Ratio estimators of intervention effects on event rates in cluster randomized trials

Xiangmei Ma, Paul Milligan, Kwok Fai Lam, Yin Bun Cheung

Research output: Contribution to journalArticleScientificpeer-review


We consider five asymptotically unbiased estimators of intervention effects on event rates in non-matched and matched-pair cluster randomized trials, including ratio of mean counts (Formula presented.), ratio of mean cluster-level event rates (Formula presented.), ratio of event rates (Formula presented.), double ratio of counts (Formula presented.), and double ratio of event rates (Formula presented.). In the absence of an indirect effect, they all estimate the direct effect of the intervention. Otherwise, (Formula presented.), (Formula presented.) and (Formula presented.) estimate the total effect, which comprises the direct and indirect effects, whereas (Formula presented.) and (Formula presented.) estimate the direct effect only. We derive the conditions under which each estimator is more precise or powerful than its alternatives. To control bias in studies with a small number of clusters, we propose a set of approximately unbiased estimators. We evaluate their properties by simulation and apply the methods to a trial of seasonal malaria chemoprevention. The approximately unbiased estimators are practically unbiased and their confidence intervals usually have coverage probability close to the nominal level; the asymptotically unbiased estimators perform well when the number of clusters is approximately 32 or more per trial arm. Despite its simplicity, (Formula presented.) performs comparably with (Formula presented.) and (Formula presented.) in trials with a large but realistic number of clusters. When the variability of baseline event rate is large and there is no indirect effect, (Formula presented.) and (Formula presented.) tend to offer higher power than (Formula presented.), (Formula presented.) and (Formula presented.). We discuss the implications of these findings to the planning and analysis of cluster randomized trials.

Original languageEnglish
Pages (from-to)128-145
Number of pages18
JournalStatistics in Medicine
Issue number1
Early online date15 Oct 2021
Publication statusPublished - Jan 2022
Publication typeA1 Journal article-refereed


  • cluster randomized trial
  • event rate
  • incidence rate ratio
  • ratio estimator
  • relative incidence

Publication forum classification

  • Publication forum level 2

ASJC Scopus subject areas

  • Epidemiology
  • Statistics and Probability


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