Sample-size calculation for a log-transformed outcome measure

Control Clin Trials. 1999 Dec;20(6):547-54. doi: 10.1016/s0197-2456(99)00032-x.


The outcome measure of interest in clinical trials sometimes requires transformation to the logarithmic scale for analysis. This paper examines sample-size calculation for both independent groups and matched-pairs trials for log-transformed outcomes. For both types of trial, we demonstrate how the calculation can be formulated in terms of a relative treatment effect and a statement of relative variability, both specified on the original scale of measurement. For a comparison of two independent groups, the relative treatment effect is the ratio of group geometric means (or alternatively, group arithmetic means) and the coefficient of variation is used as a summary of relative variability. For a matched-pairs comparison, the appropriate relative treatment effect is the geometric mean of the within-pair ratios, and relative variability can be specified as an upper bound on within-pair ratios under a null hypothesis of the relative effect being equal to 1 (i.e., no difference). We discuss the clinical study that motivated this work and demonstrate the application of the sample-size calculation to this study.

Publication types

  • Comparative Study

MeSH terms

  • Algorithms
  • Anesthetics, Local / administration & dosage
  • Case-Control Studies
  • Child
  • Humans
  • Influenza Vaccines / administration & dosage
  • Injections, Subcutaneous / adverse effects
  • Linear Models
  • Ointments
  • Outcome Assessment, Health Care / statistics & numerical data*
  • Pain / prevention & control
  • Placebos
  • Randomized Controlled Trials as Topic / statistics & numerical data*
  • Sample Size*
  • Tetracaine / administration & dosage
  • Treatment Outcome
  • Vaccination


  • Anesthetics, Local
  • Influenza Vaccines
  • Ointments
  • Placebos
  • Tetracaine