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Modeling variability in treatment effects for cluster randomized controlled trials using by-variable smooth functions

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  • 1Vanderbilt University, Nashville, TN, USA. sj.cho@vanderbilt.edu.

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Summary

Generalized additive mixed models (GAMM) offer a flexible alternative to multilevel modeling (MLM) for analyzing treatment-covariate interactions in cluster randomized controlled trials (C-RCTs). GAMM accurately captures non-linear relationships, improving statistical inference for treatment effects.

Keywords:
By-variable smooth functionCluster randomized controlled trialFunctional covariate effectsGeneralized additive mixed modelNonlinear effectsVariability in treatment effects

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Area of Science:

  • Statistics
  • Biostatistics
  • Epidemiology

Background:

  • Cluster randomized controlled trials (C-RCTs) are susceptible to variability in treatment effects.
  • Multilevel modeling (MLM) is commonly used to analyze treatment-covariate interactions (TRT COV) in C-RCTs.
  • MLM assumes linear relationships between covariates and outcomes, which may lead to biased inference if violated.

Purpose of the Study:

  • To introduce generalized additive mixed models (GAMM) for modeling non-linear cluster-specific covariate-outcome relationships in C-RCTs.
  • To demonstrate GAMM implementation using the mgcv R package.
  • To evaluate GAMM as an alternative to MLM for analyzing treatment-covariate interactions.

Main Methods:

  • Developed GAMM specifications with by-variable smooth functions for cluster-specific relationships.
  • Utilized the mgcv R package in R for GAMM implementation.
  • Conducted simulation studies and applied the models to C-RCT intervention data.

Main Results:

  • GAMM successfully recovered parameters and by-variable smooth functions in multilevel designs.
  • Misspecification of linear relationships in MLM led to biased estimates of TRT COV effects.
  • GAMM demonstrated potential as an alternative to MLM, even with linear relationships.

Conclusions:

  • GAMM provides a robust approach for analyzing treatment-covariate interactions in C-RCTs by accommodating non-linear relationships.
  • This method enhances the accuracy of statistical inference compared to traditional MLM when linearity assumptions are not met.
  • GAMM offers a valuable tool for researchers investigating complex treatment effect variations in clustered data.