Estimation of Standard Deviation for a Log-Transformed Variable Based on Summary Statistics in the Original Scale

ABSTRACT

Clinical study endpoints, including some biomarkers, are frequently analyzed after a log transformation. To calculate study power for detecting a between-treatment difference in the log scale, an estimate of the standard deviation of the log-transformed variable is needed. Often, though, only summary statistics in the original scale including arithmetic means with corresponding standard deviations or sample medians and interquartile ranges are found in the literature. In the absence of individual subjects' log-transformed data for directly calculating the sample standard deviation in the log scale, alternative approaches should be applied. This article presents methods for estimating the standard deviation of a log-transformed variable via the arithmetic means and standard deviations or medians and interquartile ranges of the untransformed variable. It further presents methods for constructing the corresponding confidence intervals. A meta-analysis approach, combining data from all sources for more robust estimation, is also discussed. Simulations and examples are provided to assess the performances of these estimates.

KEYWORDS:

• Asymptotic distribution
• Confidence interval
• Interquartile range
• Lognormal distribution

Acknowledgments

The authors thank the two referees and the associate editor for their excellent suggestions that have improved the presentation of this article.