Correcting for the effect of measurement error on the association between environmental exposure and respiratory impairment

Abstract

Exposure to environmental agents may cause respiratory impairment. The tests for respiratory impairment are prone to measurement error. The objective of this thesis is to examine how random error of measurement affects the association found between environmental exposure and respiratory impairment and to explore methods of correcting for these effects. This is dene for two types of respiratory impairment, chronic airway obstruction as measured by the change in lung function test results over time, and pneumoconiosis detected on the chest radiograph. The issues of random error of measurement in longitudinal lung function data are explored with reference to spirometric and peak flow test results in 433 men aged between 18 and 22 years at entry into the mining industry. Lung function was measured initially and the change from initial measurement calculated over the subsequent 11 years. Analysis of the association between lung function change and environmental exposure should take into account the relationship between change in Jung function and the initial level. When lung function change is regressed on the initial measurement and environmental exposure, random error of measurement in the lung function test results has several consequences: 1) The regression of lung function change on the initial lung function measurement is biased because of random error in the initial measurement. 2) If initial lung function and environmental exposure are associated, random measurement error in the initial lung function (the confounder) results in a biased regression of lung function change on environmental exposure. 3) The variance of lung function change explained by environmental exposure is underestimated if lung function change is measured with random error. Consequently statistical power, i.e. the likelihood of detecting a true association between environmental exposure and lung function change, is reduced. 4) If lung function change is dichotomized to obtain exposure-response relationships, random measurement error causes an under¬ estimation of the slope of the exposure-response relationship. With the exception of the effect on statistical power, all of the consequences of random error of measurement can be corrected at analysis stage. Several correction methods are suggested in the literature. The most attractive of them on theoretical and practical grounds is that using the reliability coefficient, defined as the ratio of the true (error-free) variance to the variance of the measured variable. This is easily estimated as the correlation between repeat measurements of the underlying true level. Correction for the effect of random measurement error requires multiplying the variance of lung function test measurements by the reliability coefficient. The corrected variance is then used to calculate regression or correlation coefficients.

The consequences of measurement error in radioqraphically- detected pneumoconiosis is explored with reference to the assessment of asbestosis by 3 independent readers in 1 680 asbestos miners and millers. Radiographically-detected pneumoconiosis is an example of a dichotomized variable, i.e. one that is analysed as a binary variable to obtain an exposure-response relationships but in fact has an underlying continuum which, in this case, is not measurable. The prevalence of abnormality and the exposure-response relationship may vary between observers because of differing random error and differences in the threshold implicitly chosen for ategorizing radiographs, even in the presence of standardized criteria. The biserial correlation coefficient can be used to measure the correlation between environmental exposure and the continuum (including random error) underlying the dichotomized readings of an observer. Normal distribution theory can then be used to estimate exposure-response relationships at any required threshold for each reader. Biserlal correlation coefficients and exposure-response relationships can be corrected for random observational error using the reliability coefficient, calculated as the tetrachoric correlation between repeat observations by the same or different readers. The methods of correcting for error of measurement described in the thesis have wide applicability in the assessment of associations between environmental exposure and respiratory impairment. The concepts are easily transferable to other areas of epidemiological research.