Berkson measurement error in designed repeated measures studies with random coefficients

Abstract

We consider repeated measures designs in which multiple subjects are exposed to different “doses” of a predictor variable and among subject variability is modeled through a random coefficients model. The true “dose” present differs from the target level by some random amount; what is known as the Berkson error model. We examine the consequences of such errors on naive analyses (which ignore measurement error) under commonly used linear and quadratic models, with a focus on both regression coefficients and variance parameters. Our investigation allows the measurement errors to have changing variances over the doses and also allows the errors to be correlated either within or among subjects. For linear regression the naive estimates of the coefficients are unbiased and inferences for the coefficients are at least approximately correct as long as there is no correlation in measurement errors among subjects. The presence of correlated measurement errors among subjects, however, results in naive tests and confidence intervals for the coefficients being incorrect. Biases in the naive estimates in the variance components are given, such biases occurring to some degree for all of the measurement error models. Similar results are given for quadratic regression, with the added complication that the naive estimate of some of the regression coefficients are biased, with the nature of the variance in measurement errors determining which coefficients are biased. Some preliminary discussion is presented concerning correcting for measurement error.