TABLE E-6 Effect of measurement error in exposure on the excess relative risk estimate in a linear excess relative risk model,a based on computer simulation of case-control data with parameters ß = 1.00 and a = 0.00. Table adapted from Howe and Armstrong (1994)

WL measurement schemeb

Standard deviation of log(WL)

Median (ß)

Median (a)

1–1

0.5

0.90

-0.075

 

1.0

0.70

-0.41

 

2.0

0.26

-0.79

1–100

0.5

1.10

0.021

 

1.0

1.10

-0.07

 

2.0

0.54

-0.32

100–100

0.5

1.01

0.026

 

1.0

1.00

0.019

 

2.0

0.77

-0.22

a Data simulated under the model: RR = 1+ß(WLM)(WL)a

b Measurement schemes for WL:

1–1: one measurement per year for all (25) exposure years;

1–100: one measurement per year increasing linearly to 100 measurements per year over exposure years;

100–100:100 measurements per year in exposure years.

Simulations also addressed the effect of measurement error on estimating the effects of time since exposure, age at risk, and exposure rate. With 100 measurements per year (scheme 3), there was little effect on the patterns of risk with any of these factors, although as previously observed, there was some bias in the main risk effect of exposure. With scheme 3, there was some induced bias when the standard deviation of the error was large 2.0. With measurement scheme 2, some bias was induced, but only in the extreme category (=25 years since exposure, =65 years of age, or exposure rate =15 WL). With a single measurement per year (scheme 1), there was marked bias.

Howe and Armstrong identified two key elements for assessing the effects of measurement error: variation of the true exposure rate, that is, the degree that the true exposure rate for individuals differed from the true mean exposure rate; and the number of measurements used to estimate the true mean exposure rate.

The authors concluded that ''measurement error leads to (a) reduction in the main effects coefficient, that is, that for cumulative exposure; (b) increasing downward bias in risk estimates with increasing time since exposure; (c) increasing downward bias in risk estimates with increasing age at risk and (d) increasing downward bias with increasing exposure rate." They further conclude that "biases are likely to be negligible if estimates are based on 100 or more samples per year and if the standard deviation of log(exposure rate) has a value of 1.0 or less." And "these conditions are met for the majority of the miners' cohort studies, and



The National Academies | 500 Fifth St. N.W. | Washington, D.C. 20001
Copyright © National Academy of Sciences. All rights reserved.
Terms of Use and Privacy Statement