Bayesian measurement error modeling with application to the area under the curve summary measure

Abstract

Measurement errors arise in a variety of circumstances and occur when a variable cannot be observed exactly, but instead is observed with error. For example, summary measures contain measurement error, as the true value of the variable is estimated from observed data that contain sampling variability. Measurement errors should be accounted for when they are present, as the impacts of ignoring measurement errors include bias in parameter estimates and a loss of power to detect effects. Measurement error models are used to account for measurement errors and correct parameter estimates for the bias induced from variables measured with error. To account for measurement errors when present, most correction methods require that the measurement error variance be known (or estimated). Common correction methods include the method of moments correction, the SIMEX correction, and Bayesian correction methods. The area under the curve (AUC) summary measure is commonly used in pharmaceutical studies to estimate the total concentration of a substance present in the blood over a given time interval. Other areas, such as Ecology, use the AUC to estimate the total count of a species present over a specified time interval. In situations where the AUC is estimated, a measure of the uncertainty associated with it is often desired. Due to the longitudinal nature of AUC data, the estimation of its variance is often not straightforward. In this research we develop a Bayesian method to estimate the variance of the AUC, where our focus is on accounting for the possible correlation structure between repeated observations on the same subject. This estimate can then be used in measurement error models to account for the measurement error induced from estimating the AUC. We study the performance of three measurement error correction methods in the simple linear regression setting, where measurement errors are present in the explanatory variable, the response variable, or both. We extend the Bayesian correction methods to account for uncorrelated and correlated measurement errors between variables. The methods were validated using both simulated and real data collected from an equine study of blood glucose measurements.