Sample size calculations based on a difference in medians for positively skewed outcomes in health care studies

• DOI: 10.1186/s12874-017-0426-1
• Publication Date: 2017-12-02T02:06:46Z
• Authors: Aidan G. O’Keeffe; Gareth Ambler; Julie A. Barber
• Keywords: Medicine (General); Log-transformation; Sample size; Clinical Studies as Topic; Median; Skewness; 03 medical and health sciences; R5-920; Treatment Outcome; 0302 clinical medicine; Data Interpretation, Statistical; Sample Size; Humans; Hypothesis test; Algorithms; Research Article; Statistical Distributions

In healthcare research, outcomes with skewed probability distributions are common. Sample size calculations for such outcomes are typically based on estimates on a transformed scale (e.g. log) which may sometimes be difficult to obtain. In contrast, estimates of median and variance on the untransformed scale are generally easier to pre-specify. The aim of this paper is to describe how to calculate a sample size for a two group comparison of interest based on median and untransformed variance estimates for log-normal outcome data.A log-normal distribution for outcome data is assumed and a sample size calculation approach for a two-sample t-test that compares log-transformed outcome data is demonstrated where the change of interest is specified as difference in median values on the untransformed scale. A simulation study is used to compare the method with a non-parametric alternative (Mann-Whitney U test) in a variety of scenarios and the method is applied to a real example in neurosurgery.The method attained a nominal power value in simulation studies and was favourable in comparison to a Mann-Whitney U test and a two-sample t-test of untransformed outcomes. In addition, the method can be adjusted and used in some situations where the outcome distribution is not strictly log-normal.We recommend the use of this sample size calculation approach for outcome data that are expected to be positively skewed and where a two group comparison on a log-transformed scale is planned. An advantage of this method over usual calculations based on estimates on the log-transformed scale is that it allows clinical efficacy to be specified as a difference in medians and requires a variance estimate on the untransformed scale. Such estimates are often easier to obtain and more interpretable than those for log-transformed outcomes.