21 Structural model

09/15/05William Wu / MS meeting22 Model of the example

09/15/05William Wu / MS meeting23 RESULT: Influence of measurement error on the estimates of regression slope relating IMT progression to dietary fiber. The LAAS ( ) ModelRegression slope*P value Viscous fiber Baseline  follow-up  Average of baseline and follow-up  Measurement error corrected  Pectin Baseline  follow-up  Average of baseline and follow-up  Measurement error corrected  * Regression slope is the regression coefficient in the structural model.

09/15/05William Wu / MS meeting24 Questions and Discussion