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

Sun-Joo Cho1, Kristopher J Preacher1

  • 1Vanderbilt University, Nashville, TN, USA.

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Multilevel modeling (MLM) can be improved by correcting for measurement error in total scores. This study provides a formula to enhance accuracy in detecting group differences in cluster randomized and observational studies.

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attenuation formulagroup differencemeasurement errormultilevel modeling

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Area of Science:

  • Statistics
  • Biostatistics
  • Psychometrics

Background:

  • Multilevel modeling (MLM) is widely used to analyze clustered data, such as in cluster randomized trials and observational studies.
  • MLM commonly utilizes pretest and posttest total scores to estimate group differences, controlling for baseline attributes.
  • Concerns exist regarding the impact of measurement error in total scores on the accuracy of MLM estimates.

Purpose of the Study:

  • To derive a measurement error correction formula for cluster-level group difference estimates obtained from MLM.
  • To address the issue of measurement error in both the outcome and covariate (pretest) scores within MLM analyses.
  • To provide practical examples of applying the correction formula in different study designs.

Main Methods:

  • Utilized ordinary least squares (OLS) regression and an attenuation formula to derive the measurement error correction.
  • Developed a formula applicable when measurement error is present in the outcome, covariate, or both.
  • Employed recently developed between-cluster reliability coefficients for illustration.

Main Results:

  • A novel measurement error correction formula for MLM estimates at the cluster level was derived.
  • The formula accounts for potential biases introduced by measurement error in pretest and posttest scores.
  • Demonstrated the application of the correction formula using examples from cluster randomized and observational studies.

Conclusions:

  • The derived formula offers a method to improve the accuracy of cluster-level group difference estimates in MLM.
  • Correcting for measurement error is crucial for reliable findings in studies employing MLM with total scores.
  • The approach is valuable for researchers conducting cluster randomized trials and observational studies.