Optimally estimating the sample mean from the sample size, median, mid-range, and/or mid-quartile range

Statistical Methods in Medical Research - Tập 27 Số 6 - Trang 1785-1805 - 2018
Dehui Luo1, Xiang Wan2, Jiming Liu2, Tiejun Tong1
11 Department of Mathematics, Hong Kong Baptist University, Hong Kong.
22 Department of Computer Science, Hong Kong Baptist University, Hong Kong.

Tóm tắt

The era of big data is coming, and evidence-based medicine is attracting increasing attention to improve decision making in medical practice via integrating evidence from well designed and conducted clinical research. Meta-analysis is a statistical technique widely used in evidence-based medicine for analytically combining the findings from independent clinical trials to provide an overall estimation of a treatment effectiveness. The sample mean and standard deviation are two commonly used statistics in meta-analysis but some trials use the median, the minimum and maximum values, or sometimes the first and third quartiles to report the results. Thus, to pool results in a consistent format, researchers need to transform those information back to the sample mean and standard deviation. In this article, we investigate the optimal estimation of the sample mean for meta-analysis from both theoretical and empirical perspectives. A major drawback in the literature is that the sample size, needless to say its importance, is either ignored or used in a stepwise but somewhat arbitrary manner, e.g. the famous method proposed by Hozo et al. We solve this issue by incorporating the sample size in a smoothly changing weight in the estimators to reach the optimal estimation. Our proposed estimators not only improve the existing ones significantly but also share the same virtue of the simplicity. The real data application indicates that our proposed estimators are capable to serve as “rules of thumb” and will be widely applied in evidence-based medicine.

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Tài liệu tham khảo

Guyatt G, 1992, J Am Med Assoc, 268, 2420, 10.1001/jama.1992.03490170092032

Abuabara K, 2012, J Invest Dermatol, 132, e2, 10.1038/jid.2012.392

Hozo SP, 2005, BMC Med Res Methodol, 5

Wan X, 2014, BMC Med Res Methodol, 14

Bland M, 2015, Int J Stat Med Res, 4, 57, 10.6000/1929-6029.2015.04.01.6

Triola MF, 2009, Elementary statistics, 11

Johnson R, 2007, Elementary statistics

Nnoaham KE, 2008, Int J Epidemiol, 37, 113, 10.1093/ije/dym247

Cohen J, 2013, Statistical power analysis for the behavioral sciences, 10.4324/9780203771587

Chinn S, 2000, Stat Med, 19, 3127, 10.1002/1097-0258(20001130)19:22<3127::AID-SIM784>3.0.CO;2-M

Davies P, 1985, Thorax, 40, 187, 10.1136/thx.40.3.187

Grange J, 1985, Tubercle, 66, 187, 10.1016/0041-3879(85)90035-2

Davies P, 1987, Eur J Resp Dis, 71, 341

Davies P, 1988, Int Med J Thailand, 4, 45

Chan T, 1994, J Trop Med Hygiene, 97, 26

Wilkinson RJ, 2000, The Lancet, 355, 618, 10.1016/S0140-6736(99)02301-6

Sasidharan P, 2002, J Assoc Phys India, 50, 554

Higgins JP, 2003, Br Med J, 327, 557, 10.1136/bmj.327.7414.557

Arnold BC, Relations, bounds and approximations for order statistics

Ahsanullah M, 2013, An introduction to order statistics, 10.2991/978-94-91216-83-1

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Thông tin xuất bản

Statistical Methods in Medical Research

Tập 27 Số 6

1785-1805

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