Effects of covariate measurement error in the initial level and rate of change of an exposure variable

When repeated measures of an exposure variable are obtained on individuals, it can be of epidemiologic interest to relate the slope of this variable over time to a subsequent response. Subject-specific estimates of this slope are measured with error, as are corresponding estimates of the level of exposure, i.e., the intercept of a linear regression over time. Because the intercept is often correlated with the slope and may also be associated with the outcome, each error-prone covariate (intercept and slope) is a potential confounder, thereby tending to accentuate potential biases due to measurement error. Under a familiar mixed linear model for the exposure measurements, we present closed-form estimators for the true parameters of interest in the case of a continuous outcome with complete and equally timed follow-up for all subjects. Generalizations to handle incomplete follow-up, other types of outcome variables, and additional fixed covariates are illustrated via maximum likelihood. We provide examples using data from the Multicenter AIDS Cohort Study. In these examples, substantial adjustments are made to uncorrected parameter estimates corresponding to the health-related effects of exposure variable slopes over time. We illustrate the potential impact of such adjustments on the interpretation of an epidemiologic analysis.