Optimally estimating the sample mean from the sample size, median, mid-range, and/or mid-quartile range
Open accessAbstract
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.
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
Missing data were handled by estimating mean and standard deviation from median and interquartile range using conventional formulae, and by prognostic imputation when both were absent.
“When studies reported a median and interquartile range, we estimated the mean and standard deviation (SD) using conventional formulae (Luo et al., 2018;Wan et al., 2014).When both of these were absent, we estimated the standard deviation using prognostic imputation (Ma et al., 2008).”
From Decision making capacity for treatment in psychiatric inpatients: a systematic review and meta-analysis (2024) · cites this paper as Luo et al., 2018
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Cites
Statistical power analysis for the behavioral sciences
Cohen, J. (1990) · Computers Environment and Urban Systems · doi:10.1016/0198-9715(90)90050-4 · Cited by 65,406 · see citing works
Measuring inconsistency in meta-analyses
Higgins, J. P. T., Thompson, S. G., Deeks, J. J., & Altman, D. G. (2003) · BMJ · doi:10.1136/bmj.327.7414.557 · Cited by 63,139 · cited 1× · see citing works
“ods seem to be close to each other, we found that the I2 indices for heterogeneity between studies are quite different (i.e., 48.54% from Hozo et al.’s method and 34.85% from our method). According to Higgins et al. (2003), the value 48.54% of I2 is very close to moderate heterogeneity level while the value 34.85% is c…”
MethodInfluentialStatistical Power Analysis for the Behavioral Sciences
Cohen, J. (2013) · doi:10.4324/9780203771587 · Cited by 25,373 · see citing works
Wan, X., Wang, W., Liu, J., & Tong, T. (2014) · BMC Medical Research Methodology · doi:10.1186/1471-2288-14-135 · Cited by 11,735 · cited 3× · see citing works
“Finally, by plugging the approximation formula (6) into the estimator (4), we propose the estimator for Scenario S1 as XðwÞ 4 4þ n0:75 aþ b 2 þ n 0:75”
BackgroundMethodSelf-citationEstimating the mean and variance from the median, range, and the size of a sample
Hozo, S. P., Djulbegovic, B., & Hozo, I. (2005) · BMC Medical Research Methodology · doi:10.1186/1471-2288-5-13 · Cited by 9,062 · see citing works
Guyatt, G. H. (1992) · JAMA · doi:10.1001/jama.1992.03490170092032 · Cited by 4,447 · cited 4× · see citing works
“’s method has a change point near n1⁄4 25 (as suggested in (1)), especially for log-normal distribution and exponential distribution.”
BackgroundMethodInfluentialWilkinson, R. J., Llewelyn, M., Toossi, Z., Patel, P., Pasvol, G., Lalvani, A., Wright, D. J., Latif, M., & Davidson, R. N. (2000) · The Lancet · doi:10.1016/s0140-6736(99)02301-6 · Cited by 768 · see citing works
Low serum vitamin D levels and tuberculosis: a systematic review and meta-analysis
Nnoaham, K. E., & Clarke, A. (2008) · International Journal of Epidemiology · doi:10.1093/ije/dym247 · Cited by 682 · see citing works
Relations, Bounds and Approximations for Order Statistics
Arnold, B. C., & Balakrishnan, N. (1989) · Lecture notes in statistics · doi:10.1007/978-1-4612-3644-3 · Cited by 243 · see citing works
Johnson, R. R. (1976) · UCLA Biblioteca de Ingenieria Civil · Cited by 160 · see citing works
Serum concentrations of vitamin D metabolites in untreated tuberculosis.
Davies, P. D. O., Brown, R. C., & Woodhead, J. S. (1985) · Thorax · doi:10.1136/thx.40.3.187 · Cited by 157 · see citing works
An Introduction to Order Statistics
Ahsanullah, M., Nevzorov, V. B., & Shakil, M. (2013) · Atlantis studies in probability and statistics · doi:10.2991/978-94-91216-83-1 · Cited by 136 · see citing works
Estimating Mean and Standard Deviation from the Sample Size, Three Quartiles, Minimum, and Maximum
Bland, M. (2014) · International Journal of Statistics in Medical Research · doi:10.6000/1929-6029.2015.04.01.6 · Cited by 130 · cited 2× · see citing works
“Note that the optimal weight woptðnÞ in (5) may not be readily accessible for practitioners as it involves some complicated statistical computation.”
BackgroundA study of vitamin d levels in indonesian patients with untreated pulmonary tuberculosis
Grange, J. M., Davies, P. D. O., Brown, R. C., Woodhead, J. S., & Kardjito, T. (1985) · Tubercle · doi:10.1016/0041-3879(85)90035-2 · Cited by 106 · cited 2× · see citing works
“Finally, by plugging the approximation formula (14) into the estimator (12), we propose the estimator for scenario S3 as Xðw1,w2Þ 2:2 2:2þ n0:75 aþ b 2 þ 0:7 0:72 n0:55 q1 þ q3 2 þ 0:3þ 0:72 n0:55 2:2 2:2þ n0:75 m ð15Þ”
BackgroundTuberculosis and vitamin D deficiency.
Sasidharan, P., Rajeev, E., & Vijayakumari, V. (2002) · PubMed · Cited by 95 · see citing works
(2009) · Princeton University Press eBooks · doi:10.2307/j.ctvcm4hsb.13 · Cited by 76 · see citing works
Raised serum calcium in tuberculosis patients in Africa.
Davies, P. D. O., Church, H., Brown, R. C., & Woodhead, J. S. (1987) · PubMed · Cited by 55 · see citing works
A study of calcium and vitamin D metabolism in Chinese patients with pulmonary tuberculosis.
Chan, T., Poon, P., Pang, J., Swaminathan, R., Chan, C. H. S., Nisar, M. K., Williams, C. S., & Davies, P. D. O. (1994) · PubMed · Cited by 53 · see citing works
The Role of Systematic Reviews and Meta-analysis in Dermatology
Abuabara, K., Freeman, E. E., & Dellavalle, R. P. (2012) · Journal of Investigative Dermatology · doi:10.1038/jid.2012.392 · Cited by 49 · cited 3× · see citing works
“We also note that an equal weight is assigned to each summary statistic in the estimator (2).”
BackgroundMethodWilson, W. J., & Johnson, E. R. (1990) · Technometrics · doi:10.2307/1269873 · Cited by 27 · see citing works
A simple method for converting an odds ratio to effect size for use in meta-analysis
Chinn, S. (2000) · Statistics in Medicine · doi:10.1002/1097-0258(20001130)19:22
Flagged first, then by citations
Research works printed but not linked: 1
- Davies P, Church H, Charumilind A, et al. Altered vitamin D homeostasis in tuberculosis. Int Med J Thailand 1988; 4: 45-47.
Cited by
Sorted by citations
Estimating the sample mean and standard deviation from commonly reported quantiles in meta-analysis
McGrath, S., Zhao, X., Steele, R. J., Thombs, B. D., Benedetti, A., Levis, B., Riehm, K. E., Saadat, N., Levis, A. W., Azar, M., et al. (2020) · Statistical Methods in Medical Research · doi:10.1177/0962280219889080 · Cited by 869 · see citing works
Association of inflammatory markers with the severity of COVID-19: A meta-analysis
Zeng, F., Huang, Y., Guo, Y., Yin, M., Chen, X., Liang, X., & Deng, G. (2020) · International Journal of Infectious Diseases · doi:10.1016/j.ijid.2020.05.055 · Cited by 666 · see citing works
“Stratified data or interquartile range (IQR) were converted to mean ( SD) using mathematical formulas for meta-analysis (Luo et al., 2018; Wan et al., 2014).”
MethodOptimally estimating the sample standard deviation from the five‐number summary
Shi, J., Luo, D., Weng, H., Zeng, X., Lin, L., Chu, H., & Tong, T. (2020) · Research Synthesis Methods · doi:10.1002/jrsm.1429 · Cited by 620 · see citing works
“To have an approximation formula for the optimal weight, we numerically compute the true values of J(n) and wopt(n) for different values of n using formulas (7) and (8).”
BackgroundMethodSelf-citationFernández‐de‐las‐Peñas, C., Palacios‐Ceña, D., Gómez‐Mayordomo, V., Florêncio, L. L., Cuadrado, M. L., Plaza‐Manzano, G., & Navarro‐Santana, M. J. (2021) · European Journal of Internal Medicine · doi:10.1016/j.ejim.2021.06.009 · Cited by 575 · see citing works
Hassan, C., Spadaccini, M., Iannone, A., Maselli, R., Jovani, M., Chandrasekar, V. T., Antonelli, G., Yu, H., Areia, M., Dinis-Ribeiro, M., et al. (2021) · Gastrointestinal Endoscopy · doi:10.1016/j.gie.2020.06.059 · Cited by 529 · see citing works
“…mean and standard deviation were not reported for continuous outcomes, we calculated these statistics from median and interquartile range, according to the methods described by Luo et al 16 and Wan et al. 17 We calculated pooled estimates using the DerSimonian and Laird random-effects model 18 .”
MethodDetecting the skewness of data from the five-number summary and its application in meta-analysis
Shi, J., Luo, D., Wan, X., Liu, Y., Liu, J., Bian, Z., & Tong, T. (2023) · Statistical Methods in Medical Research · doi:10.1177/09622802231172043 · Cited by 341 · see citing works
“Despite the elegant analytical results, the asymptotic test by equation (3) will have a serious limitation that the convergence rate is relatively slow at the order of √ 2 ln(n)ξ(n).”
BackgroundInfluentialSelf-citationMarx, W., McGuinness, A. J., Rocks, T., Ruusunen, A. A., Cleminson, J. R., Walker, A. J., Gomes‐da‐Costa, S., Lane, M. M., Sanches, M., Díaz, A. P., et al. (2020) · Molecular Psychiatry · doi:10.1038/s41380-020-00951-9 · Cited by 327 · see citing works
Danopoulos, E., Jenner, L. C., Twiddy, M., & Rotchell, J. M. (2020) · Environmental Health Perspectives · doi:10.1289/ehp7171 · Cited by 302 · see citing works
“The calculator draws on the methods developed by Luo et al. (2018) for the estimation of the mean of the sample and the methods by Wan et al. (2014) for the estimation of the SD.”
Kuswardhani, R. A. T., Henrina, J., Pranata, R., Lim, M. A., Lawrensia, S., & Suastika, K. (2020) · Diabetes & Metabolic Syndrome Clinical Research & Reviews · doi:10.1016/j.dsx.2020.10.022 · Cited by 295 · see citing works
Edinger, J. D., Arnedt, J. T., Bertisch, S. M., Carney, C. E., Harrington, J. J., Lichstein, K. L., Sateia, M. J., Troxel, W. M., Zhou, E. S., Kazmi, U., et al. (2021) · Journal of Clinical Sleep Medicine · doi:10.5664/jcsm.8988 · Cited by 309 · see citing works
“These, too, were converted into data expressed as means and standard deviations.(55,56) The pooled results for each continuous outcome measure are expressed herein as the mean difference or standardized mean differences between the intervention and comparator groups.”
Sangkaew, S., Ming, D. K. Y., Boonyasiri, A., Honeyford, K., Kalayanarooj, S., Yacoub, S., Dorigatti, I., & Holmes, A. H. (2021) · The Lancet Infectious Diseases · doi:10.1016/s1473-3099(20)30601-0 · Cited by 299 · see citing works
The economic burden of antibiotic resistance: A systematic review and meta-analysis
Poudel, A. N., Zhu, S., Cooper, N. J., Little, P. S., Tarrant, C., Hickman, M., & Yao, G. (2023) · PLoS ONE · doi:10.1371/journal.pone.0285170 · Cited by 269 · see citing works
Zheng, G., Qiu, P., Xia, R., Lin, H., Ye, B., Tao, J., & Chen, L. (2019) · Frontiers in Aging Neuroscience · doi:10.3389/fnagi.2019.00098 · Cited by 242 · see citing works
“If the data were reported as median interquartile range (IQR), we calculated mean and standard deviation utilizing the Wan and Luo formulae (Wan et al., 2014; Luo et al., 2015).”
MethodZhang, Y., Zhang, C., Shu, J., Guo, J., Chang, H., Leung, P. C. K., Sheng, J., & Huang, H. (2019) · Human Reproduction Update · doi:10.1093/humupd/dmz046 · Cited by 232 · see citing works
Occupational heat strain in outdoor workers: A comprehensive review and meta-analysis
Ioannou, L. G., Foster, J., Morris, N. B., Piil, J. F., Havenith, G., Mekjavić, I. B., Kenny, G. P., Nybo, L., & Flouris, A. D. (2022) · Temperature · doi:10.1080/23328940.2022.2030634 · Cited by 236 · see citing works
“In studies where only median and quartiles/ranges were reported, the extracted data were converted to means and standard deviations following previous methodology [77,78].”
MethodChiavaroli, L., Lee, D., Ahmed, A., Cheung, A., Khan, T. A., Blanco, S., Mejia, Mirrahimi, A., Jenkins, D. J. A., Livesey, G., et al. (2021) · BMJ · doi:10.1136/bmj.n1651 · Cited by 215 · see citing works
Bisch, S. P., Jago, C. A., Kalogera, E., Ganshorn, H., Meyer, L. A., Ramirez, P. T., Dowdy, S. C., & Nelson, G. S. (2020) · Gynecologic Oncology · doi:10.1016/j.ygyno.2020.12.035 · Cited by 209 · see citing works
Viguiliouk, E., Kendall, C. W., Kahleová, H., Rahelić, D., Salas-Salvadó, J., Choo, V. L., Mejia, S. B., Stewart, S. E., Leiter, L. A., Jenkins, D. J., et al. (2019) · Clinical Nutrition · doi:10.1016/j.clnu.2018.05.032 · Cited by 201 · see citing works
Meta‐analysis of the difference of medians
McGrath, S., Sohn, H., Steele, R. J., & Benedetti, A. (2019) · Biometrical Journal · doi:10.1002/bimj.201900036 · Cited by 206 · see citing works
“To estimate the standard deviation, Luo et al [19] recommend the methods previously described by Wan et al [26].”
MethodInfluentialSuárez, S., Conde‐Agudelo, A., Borovac‐Pinheiro, A., Suarez-Rebling, D., Eckardt, M. J., Theron, G. B., & Burke, T. F. (2020) · American Journal of Obstetrics and Gynecology · doi:10.1016/j.ajog.2019.11.1287 · Cited by 198 · see citing works
Fernández‐de‐las‐Peñas, C., Notarte, K. I., Macasaet, R., Velasco, J. V., Catahay, J. A., Ver, A. T., Chung, W., Valera‐Calero, J. A., & Navarro‐Santana, M. J. (2023) · Journal of Infection · doi:10.1016/j.jinf.2023.12.004 · Cited by 197 · see citing works
Liao, C.-D., Chen, H.-C., Huang, S.-W., & Liou, T.-H. (2019) · Nutrients · doi:10.3390/nu11081713 · Cited by 189 · see citing works
“If data were reported as median (range), they were re-calculated algebraically from the trial data to impute the sample mean and SD [25,32].”
Ni, X., Jia, D. T., Chen, Y., Wang, L., & Suo, J. (2019) · Journal of Gastrointestinal Surgery · doi:10.1007/s11605-019-04170-8 · Cited by 177 · see citing works
Clinical recovery from concussion–return to school and sport: a systematic review and meta-analysis
Putukian, M., Purcell, L. K., Schneider, K., Black, A. M., Burma, J. S., Chandran, A. S., Boltz, A. J., Master, C. L., Register‐Mihalik, J. K., Anderson, V. A., et al. (2023) · British Journal of Sports Medicine · doi:10.1136/bjsports-2022-106682 · Cited by 184 · see citing works
Coronavirus disease (COVID-19) and the liver: a comprehensive systematic review and meta-analysis
Kumar, P. M., Mishra, S., Jha, D. K., Shukla, J., Choudhury, A. R., Mohindra, R., Mandavdhare, H. S., Dutta, U., & Sharma, V. (2020) · Hepatology International · doi:10.1007/s12072-020-10071-9 · Cited by 175 · see citing works
“For studies reporting median and interquartile range or median and range, the mean and standard deviation were computed from the reported values based on Luo 2018 and Wan 2014 methodology [12, 13].”
MethodGreaves, D., Psaltis, P. J., Davis, D. H. J., Ross, T. J., Ghezzi, E. S., Lampit, A., Smith, A. E., & Keage, H. A. D. (2020) · Journal of the American Heart Association · doi:10.1161/jaha.120.017275 · Cited by 173 · see citing works
A systematic review and meta-analysis of inflammatory biomarkers in Parkinson’s disease
Qu, Y., Li, J., Qin, Q., Wang, D., Zhao, J., An, K., Mao, Z., Min, Z., Xiong, Y., Li, J., et al. (2023) · npj Parkinson s Disease · doi:10.1038/s41531-023-00449-5 · Cited by 172 · see citing works
Vetkas, A., Fomenko, A., Germann, J., Sarica, C., Iorio‐Morin, C., Samuel, N., Yamamoto, K., Milano, V., Cheyuo, C., Zemmar, A., et al. (2022) · Epilepsia · doi:10.1111/epi.17157 · Cited by 170 · see citing works
Efficacy of CytoSorb®: a systematic review and meta-analysis
Becker, S., Lang, H., Barbosa, C. V., Tian, Z., Melk, A., & Schmidt, B. M. W. (2023) · Critical Care · doi:10.1186/s13054-023-04492-9 · Cited by 171 · see citing works
“Medians reported with interquartile ranges or minimum and maximum values were converted to mean values and standard deviation using the method of Luo et al. [6] Subsequently, the effect of mean values was assessed using a random effect model with the DerSimonian-Laird method.”
MethodDavis, K. T., Peeler, J. L., Fargione, J., Haugo, R. D., Metlen, K. L., Robles, M. D., & Woolley, T. J. (2024) · Forest Ecology and Management · doi:10.1016/j.foreco.2024.121885 · Cited by 169 · see citing works
“In the case that the first quartile was < 0 (2.6% of observations), we used the estimator for the mean from Luo et al. (2018) and the estimator for the standard deviation from Wan et al. (2014) because the MLN method requires positive values.”
MethodInfluentialPrognostic Value of Leukocytosis and Lymphopenia for Coronavirus Disease Severity
Huang, G., Kovalic, A. J., & Graber, C. J. (2020) · Emerging infectious diseases · doi:10.3201/eid2608.201160 · Cited by 167 · see citing works
Barreto, B. B., Luz, M., Rios, M. N. D. O., Lopes, A., & Gusmao-Flores, D. (2019) · Critical Care · doi:10.1186/s13054-019-2678-0 · Cited by 138 · see citing works
Du, X., Xu, X., Yao, J., Deng, K., Chen, S., Shen, Z., Yang, L., & Feng, G. (2019) · American Journal of Infection Control · doi:10.1016/j.ajic.2019.03.003 · Cited by 158 · see citing works
“For studies providing median and range (or interquartile range) only for continuous outcomes, the mean value and variance were estimated using the median and range.(21,22) To assess the possibility of publication bias, the funnel plot for asymmetry and the Egger test were performed.”
MethodHuang, W., Wang, W., Xie, W., Chen, Z., & Liu, Y. (2020) · Journal of Clinical Anesthesia · doi:10.1016/j.jclinane.2020.109900 · Cited by 156 · see citing works
Protein Intake and Sarcopenia in Older Adults: A Systematic Review and Meta-Analysis
Coelho‐Júnior, H. J., Calvani, R., Azzolino, D., Picca, A., Tosato, M., Landi, F., Cesari, M., & Marzetti, E. (2022) · International Journal of Environmental Research and Public Health · doi:10.3390/ijerph19148718 · Cited by 156 · see citing works
“SDs were calculated from confidence intervals (CIs) and standard errors (SEs), according to the following formulas: SD1 = √ N × (Upper limit − Lower limit)/3.92 (1) SD2 = SE × √ N (2) From the interquartile range, SDs were obtained according to the formulas proposed by Luo [29] and Shi [30].”
MethodInfluentialGuo, Z., Li, M., Han, B., & Qi, X. (2018) · Digestive and Liver Disease · doi:10.1016/j.dld.2018.08.012 · Cited by 147 · see citing works
López‐Medina, C., Ramiro, S., van der Heijde, D. M. F. M., Sieper, J., Dougados, M., & Moltó, A. (2019) · RMD Open · doi:10.1136/rmdopen-2019-001108 · Cited by 147 · see citing works
“24 For continuous variables, a pooled comparison between r-axSpA and nr-axSpA was performed using the standardised mean difference (SMD), which expresses the distance between two group means.”
Cai, S., Zhou, J., & Pan, J. (2021) · Statistical Methods in Medical Research · doi:10.1177/09622802211047348 · Cited by 144 · see citing works
“For S3, μ̃ and σ̃ are, respectively, given by (8) and (9).”
Comparative analysis of laboratory indexes of severe and non-severe patients infected with COVID-19
Bao, J., Li, C., Zhang, K., Kang, H., Chen, W., & Gu, B. (2020) · Clinica Chimica Acta · doi:10.1016/j.cca.2020.06.009 · Cited by 143 · see citing works
“The sample mean was estimated by Luo et al.'s method [11] and variance by Wan et al.'s [12] from the sample size, median and IQR.”
van Lanen, A., de Bree, A., & Greyling, A. (2021) · European Journal of Nutrition · doi:10.1007/s00394-020-02473-0 · Cited by 151 · see citing works
Oh, S. K., Lim, B. G., Won, Y. J., Lee, D. K., & Kim, S. S. (2022) · Journal of Clinical Anesthesia · doi:10.1016/j.jclinane.2022.110647 · Cited by 141 · see citing works
Jiang, S., Huang, Q., Xie, W., Lv, C., & Quan, X. (2020) · British Journal of Haematology · doi:10.1111/bjh.16817 · Cited by 136 · see citing works
“To be included in the analysis, the studies had to report the mean and ( standard deviation, SD) of the platelet count in both severe and non-severe COVID-19 patients, or report the median and interquartile range (IQR) or median and range of platelet count, from which we could extract information about the mean ( SD).…”
MethodPrognostic and Therapeutic Role of Vitamin D in COVID-19: Systematic Review and Meta-analysis
Dissanayake, H. A., de Silva, N. L., Sumanatilleke, M., de Silva, S. D. N., Gamage, K. K. K., Dematapitiya, C., Kuruppu, C., Ranasinghe, P. D., Pathmanathan, S., & Katulanda, P. (2021) · The Journal of Clinical Endocrinology & Metabolism · doi:10.1210/clinem/dgab892 · Cited by 129 · see citing works
Meta-analysis of the impact of freeze–thaw cycles on soil microbial diversity and C and N dynamics
Ji, X., Liu, M., Yang, J., & Feng, F. (2022) · Soil Biology and Biochemistry · doi:10.1016/j.soilbio.2022.108608 · Cited by 129 · see citing works
Preoperative inflammatory mediators and postoperative delirium: systematic review and meta-analysis
Noah, M. A., Almghairbi, D., Evley, R., & Moppett, I. K. (2021) · British Journal of Anaesthesia · doi:10.1016/j.bja.2021.04.033 · Cited by 127 · see citing works
Microplastics stimulated nitrous oxide emissions primarily through denitrification: A meta-analysis
Su, P., Gao, C., Zhang, X., Zhang, D., Liu, X., Xiang, T., Luo, Y., Chu, K., Zhang, G., Bu, N., et al. (2022) · Journal of Hazardous Materials · doi:10.1016/j.jhazmat.2022.130500 · Cited by 127 · see citing works
Xu, Y., Wang, M., Chen, D., Jiang, X., & Xiong, Z. (2022) · Aging Clinical and Experimental Research · doi:10.1007/s40520-021-02022-7 · Cited by 126 · see citing works
The Effect of Coconut Oil Consumption on Cardiovascular Risk Factors
Neelakantan, N., Seah, J. Y. H., & van Dam, R. M. (2020) · Circulation · doi:10.1161/circulationaha.119.043052 · Cited by 125 · see citing works
Spadaccini, M., Iannone, A., Maselli, R., Badalamenti, M., Desai, M., Chandrasekar, V. T., Patel, H. K., Fugazza, A., Pellegatta, G., Galtieri, P. A., et al. (2021) · The Lancet. Gastroenterology & hepatology · doi:10.1016/s2468-1253(21)00215-6 · Cited by 131 · see citing works
Robot-assisted Radical Nephrectomy: A Systematic Review and Meta-analysis of Comparative Studies
Crocerossa, F., Carbonara, U., Cantiello, F., Marchioni, M., Ditonno, P., Mir, M. C., Porpiglia, F., Derweesh, I., Hampton, L. J., Damiano, R., et al. (2020) · European Urology · doi:10.1016/j.eururo.2020.10.034 · Cited by 124 · see citing works
Surgical Outcomes after Colorectal Surgery for Endometriosis: A Systematic Review and Meta-analysis
Bendifallah, S., Puchar, A., Vesale, E., Moawad, G., Daraï, E., & Roman, H. (2021) · Journal of Minimally Invasive Gynecology · doi:10.1016/j.jmig.2020.08.015 · Cited by 119 · see citing works
Ten circumstances and solutions for finding the sample mean and standard deviation for meta-analysis
Chi, K., Li, M.-Y., Chen, C., Kang, E. Y.-N., & Taiwan, C. (2023) · Systematic Reviews · doi:10.1186/s13643-023-02217-1 · Cited by 129 · see citing works
Moutchia, J., Pokharel, P., Kerri, A., McGaw, K., Uchai, S., Nji, M., & Goodman, M. G. (2020) · PLoS ONE · doi:10.1371/journal.pone.0239802 · Cited by 119 · see citing works
“Where the studies reported only median (IQR or total range) values, we computed mean (SD) using methods previously described [27, 28].”
MethodMahat, R. K., Panda, S., Rathore, V., Swain, S., Yadav, L., & Sah, S. (2021) · Clinical Epidemiology and Global Health · doi:10.1016/j.cegh.2021.100727 · Cited by 117 · see citing works
Fernández‐de‐las‐Peñas, C., Navarro‐Santana, M. J., Plaza‐Manzano, G., Palacios‐Ceña, D., & Arendt‐Nielsen, L. (2021) · Pain · doi:10.1097/j.pain.0000000000002496 · Cited by 118 · see citing works
Fernández, T., Viñuela, M., Vidal, C., & Barrera, F. (2022) · PLoS ONE · doi:10.1371/journal.pone.0263931 · Cited by 117 · see citing works
Ismail, M., Armoiry, X., Tau, N., Zhu, F., Sadeh-Gonik, U., Piotin, M., Blanc, R., Mazighi, M., Bracard, S., Anxionnat, R., et al. (2018) · Journal of NeuroInterventional Surgery · doi:10.1136/neurintsurg-2018-014249 · Cited by 114 · see citing works
Long, J., Yang, Z., Wang, L., Han, Y., Peng, C. Y., Yan, C., & Yan, D. (2020) · BMC Endocrine Disorders · doi:10.1186/s12902-020-00653-x · Cited by 115 · see citing works
Heybati, K., Zhou, F., Ali, S. H., Deng, J., Mohananey, D., Villablanca, P., & Ramakrishna, H. (2022) · British Journal of Anaesthesia · doi:10.1016/j.bja.2022.06.020 · Cited by 115 · see citing works
Ng, E. T., Ang, R. Z., Tran, B. X., Ho, C. S. H., Zhang, Z., Tan, W., Bai, Y., Zhang, M., Tam, W., & Ho, R. (2019) · International Journal of Environmental Research and Public Health · doi:10.3390/ijerph16244970 · Cited by 113 · see citing works
Fang, Q., Ghanouni, P., Anderson, S. E., Touchett, H. N., Shirley, R., Fang, F., & Fang, C. (2019) · Games for Health Journal · doi:10.1089/g4h.2019.0016 · Cited by 114 · see citing works
“50,51 Pooled effect sizes were categorized as small (Hedges’ g < 0.2), moderate (0.2 < Hedges’ g < 0.8), and large (Hedges’ g > 0.8).”
InfluentialBarbosa, E. C., Espírito Santo, P. A., Baraldo, S., & Meine, G. C. (2024) · British Journal of Anaesthesia · doi:10.1016/j.bja.2024.02.005 · Cited by 111 · see citing works
Navarro‐Santana, M. J., Sánchez-Infante, J., Fernández‐de‐las‐Peñas, C., Cleland, J. A., Martín‐Casas, P., & Plaza‐Manzano, G. (2020) · Journal of Clinical Medicine · doi:10.3390/jcm9103300 · Cited by 109 · see citing works
Liu, W., Lin, H., He, X., Chen, L., Dai, Y., Jia, W., Xue, X., Tao, J., & Chen, L. (2020) · Translational Psychiatry · doi:10.1038/s41398-020-0801-2 · Cited by 111 · see citing works
Udomsinprasert, W., Jittikoon, J., Sangroongruangsri, S., & Chaikledkaew, U. (2020) · Journal of Clinical Immunology · doi:10.1007/s10875-020-00899-z · Cited by 108 · see citing works
“For some analyses, the median was converted to mean, IQR was converted to SD, and the range was transformed to SD, according to previously published studies [38, 39].”
MethodYassin, A., Nawaiseh, M. B., Shaban, A., Alsherbini, K. A., El‐Salem, K., Soudah, O., & Abu-Rub, M. (2021) · BMC Neurology · doi:10.1186/s12883-021-02161-4 · Cited by 109 · see citing works
Appel, M., Forsthuber, M., Ramos, R., Widhalm, R., Granitzer, S., Uhl, M., Hengstschläger, M., Stamm, T., & Gundacker, C. (2022) · Journal of Toxicology and Environmental Health, Part B · doi:10.1080/10937404.2021.2009946 · Cited by 104 · see citing works
Kwon, S., Park, J. K., & Koh, Y. H. (2023) · Journal of NeuroEngineering and Rehabilitation · doi:10.1186/s12984-023-01219-3 · Cited by 105 · see citing works
Falz, R., Bischoff, C., Thieme, R., Lässing, J., Mehdorn, M., Stelzner, S., Busse, M., & Gockel, I. (2022) · Journal of Cancer Research and Clinical Oncology · doi:10.1007/s00432-022-04088-w · Cited by 104 · see citing works
“For continuous variables, data for meta-analysis were obtained directly from the study results or on request from articles’ authors or calculated from the mean, variance 95% confidence intervals or median and Interquartile range (Higgins et al. 2021; Luo et al. 2018; Shi et al. 2020; Wan et al. 2014).”
MethodShao, M., Li, X.-M., Liu, F., Tian, T., Luo, J., & Yang, Y. (2020) · Pharmacological Research · doi:10.1016/j.phrs.2020.105107 · Cited by 100 · see citing works
Cheng, I., Sasegbon, A., & Hamdy, S. (2020) · Neuromodulation Technology at the Neural Interface · doi:10.1111/ner.13327 · Cited by 104 · see citing works
“For studies that reported median and interquartile range, the mean and standard deviations were estimated using methods previously described (32,33).”
MethodAntonelli, M., Donelli, D., & Fioravanti, A. (2018) · Rheumatology International · doi:10.1007/s00296-018-4081-6 · Cited by 102 · see citing works
Li, G., Feng, H., Mao, X.-L., Deng, Y., Wang, X.-B., Zhang, Q., Guo, Y., & Xiao, S. (2023) · Journal of Translational Medicine · doi:10.1186/s12967-023-04306-0 · Cited by 99 · see citing works
“If the study presented data in medians and quartiles, the mean and SD values were estimated [20, 21].”
MethodLex, J. R., Edwards, T. C., Packer, T., Jones, G. G., & Ravi, B. (2020) · The Journal of Arthroplasty · doi:10.1016/j.arth.2020.10.010 · Cited by 98 · see citing works
Woldendorp, K., Indja, B., Bannon, P. G., Fanning, J. P., Plunkett, B., & Grieve, S. M. (2021) · European Heart Journal · doi:10.1093/eurheartj/ehab002 · Cited by 97 · see citing works
Omega-3 world map: 2024 update
Schuchardt, J. P., Beinhorn, P., Hu, X. F., Chan, H. M., Roke, K., Bernasconi, A. A., Hahn, A., Sala‐Vila, A., Stark, K. D., & Harris, W. S. (2024) · Progress in Lipid Research · doi:10.1016/j.plipres.2024.101286 · Cited by 100 · see citing works
Nielsen, S., Picco, L., Murnion, B. P., Winters, B. L., Matheson, J., Graham, M., Campbell, G., Parvaresh, L., Khor, K. E., Betz‐Stablein, B., et al. (2022) · Neuropsychopharmacology · doi:10.1038/s41386-022-01322-4 · Cited by 103 · see citing works
Silent Brain Infarcts Following Cardiac Procedures: A Systematic Review and Meta‐Analysis
Indja, B., Woldendorp, K., Vallely, M. P., & Grieve, S. M. (2019) · Journal of the American Heart Association · doi:10.1161/jaha.118.010920 · Cited by 96 · see citing works
Flükiger, J., Hollinger, A., Speich, B., Meier, V., Tontsch, J., Zehnder, T., & Siegemund, M. (2018) · Annals of Intensive Care · doi:10.1186/s13613-018-0437-z · Cited by 92 · see citing works
Bakaloudi, D. R., Chrysoula, L., Kotzakioulafi, E., Theodoridis, X., & Chourdakis, M. (2021) · Nutrients · doi:10.3390/nu13051514 · Cited by 92 · see citing works
Maski, K. P., Trotti, L. M., Kotagal, S., Auger, R. R., Swick, T. J., Rowley, J. A., Hashmi, S. D., & Watson, N. F. (2021) · Journal of Clinical Sleep Medicine · doi:10.5664/jcsm.9326 · Cited by 92 · see citing works
Wang, J., Hu, K., Wang, Y., Wu, Y., Bao, E., Wang, J., Tan, C., & Tang, T. (2023) · Journal of Robotic Surgery · doi:10.1007/s11701-023-01714-8 · Cited by 92 · see citing works
“When continuous variables were reported as median and quartiles, we calculated the mean ± standard deviation using appropriate mathematical methods [31, 32].”
MethodBenefits of physical activity in children and adolescents with type 1 diabetes: A systematic review
Absil, H., Baudet, L., Robert, A. R., & Lysy, P. A. (2019) · Diabetes Research and Clinical Practice · doi:10.1016/j.diabres.2019.107810 · Cited by 96 · see citing works
Su, M., Jia, Y., Li, Y., Zhou, D., & Jia, J. (2020) · Respiratory Care · doi:10.4187/respcare.07097 · Cited by 91 · see citing works
Effects of ocean acidification on Antarctic marine organisms: A meta‐analysis
Hancock, A. M., King, C. K., Stark, J. S., McMinn, A., & Davidson, A. T. (2020) · Ecology and Evolution · doi:10.1002/ece3.6205 · Cited by 92 · see citing works
Qin, R., He, L., Yang, Z., Jia, N., Chen, R., Xie, J., Fu, W., Chen, H., Lin, X., Huang, R., et al. (2022) · Clinical Reviews in Allergy & Immunology · doi:10.1007/s12016-021-08908-8 · Cited by 93 · see citing works
“For the meta-analysis, we transformed the format of laboratory variables presented as “median [interquartile range (IQR)]” into that of “mean [standard deviation (SD)]” [18, 19].”
MethodLowe, E. B., Groves, R. L., & Gratton, C. (2021) · Agriculture Ecosystems & Environment · doi:10.1016/j.agee.2020.107290 · Cited by 90 · see citing works
“If a study reported the median and interquartile range (IQR), we used an online calculator based on methods developed by Luo et al. (2018) and Shi et al. (2020) which are accurate for skewed data, to backcalculate an estimate of the mean and standard deviation.”
MethodHuang, Y., Yin, X.-S., & Li, Z. (2022) · Frontiers in Immunology · doi:10.3389/fimmu.2022.1090305 · Cited by 90 · see citing works
Factors related to the resilience and mental health of adult cancer patients: a systematic review
Tamura, S., Suzuki, K., Ito, Y., & Fukawa, A. (2021) · Supportive Care in Cancer · doi:10.1007/s00520-020-05943-7 · Cited by 89 · see citing works
“Further, when the median and quartile were described, these values were converted into the mean and standard deviation by the conversion formula of previous studies [15, 16] and such articles were included in the meta-analysis.”
MethodProtein intake and physical function in older adults: A systematic review and meta-analysis
Coelho-Júnior, H. J., Calvani, R., Tosato, M., Landi, F., Picca, A., & Marzetti, E. (2022) · Ageing Research Reviews · doi:10.1016/j.arr.2022.101731 · Cited by 86 · see citing works
Brain Selenium in Alzheimer’s Disease (BRAIN SEAD Study): a Systematic Review and Meta-Analysis
Varikasuvu, S. R., Prasad, S., Kothapalli, J., & Munikumar, M. (2018) · Biological Trace Element Research · doi:10.1007/s12011-018-1492-x · Cited by 86 · see citing works
Louwen, C., Reidlinger, D. P., & Milne, N. (2023) · BMC Medical Education · doi:10.1186/s12909-023-04003-y · Cited by 97 · see citing works
Triglyceride-glucose index and obstructive sleep apnea: a systematic review and meta-analysis
Behnoush, A. H., Khalaji, A., Ghondaghsaz, E., Masrour, M., Varniab, Z. S., Khalaji, S., & Cannavò, A. (2024) · Lipids in Health and Disease · doi:10.1186/s12944-024-02005-3 · Cited by 86 · see citing works
“In the case of median and interquartile range reporting, they were converted to the mean and standard deviation using methods developed by Luo et al. [27] and Wan et al. [28].”
MethodMalignant transformation of oral leukoplakia: Systematic review and comprehensive meta‐analysis
de Barros, L. A. P., Ramos‐García, P., González‐Moles, M. Á., Urízar, J. M. A., & Warnakulasuriya, S. (2024) · Oral Diseases · doi:10.1111/odi.15140 · Cited by 100 · see citing works
Carbonara, U., Srinath, M., Crocerossa, F., Ferro, M., Cantiello, F., Lucarelli, G. T., Porpiglia, F., Battaglia, M., Ditonno, P., & Riccardo Autorino, B. (2021) · World Journal of Urology · doi:10.1007/s00345-021-03687-5 · Cited by 85 · see citing works
“[11] was used, while, for time-based data or other data suspected of being skewed, the Box–Cox and quantile estimation methods described by McGarth et al.”
MethodRawat, D., Roy, A., Maitra, S., Gulati, A., Khanna, P., & Baidya, D. K. (2021) · Diabetes & Metabolic Syndrome Clinical Research & Reviews · doi:10.1016/j.dsx.2021.102324 · Cited by 84 · see citing works
Distribution of delirium motor subtypes in the intensive care unit: a systematic scoping review
la Cour, K. N., Andersen‐Ranberg, N. C., Weihe, S., Poulsen, L. M., Mortensen, C. B., Kjer, C. K. W., Collet, M. O., Estrup, S., & Mathiesen, O. (2022) · Critical Care · doi:10.1186/s13054-022-03931-3 · Cited by 85 · see citing works
Jayedi, A., Zeraattalab-Motlagh, S., Ganjeh, B. J., Hosseini, Y., Jibril, A. T., Shahinfar, H., Mirrafiei, A., Hosseini, F. Z., & Shab‐Bidar, S. (2022) · American Journal of Clinical Nutrition · doi:10.1093/ajcn/nqac066 · Cited by 85 · see citing works
van Reijen, N. S., Ponchant, K., Ubbink, D. T., & Koelemay, M. J. W. (2019) · European Journal of Vascular and Endovascular Surgery · doi:10.1016/j.ejvs.2019.03.040 · Cited by 86 · see citing works
Qu, Y., Ma, Y., Huang, Y., Ou, Y., Shen, X., Chen, S.-D., Dong, Q., Tan, L., & Yu, J. (2021) · Neuroscience & Biobehavioral Reviews · doi:10.1016/j.neubiorev.2021.07.007 · Cited by 82 · see citing works
- Authors
- Luo, D., Wan, X., Liu, J., & Tong, T.
- Affiliations
- Hong Kong Baptist University (HK)
- Corresponding author
- Wan, Xiang
- Venue
- Statistical Methods in Medical Research
- Publisher
- SAGE Publications
- Published
- 2016-09-27
- Volume
- 27
- Issue
- 6
- Pages
- 1785-1805
- ISSN
- 0962-2802 (ISSN-L)
- 1477-0334
- OpenAlex
- W1534181333
- Cited by
- 4,066
- References
- 21
- Citations by year
- 2026: 789 · 2025: 833 · 2024: 700 · 2023: 601 · 2022: 462 · 2021: 379 · 2020: 188 · 2019: 91 · 2018: 20 · 2017: 1
- FWCI
- 34.66
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Statistical Methods in Medical Research (publishedVersion)
- PubMed (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Funders
- Hong Kong Baptist University (FRG2/14-15/077, FRG1/14-15/084, FRG2/15-16/019)
- Topics
- Social Sciences › Decision Sciences › Statistics, Probability and Uncertainty › Meta-analysis and systematic reviews
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods in Epidemiology
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods in Clinical Trials
- Keywords
- sample mean estimation, meta-analysis, median, sample size, standard deviation estimation, optimal estimators, evidence-based medicine
- MeSH terms
- Algorithms, Sampling Studies, Meta-Analysis as Topic, Sample Size, Evidence-Based Medicine
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
