Regression Calibration in Studies with Correlated Variables Measured with Error

Regression calibration is a technique that corrects biases in regression results in situations where exposure variables are measured with error. The existence of a calibration substudy, where accurate and crude measurement methods are related by a second regression analysis, is assumed. The cost of measurement error in multivariate analyses is loss of statistical power. In this paper, calibration data from California Seventh-day Adventists are used to simulate study populations and new calibration studies. Applying regression calibration logistic analyses, the authors estimate power for pairs of nutritional variables. The results demonstrate substantial loss of power if variables measured with error are strongly correlated. Biases in estimated effects in cases where regression calibration is not performed can be large and are corrected by regression calibration. When the true coefficient has zero value, the corresponding coefficient in a crude analysis will usually have a nonzero expected value. Then type I error probabilities are not nominal, and the erroneous appearance of statistical significance can readily occur, particularly in large studies. Major determinants of power with use of regression calibration are collinearity between the variables measured with error and the size of correlations between crude and corresponding true variables. Where there is important collinearity, useful gains in power accrue with calibration study size up to 1,000 subjects.