Meta-Analysis
Copyright ©The Author(s) 2015. Published by Baishideng Publishing Group Inc. All rights reserved.
World J Meta-Anal. Oct 26, 2015; 3(5): 215-224
Published online Oct 26, 2015. doi: 10.13105/wjma.v3.i5.215
How to impute study-specific standard deviations in meta-analyses of skewed continuous endpoints?
Teresa Greco, Giuseppe Biondi-Zoccai, Marco Gemma, Claude Guérin, Alberto Zangrillo, Giovanni Landoni
Teresa Greco, Laboratorio di Statistica Medica, Biometria ed Epidemiologia “G. A. Maccacaro”, Dipartimento di Scienze Cliniche e di Comunità, University of Milan, 20133 Milan, Italy
Teresa Greco, Marco Gemma, Alberto Zangrillo, Giovanni Landoni, Anaesthesia and Intensive Care Department, IRCCS San Raffaele Scientific Institute, 20132 Milan, Italy
Giuseppe Biondi-Zoccai, Department of Medico-Surgical Sciences and Biotechnologies, Sapienza University of Rome, 04100 Latina, Italy
Giuseppe Biondi-Zoccai, Eleonora Lorillard Spencer Cenci Foundation, 00185 Rome, Italy
Giuseppe Biondi-Zoccai, Meta-analysis and Evidence Based Medicine Training in Cardiology (METCARDIO), 18014 Ospedaletti, Italy
Claude Guérin, Medical Intensive Care, Hospital de La Croix Rousse, 69317 Lyon, France
Author contributions: All authors contributed equally to this work; Greco T conceived the study, participated in its design and coordination, did the analyses and revised the manuscript critically; Biondi-Zoccai G and Gemma M conceived the study, helped in interpretation of data and to draft the manuscript; Guérin C, Zangrillo A and Landoni G conceived the study, participated in its design and coordination, and drafted the manuscript; all authors read and approved the manuscript.
Conflict-of-interest statement: The authors declare that there are no conflicts of interest. This research received no specific grant from any funding agency in the public, commercial, or not-for-profit sectors. This work is part of the PhD program in Biomedical Statistics, University of Milan, Italy.
Data sharing statement: Technical appendix, statistical code, and dataset are available in the Supplemental Material and from the corresponding author (at greco.teresa@hotmail.it), who will provide a permanent, citable, and open-access home for the dataset.
Open-Access: This article is an open-access article which was selected by an in-house editor and fully peer-reviewed by external reviewers. It is distributed in accordance with the Creative Commons Attribution Non Commercial (CC BY-NC 4.0) license, which permits others to distribute, remix, adapt, build upon this work non-commercially, and license their derivative works on different terms, provided the original work is properly cited and the use is non-commercial. See: http://creativecommons.org/licenses/by-nc/4.0/
Correspondence to: Teresa Greco, MSc, Laboratorio di Statistica Medica, Biometria ed Epidemiologia “G. A. Maccacaro”, Dipartimento di Scienze Cliniche e di Comunità, University of Milan, Via Festa del Perdono 7, 20133 Milan, Italy. greco.teresa@hotmail.it
Telephone: +39-02-26436153
Received: January 8, 2015
Peer-review started: January 10, 2015
First decision: June 3, 2015
Revised: June 26, 2015
Accepted: July 24, 2015
Article in press: July 27, 2015
Published online: October 26, 2015
Processing time: 294 Days and 21.6 Hours
Abstract

AIM: To compare four methods to approximate mean and standard deviation (SD) when only medians and interquartile ranges are provided.

METHODS: We performed simulated meta-analyses on six datasets of 15, 30, 50, 100, 500, and 1000 trials, respectively. Subjects were iteratively generated from one of the following seven scenarios: five theoretical continuous distributions [Normal, Normal (0, 1), Gamma, Exponential, and Bimodal] and two real-life distributions of intensive care unit stay and hospital stay. For each simulation, we calculated the pooled estimates assembling the study-specific medians and SD approximations: Conservative SD, less conservative SD, mean SD, or interquartile range. We provided a graphical evaluation of the standardized differences. To show which imputation method produced the best estimate, we ranked those differences and calculated the rate at which each estimate appeared as the best, second-best, third-best, or fourth-best.

RESULTS: Our results demonstrated that the best pooled estimate for the overall mean and SD was provided by the median and interquartile range (mean standardized estimates: 4.5 ± 2.2, P = 0.14) or by the median and the SD conservative estimate (mean standardized estimates: 4.5 ± 3.5, P = 0.13). The less conservative approximation of SD appeared to be the worst method, exhibiting a significant difference from the reference method at the 90% confidence level. The method that ranked first most frequently is the interquartile range method (23/42 = 55%), particularly when data were generated according to the Standard Normal, Gamma, and Exponential distributions. The second-best is the conservative SD method (15/42 = 36%), particularly for data from a bimodal distribution and for the intensive care unit stay variable.

CONCLUSION: Meta-analytic estimates are not significantly affected by approximating the missing values of mean and SD with the correspondent values for median and interquartile range.

Keywords: Imputation; Interquartile range; Meta-analysis; Randomized controlled trial; Standard deviation

Core tip: Meta-analyses of continuous endpoints are generally supposed to deal with normally distributed data and the pooled estimate of the treatment effect relies on means and standard deviations. However, if the outcome distribution is skewed, some authors correctly report the median together with the corresponding quartiles. In the present work, we compared methods for the approximation of means and standard deviations when only medians with quartiles are provided. Our results demonstrate that meta-analytic estimates are not significantly affected by approximating the missing values of mean and standard deviation with the correspondent values for median and interquartile range.