U.S. Environmental Protection Agency
Measurement error in predictor variables has the potential for distorting health effects estimates in daily time series epidemiology studies relating mortality or morbidity to air pollution and weather. When only a single predictor has substantial measurement error, regression coefficients are attenuated in size and statistical significance. When two or more correlated predictor variables have substantial measurement error, and the measurement errors may also be correlated among themselves, then estimates may be attenuated, inflated, or reversed in sign. We evaluated the bias in ordinary least squares regression coefficients with two correlated error-prone predictors. Null predictors or weak predictors are able to appear stronger than true positive predictors only under unusual circumstances. The conditions usually necessary to severely distort regression models are (1) true predictors must have correlation less than -0.9 or greater than 0.9, (2) measurement errors must be substantially larger than have the standard deviation of the true predictors, and (3) measurement errors must have a large negative correlation. It is unlikely that air pollution measurement errors have caused more than a modest attenuation of the estimated health effects of fine particulate matter and other air pollutants used as predictors in these models.