Longitudinal MRI data analysis in presence of measurement error but absence of replicates

Abstract

ABSTRACTLongitudinal data analysis has found immense importance in biomedical fields to assess relationships between an outcome and its explanatory variables over time. However, this analysis is unreliable in presence of measurement errors in response data because the errors confound the effect of any signal caused by process changes. This confounding can be easily resolved by estimating and isolating the measurement errors using replicated measurements; i.e., multiple measurements in a small (stationary) time interval. However, in many medical applications, such as in magnetic resonance imaging (MRI), taking replicated measurements is not possible due to cost and/or risk considerations. This makes measurement error estimation and data analysis very challenging. In this article, we propose a novel method for the analysis of unreplicated longitudinal data under the presence of measurement errors. We formulate the problem using mixed-effect regression and develop a new EM-Variogram technique to estimate regression coefficients as well as variance components. The proposed approach decouples the confounded observed variance into the process and measurement system variances, and helps construct precise confidence intervals, leading to a more powerful statistical hypothesis test for the model parameters. We validate the proposed method using simulation and also apply it to a longitudinal MRI data for patients with neurodegenerative diseases. The results show improved statistical power in measuring their hippocampal volume loss, and a quicker degeneration detection. We also demonstrate the robustness of the proposed method with respect to missing values, a common issue in longitudinal data.