The design and analysis of randomized trials with recurrent events

Stat Med. 1995 Oct 15;14(19):2081-98. doi: 10.1002/sim.4780141903.


This paper describes a method for planning the duration of a randomized parallel group study in which the response of interest is a potentially recurrent event. At the design stage we assume patients accrue at a constant rate, we model events via a homogeneous Poisson process, and we utilize an independent exponential censoring mechanism to reflect loss to follow-up. We derive the appropriate study duration to ensure satisfaction of power requirements for the effect size of interest under a Poisson regression model. An application to a kidney transplant study illustrates the potential savings of the Poisson-based design relative to a design based on the time to the first event. Revised design criteria are also derived to accommodate overdispersed Poisson count data. We examine the frequency properties of two non-parametric tests recently proposed by Lawless and Nadeau for trials based on the above design criteria. In simulation studies involving homogeneous and non-homogeneous Poisson processes they performed well with respect to their type I error rate and power. Results from supplementary simulation studies indicate that these tests are also robust to extra-Poisson variation and to clustering in the event times, making these tests attractive in their generality. We illustrate both tests by application to data from a completed kidney transplant study.

Publication types

  • Research Support, Non-U.S. Gov't
  • Research Support, U.S. Gov't, P.H.S.

MeSH terms

  • Algorithms
  • Animals
  • Antilymphocyte Serum / therapeutic use
  • Data Interpretation, Statistical
  • Effect Modifier, Epidemiologic
  • Graft Rejection / prevention & control
  • Humans
  • Immunosuppressive Agents / therapeutic use
  • Kidney Transplantation / immunology
  • Muromonab-CD3 / therapeutic use
  • Poisson Distribution*
  • Rabbits
  • Randomized Controlled Trials as Topic / statistics & numerical data*
  • Recurrence
  • Reproducibility of Results
  • Research Design*
  • Sample Size
  • Statistics, Nonparametric
  • Time Factors


  • Antilymphocyte Serum
  • Immunosuppressive Agents
  • Muromonab-CD3