Estimating sample means and standard deviations from the log-normal distribution using medians and quartiles:...

Clinical trials often report medians and quartiles due to skewed data distributions. We sought to evaluate the methods currently used in meta-analyses in anesthesiology to estimate means and standard deviations (SDs) from medians and quartiles.

We simulated sample sizes (n = 15, 27, 51) and coefficients of variation (CV = 0.15, 0.3, 0.5), representative scenarios in anesthesiology studies, generating data that have a log-normal distribution with zero log-scale means. We calculated generalized confidence intervals for the ratios of means and ratios of SDs using means and SDs estimated from three quartiles in time scale, using Luo et al.'s and Wan et al.'s methods, McGrath et al.'s quantile estimation and Box-Cox transformation, and Cai et al.'s maximum likelihood estimation method.

The method by Luo et al. and Wan et al. produced 95% confidence intervals for the ratio of means with coverage ranging from 92.4% to 93.6%, and for SDs from 79.2 to 89.6. McGrath et al.'s quantile estimation method yielded coverage for mean ratios between 88.5% and 91.5% and SDs between 78.0 and 82.7. McGrath et al.'s Box-Cox transformation method showed coverage for mean ratios from 86.6% to 94.4% and SDs from 67.1 to 83.1. The maximum likelihood estimation method by Cai et al. for nonnormal distributions showed coverage for mean ratios from 78.9% to 86.4% and SDs from 67.6 to 78.0.

All evaluated methods of estimating means and standard deviations from quartiles of log-normal distributed data result in confidence interval coverages below the expected 95%. Because these methods are widely used in meta-analyses of anesthesiology data, P values reported as < 0.05 cannot be trusted. Anesthesiology journals and investigators should revise reporting requirements for continuous skewed variables. We advise reporting the quartiles, mean, and SD, or the quartiles and including the raw data for the relevant variables as supplemental content. This holistic approach could improve the reliability of statistical inferences in meta-analyses of anesthesiology research, particularly when skewed distributions are involved.