title: Estimate of standard deviation for a log-transformed variable using arithmetic means and standard deviations.
abstract: Analyses of study variables are frequently based on log transformations. To calculate the power for detecting the between-treatment difference in the log scale, we need an estimate of the standard deviation of the log-transformed variable. However, in many situations a literature search only provides the arithmetic means and the corresponding standard deviations. Without individual log-transformed data to directly calculate the sample standard deviation, we need alternative methods to estimate it. This paper presents methods for estimating and constructing confidence intervals for the standard deviation of a log-transformed variable given the mean and standard deviation of the untransformed variable. It also presents methods for estimating the standard deviation of change from baseline in the log scale given the means and standard deviations of the untransformed baseline value, on-treatment value and change from baseline. Simulations and examples are provided to assess the performance of these estimates.
authors.affiliation: Clinical Biostatistics and Research Decision Sciences, RY 34-A320, Merck Research Laboratories, P.O. Box 2000, Rahway, NJ 07065, USA. hui_quan@merck.com
authors.forename: Hui
authors.initials: H
authors.lastname: Quan
authors.forename: Ji
authors.initials: J
authors.lastname: Zhang
mesh_terms: D016001:Confidence Intervals; D008433:Mathematics; D015233:Models, Statistical; D013223:Statistics as Topic / Q000379:methods*