Symbolic two-step method compared with single-step methods to model the center-mean outcome in cluster randomized trials

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Background: A recently developed two-step method provides an alternative to single-step methods in the analysis of cluster randomized trials (CRTs). This method, called the symbolic two-step method because it was developed within the symbolic data analysis framework, adjusts for patient-level factors when estimating and testing effects of center-level factors on both the average center-level outcome and its variation. Estimation/testing of center-level effects on center-outcome variation is the innovation of the method; identifying such effects may lead to practice changes to reduce such variation. We evaluated the performance of our method in challenging settings and recommend when this method is preferred over single-step methods. Methods: The method was compared to single-step multilevel linear models – one that permitted heterogeneous within-center variances and one that did not – via simulation. We applied each method to a CRT. Results: After adjusting for patient-level factors in the setting of varying center sizes without any correlation between patient and center-level factors, the single-step models led to increased statistical power for center-level factors. In the presence of correlation, our method was more powerful. Applying these methods to model the center-mean outcome from the CRT led to similar conclusions; however, because the two-step method also models the within-center variability of that outcome we identified a factor predicting the within-center variance that was not possible with the single-step methods. Conclusions: We recommend single-step methods under the restrictive assumptions of no correlation between patient- and center-level factors and no center-level factor affecting center-outcome variation. Otherwise, we recommend the symbolic two-step method.

Original languageEnglish (US)
Article number106684
JournalContemporary Clinical Trials
StatePublished - Mar 2022


  • Care delivery research
  • Cluster randomized trials
  • Symbolic data analysis

ASJC Scopus subject areas

  • Pharmacology (medical)


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