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Abstract
Researchers increasingly use meta-analysis to synthesize the results of several studies in order to estimate a common effect. When the outcome variable is continuous, standard meta-analytic approaches assume that the primary studies report the sample mean and standard deviation of the outcome. However, when the outcome is skewed, authors sometimes summarize the data by reporting the sample median and one or both of (i) the minimum and maximum values and (ii) the first and third quartiles, but do not report the mean or standard deviation. To include these studies in meta-analysis, several methods have been developed to estimate the sample mean and standard deviation from the reported summary data. A major limitation of these widely used methods is that they assume that the outcome distribution is normal, which is unlikely to be tenable for studies reporting medians. We propose two novel approaches to estimate the sample mean and standard deviation when data are suspected to be non-normal. Our simulation results and empirical assessments show that the proposed methods often perform better than the existing methods when applied to non-normal data.
References
| 1. | Higgins, JP, Green, S. Cochrane handbook for systematic reviews of interventions 5.1.0. The Cochrane Collaboration 2011, http://handbook-5-1.cochrane.org/ (accessed 24 March 2019). Google Scholar |
| 2. | Sohn, H. Improving tuberculosis diagnosis in vulnerable populations: impact and cost-effectiveness of novel, rapid molecular assays. Thesis, McGill University, Montreal, 2016. Google Scholar |
| 3. | Qin, Z. Delays in diagnosis and treatment of pulmonary tuberculosis, and patient care-seeking pathways in China: a systematic review and meta-analysis. Master’s Thesis, McGill University, Montreal, 2015. Google Scholar |
| 4. | Mitchell, E, Macdonald, S, Campbell, NC, et al. Influences on pre-hospital delay in the diagnosis of colorectal cancer: a systematic review. Br J Cancer 2008; 98: 60–70. Google Scholar | Crossref | Medline |
| 5. | Siemieniuk, RA, Meade, MO, Alonso-Coello, P, et al. Corticosteroid therapy for patients hospitalized with community-acquired pneumonia: a systematic review and meta-analysis. Ann Intern Med 2015; 163: 519–528. Google Scholar | Crossref | Medline | ISI |
| 6. | Dasari, BV, Tan, CJ, Gurusamy, KS, et al. Surgical versus endoscopic treatment of bile duct stones. Cochrane Database Syst Rev 2013; 12: CD003327. Google Scholar |
| 7. | Grocott, MP, Dushianthan, A, Hamilton, MA, et al. Perioperative increase in global blood flow to explicit defined goals and outcomes after surgery: a Cochrane Systematic Review. Br J Anaesth 2013; 111: 535–548. Google Scholar | Crossref | Medline | ISI |
| 8. | Maffiuletti, NA, Roig, M, Karatzanos, E, et al. Neuromuscular electrical stimulation for preventing skeletal-muscle weakness and wasting in critically ill patients: a systematic review. BMC Med 2013; 11: 137. Google Scholar | Crossref | Medline |
| 9. | Xie, X, Pan, L, Ren, D, et al. Effects of continuous positive airway pressure therapy on systemic inflammation in obstructive sleep apnea: a meta-analysis. Sleep Med 2013; 14: 1139–1150. Google Scholar | Crossref | Medline |
| 10. | Cucchetti, A, Cescon, M, Ercolani, G, et al. A comprehensive meta-regression analysis on outcome of anatomic resection versus nonanatomic resection for hepatocellular carcinoma. Ann Surg Oncol 2012; 19: 3697–3705. Google Scholar | Crossref | Medline |
| 11. | de Kieviet, JF, Piek, JP, Aarnoudse-Moens, CS, et al. Motor development in very preterm and very low-birth-weight children from birth to adolescence: a meta-analysis. JAMA 2009; 302: 2235–2242. Google Scholar | Crossref | Medline | ISI |
| 12. | Chen, K, Xu, XW, Zhang, RC, et al. Systematic review and meta-analysis of laparoscopy-assisted and open total gastrectomy for gastric cancer. World J Gastroenterol 2013; 19: 5365–5376. Google Scholar | Crossref | Medline | ISI |
| 13. | Hozo, SP, Djulbegovic, B, Hozo, I. Estimating the mean and variance from the median, range, and the size of a sample. BMC Med Res Methodol 2005; 5: 13. Google Scholar | Crossref | Medline |
| 14. | Bland, M. Estimating mean and standard deviation from the sample size, three quartiles, minimum, and maximum. Int J Stat Med Res 2014; 4: 57–64. Google Scholar | Crossref |
| 15. | Wan, X, Wang, W, Liu, J, et al. Estimating the sample mean and standard deviation from the sample size, median, range and/or interquartile range. BMC Med Res Methodol 2014; 14: 135. Google Scholar | Crossref | Medline | ISI |
| 16. | Kwon, D, Reis, IM. Simulation-based estimation of mean and standard deviation for meta-analysis via Approximate Bayesian Computation (ABC). BMC Med Res Methodol 2015; 15: 61. Google Scholar | Crossref | Medline |
| 17. | Luo, D, Wan, X, Liu, J, et al. Optimally estimating the sample mean from the sample size, median, mid-range, and/or mid-quartile range. Stat Methods Med Res 2018; 27: 1785–1805. Google Scholar | SAGE Journals | ISI |
| 18. | Blom, G. Statistical estimates and transformed beta-variables. New York, NY: Wiley, 1958, p.176. Google Scholar |
| 19. | McGrath, S, Zhao, X, Steele, R, et al. estmeansd: Estimating the sample mean and standard deviation from commonly reported quantiles in meta-analysis. R package version 0.1.0, https://CRAN.R-project.org/package=estmeansd (2019). Google Scholar |
| 20. | McGrath, S, Sohn, H, Steele, R, et al. Meta-analysis of the difference of medians. Biom J 2019 2019/09/26. Google Scholar |
| 21. | McGrath, S, Zhao, X, Qin, ZZ, et al. One-sample aggregate data meta-analysis of medians. Stat Med 2019; 38: 969–984. Google Scholar | Crossref | Medline |
| 22. | Brent, R. Algorithms for minimization without derivatives. Mineola, New York: Courier Corporation, 2013. Google Scholar |
| 23. | Box, GE, Cox, DR. An analysis of transformations. J Royal Stat Soc Ser B (Methodological) 1964; 26: 211–252. Google Scholar |
| 24. | Thombs, BD, Benedetti, A, Kloda, LA, et al. The diagnostic accuracy of the Patient Health Questionnaire-2 (PHQ-2), Patient Health Questionnaire-8 (PHQ-8), and Patient Health Questionnaire-9 (PHQ-9) for detecting major depression: protocol for a systematic review and individual patient data meta-analyses. Syst Rev 2014; 3: 124. Google Scholar | Medline |
| 25. | Levis, B, Benedetti, A, Thombs, BD, et al. The diagnostic accuracy of the Patient Health Questionnaire-9 (PHQ-9) for detecting major depression. BMJ 2014; 3: 124. Google Scholar |
| 26. | Tomitaka, S, Kawasaki, Y, Ide, K, et al. Stability of the distribution of patient health questionnaire-9 scores against age in the general population: data from the National Health and Nutrition Examination Survey. Front Psychiatry 2018; 9: 390. Google Scholar | Crossref | Medline |
| 27. | Kocalevent, RD, Hinz, A, Brahler, E. Standardization of the depression screener patient health questionnaire (PHQ-9) in the general population. Gen Hosp Psychiatry 2013; 35: 551–555. Google Scholar | Crossref | Medline | ISI |
| 28. | Rief, W, Nanke, A, Klaiberg, A, et al. Base rates for panic and depression according to the Brief Patient Health Questionnaire: a population-based study. J Affect Disord 2004; 82: 271–276. Google Scholar | Crossref | Medline | ISI |
| 29. | Cormen, TH, Leiserson, CE, Rivest, RL, et al. Introduction to algorithms. Cambridge, MA: MIT Press, 2009. Google Scholar |
| 30. | Langan, D, Higgins, JPT, Jackson, D, et al. A comparison of heterogeneity variance estimators in simulated random-effects meta-analyses. Res Synth Meth 2018; 10: 83--98. Google Scholar |
| 31. | Higgins, JP, Thompson, SG. Quantifying heterogeneity in a meta-analysis. Stat Med 2002; 21: 1539–1558. Google Scholar | Crossref | Medline | ISI |
| 32. | Kenney, JF, Keeping, ES. Mathematics of statistics, Part 1. 3rd ed. Princeton, NJ: Van Nostrand, 1962. Google Scholar |
| 33. | Kwon, D, Reis, IM. Approximate Bayesian computation (ABC) coupled with Bayesian model averaging method for estimating mean and standard deviation. arXiv preprint arXiv:160703080 2016. Google Scholar |
