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Sample size estimation for modified Poisson analysis of cluster randomized trials with a binary outcome.

Fan Li1,2,3, Guangyu Tong1,3

  • 1Department of Biostatistics, Yale School of Public Health, New Haven, CT, USA.

Statistical Methods in Medical Research
|April 7, 2021
PubMed
Summary

Sample size formulas for modified Poisson regression in cluster randomized trials are now available. These formulas, adapted from log-binomial regression, are validated and account for variable cluster sizes, offering robust estimates.

Keywords:
Intraclass correlation coefficientslog-binomial regressionmodified Poisson regressionpragmatic clinical trialsrelative riskvariable cluster sizes

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Area of Science:

  • Biostatistics
  • Clinical Trials Methodology
  • Epidemiology

Background:

  • Modified Poisson regression is a robust alternative to log-binomial regression for estimating relative risk in cluster randomized trials.
  • Existing sample size formulas are not available for modified Poisson regression in this context.

Purpose of the Study:

  • To derive and validate sample size formulas for modified Poisson regression in cluster randomized trials.
  • To extend these formulas to accommodate variable cluster sizes.

Main Methods:

  • Analytical derivations comparing modified Poisson and log-binomial regression efficiency.
  • Development of sample size formulas for modified Poisson regression.
  • Monte Carlo simulations to validate the proposed formulas.
  • Extension of formulas for variable cluster sizes.

Main Results:

  • Modified Poisson regression shows no loss of asymptotic efficiency compared to log-binomial regression for marginal relative risk estimation.
  • Existing sample size formulas for log-binomial regression are applicable to modified Poisson regression.
  • Proposed formulas demonstrate satisfactory performance with variable cluster sizes when finite-sample corrections are applied and cluster count is sufficient.
  • Exchangeable working correlation is more robust to cluster size variability than independence working correlation.

Conclusions:

  • Sample size formulas for modified Poisson regression in cluster randomized trials are now available and validated.
  • The use of exchangeable working correlation is recommended for both design and analysis due to its robustness.
  • The findings are illustrated using the Stop Colorectal Cancer (STOP CRC) trial data.