Measurement Error Correction Formula for Cluster-Level Group Differences in Cluster Randomized and Observational Studies.

Multilevel modeling (MLM) is frequently used to detect cluster-level group differences in cluster randomized trial and observational studies. Group differences on the outcomes (posttest scores) are detected by controlling for the covariate (pretest scores) as a proxy variable for unobserved factors that predict future attributes. The pretest and posttest scores that are most often used in MLM are total scores. In prior research, there have been concerns regarding measurement error in the use of total scores in using MLM. In this article, using ordinary least squares and an attenuation formula, we derive the measurement error correction formula for cluster-level group difference estimates from MLM in the presence of measurement error in the outcome, the covariate, or both. Examples are provided to illustrate the correction formula in cluster randomized and observational studies using between-cluster reliability coefficients recently developed.