The DOI matches its Crossref record; 21 of the 21 references it cites were found in a registry or an index.
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.
Overview
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
Verification
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?
The cited source says what the claim attributes to it.
In the citing paper
“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.
Citations
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 65,417
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×
“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
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×
“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
Guyatt, G. H. (1992) · JAMA · doi:10.1001/jama.1992.03490170092032 · Cited by 4,577 · cited 4×
“’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
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
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
Johnson, R. R. (1976) · UCLA Biblioteca de Ingenieria Civil · Cited by 160
Research works printed but not linked: 4
- 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
- Sasidharan P, 2002, J Assoc Phys India, 50, 554
Cited by
Sorted by citations
Items 501–600 of 1,006
Partelli, S., Ricci, C., Cinelli, L., Montorsi, R. M., Ingaldi, C., Andreasi, V., Crippa, S., Alberici, L., Casadei, R., & Falconi, M. (2021) · The American Journal of Surgery · doi:10.1016/j.amjsurg.2021.03.066 · Cited by 31
Risk Factors for Delirium after Vascular Surgery: A Systematic Review and Meta-Analysis
Visser, L., Prent, A., Banning, L. B. D., van Leeuwen, B. L., Zeebregts, C. J., & Pol, R. A. (2021) · Annals of Vascular Surgery · doi:10.1016/j.avsg.2021.03.034 · Cited by 30
Meng, C., Du, C., Peng, L., Li, J., Li, J., Li, Y., & Wu, J. (2021) · Frontiers in Oncology · doi:10.3389/fonc.2021.667985 · Cited by 31
“When continuous variables reported as other forms in the main literature, we calculated the mean and standard deviation (6).”
MethodAvendaño‐Coy, J., Muñoz, P. L., Serrano‐Muñoz, D., Comino‐Suárez, N., Avendaño-López, C., & Espinosa, N. M. M. (2021) · Journal of Tissue Viability · doi:10.1016/j.jtv.2021.12.002 · Cited by 31
Mitchell, C., Mitchell, C., Cheuk, S. J., O’Donnell, C. M., Bampoe, S., & Walker, D. A. (2022) · Perioperative Medicine · doi:10.1186/s13741-022-00243-6 · Cited by 38
Cavaleri, D., Bartoli, F., Capogrosso, C. A., Guzzi, P., Moretti, F., Riboldi, I., Misiak, B., Kishi, T., Rubín, R. T., Fuchs, D., et al. (2022) · Progress in Neuro-Psychopharmacology and Biological Psychiatry · doi:10.1016/j.pnpbp.2022.110633 · Cited by 32
Shobeiri, P., Seyedmirzaei, H., Karimi, N., Rashidi, F., Teixeira, A. L., Brand, S., Bahmani, D. S., & Rezaei, N. (2022) · European journal of medical research · doi:10.1186/s40001-022-00814-9 · Cited by 35
Ryan, O. K., Doogan, K. L., Ryan, É. J., Donnelly, M., Reynolds, I. S., Creavin, B., Davey, M. G., Kelly, M. E., Kennelly, R. P., Hanly, A. M., et al. (2023) · European Journal of Surgical Oncology · doi:10.1016/j.ejso.2023.04.003 · Cited by 31
Salpingectomy at the Time of Cesarean Delivery
Roeckner, J. T., Sawangkum, P. S., Sanchez‐Ramos, L., & Duncan, J. R. (2020) · Obstetrics and Gynecology · doi:10.1097/aog.0000000000003673 · Cited by 31
Yang, M., Wang, C., Zhao, G., Kong, D., Liu, L., Yuan, S., Chen, W., Feng, C., & Li, Z. (2022) · Current Neuropharmacology · doi:10.2174/1570159x20666220706101021 · Cited by 31
“The outcome values were converted to mean and standard deviation (SD) if they were not in the required forms [50-52].”
Efficacy of probiotics in the management of halitosis: a systematic review and meta-analysis
Huang, N., Li, J., Qiao, X., Wu, Y., Liu, Y., Wu, C., & Li, L. (2022) · BMJ Open · doi:10.1136/bmjopen-2022-060753 · Cited by 30
Wheeler, G., Grassberger, C., Samers, J., Dwyer, M. K. R., Wiltshire, K. L., Daly, P., Álvarez, B., Campbell, B. A., Kerr, A. J., Kron, T., et al. (2023) · International Journal of Radiation Oncology*Biology*Physics · doi:10.1016/j.ijrobp.2023.04.024 · Cited by 30
Wen, J., Ding, X., Liu, C., Jiang, W., Xu, Y., Wei, X., & Liu, X. (2023) · PLoS ONE · doi:10.1371/journal.pone.0294292 · Cited by 30
Yu, M., Ma, Y., Han, F., & Gao, X. (2023) · PLoS ONE · doi:10.1371/journal.pone.0292832 · Cited by 38
“If the mean (M) and standard deviation (SD) were not reported in the study, the estimated values were used in the meta-analysis [24, 25].”
Zong, J., Ye, W., Yu, J., Zhang, X., Cui, J., Chen, Z., Li, Y., Wang, S., Ran, S., Niu, Y., et al. (2024) · Transplantation · doi:10.1097/tp.0000000000005017 · Cited by 30
“When mean values were not provided, medians and IQRs were converted to means and SDs using the established methods described by Luo et al 8 and Wan et al. 9 When outcomes were reported solely as percentages, absolute numbers were estimated.”
He, Z., Yang, X., Li, Y., Zhao, X., Li, J., & Li, B. (2024) · Epilepsia Open · doi:10.1002/epi4.12939 · Cited by 30
Guo, L., Wang, J., Li, J., Yao, J., & Zhao, H. (2024) · Frontiers in Immunology · doi:10.3389/fimmu.2024.1455346 · Cited by 30
Wang, X., Si, J., Li, Y., Tse, P., Zhang, G., Wang, X., Ren, J., Xu, J., Sun, J., & Yao, X. (2025) · Diabetology & Metabolic Syndrome · doi:10.1186/s13098-025-01819-0 · Cited by 30
“For data presented as median values with interquartile ranges (IQR), we estimated the mean and standard deviation using validated meth-ods for skewed distributions [51, 52].”
Țăruș, A., Tinică, G., Bacusca, A., Artene, B., Popa, I., & Burlacu, A. (2020) · Journal of cardiac surgery · doi:10.1111/jocs.14814 · Cited by 22
Vésale, E., Roman, H., Moawad, G., Benoit, L., Touboul, C., Daraï, É., & Bendifallah, S. (2020) · Journal of Minimally Invasive Gynecology · doi:10.1016/j.jmig.2020.07.019 · Cited by 31
Chen, X., Lu, M., Xu, W., Wang, X., Xue, M., Dai, J., Zhang, Z., & Chen, G. (2020) · Orthopaedics & Traumatology Surgery & Research · doi:10.1016/j.otsr.2020.06.012 · Cited by 30
Rehabilitation therapy for patients with glioma
Zhao, K., Yu, C., Gan, Z., Huang, M., Wu, T., & Zhao, N. (2020) · Medicine · doi:10.1097/md.0000000000023087 · Cited by 30
Cochlear Implantation in Meniere's Disease: A Systematic Review and Meta‐Analysis
Villavisanis, D. F., Mavrommatis, M. A., Berson, E. R., Bellaire, C. P., Rutland, J. W., Fan, C. J., Wanna, G. B., & Cosetti, M. K. (2021) · The Laryngoscope · doi:10.1002/lary.29393 · Cited by 31
“range, which were used to estimate the mean and standard deviation in accordance with Luo et al.(17) and Wan et al.”
MethodInfluentialQian, Y., Bi, Y., Liu, S., Li, X., Dong, S., & Ju, M. (2021) · Annals of Palliative Medicine · doi:10.21037/apm-21-338 · Cited by 29
“Pooled odds ratios (ORs) and 95% CIs were calculated to express binary outcome results, while the weighted mean difference (WMD) and 95% CIs were used to express continuous outcome results (11,12).”
MethodZhu, W., Dai, Y., Huang, M. J., & Li, J. (2021) · Journal of Nursing Scholarship · doi:10.1111/jnu.12691 · Cited by 30
He, H., Ma, Y., Zheng, Z., Deng, X., Zhu, J., & Wang, Y. (2021) · International Journal of Nursing Studies · doi:10.1016/j.ijnurstu.2021.104120 · Cited by 30
Ramos‐García, P., & González‐Moles, M. Á. (2022) · Cancers · doi:10.3390/cancers14030479 · Cited by 30
Shen, W., Fan, X., Wang, L., & Zhang, Y. (2022) · Frontiers in Pharmacology · doi:10.3389/fphar.2022.816333 · Cited by 30
Yu, R., Wang, Z., Ma, M., Xu, P., Liu, L., Tinkov, A. A., Lei, X. G., & Zhou, J. (2022) · Antioxidants · doi:10.3390/antiox11071263 · Cited by 32
Barone, M., Iannone, A., Cristofori, F., Dargenio, V. N., Indrio, F., Verduci, E., Leo, A. D., & Francavilla, R. (2022) · Nutrition Reviews · doi:10.1093/nutrit/nuac052 · Cited by 31
Effects of SGLT2 inhibitors on hepatic fibrosis and steatosis: A systematic review and meta-analysis
Zhou, P., Tan, Y., Hao, Z., Xu, W., Zhou, X., & Yu, J. (2023) · Frontiers in Endocrinology · doi:10.3389/fendo.2023.1144838 · Cited by 35
Chen, C., Zhou, N., Hu, N., Feng, J., & Wang, X. (2023) · Neuropsychiatric Disease and Treatment · doi:10.2147/ndt.s401032 · Cited by 37
“Meanwhile, when the MD and SD change scores were not provided by the study authors, we calculated the MD and SD of the mean change in depression scores using the following formulas: https://doi.org/10.2147/NDT.S401032 DovePress Neuropsychiatric Disease and Treatment 2023:19 588 Powered by TCPDF (www.tcpdf.org) The dat…”
MethodInfluentialBehnoush, A. H., Khalaji, A., Bahiraie, P., Alehossein, P., Shobeiri, P., Peisepar, M., & Cannavò, A. (2023) · Hypertension Research · doi:10.1038/s41440-023-01402-y · Cited by 31
Partial ALPPS versus complete ALPPS for staged hepatectomy
Wu, X., Rao, J., Zhou, X., Deng, R., & Ma, Y. (2019) · BMC Gastroenterology · doi:10.1186/s12876-019-1090-1 · Cited by 30
Detecting the skewness of data from the sample size and the five-number summaryPreprint
Shi, J., Luo, D., Wan, X., Liu, Y., Liu, J., Bian, Z., & Tong, T. (2020) · arXiv (Cornell University) · Cited by 30
Self-citationLee, Y., Liao, W., Yang, S., Luo, C., Tsai, Y., Tsai, M., Lee, Y., & Hsin, L. (2021) · Scientific Reports · doi:10.1038/s41598-021-03483-6 · Cited by 29
Wang, H., Chen, X., Xu, J., & Yao, K. (2023) · PLoS ONE · doi:10.1371/journal.pone.0284181 · Cited by 29
Liu, S., Chen, J., Shi, H., Li, J., Zeng, G., Liu, W., Hu, W., Li, S., Gao, W., Song, W., et al. (2024) · Canadian Journal of Anesthesia/Journal canadien d anesthésie · doi:10.1007/s12630-024-02696-3 · Cited by 29
“20 If no skewness was seen in the data, we converted the data into means and standard deviations according to the method proposed by Shi et al ., 21,22 Luo et al ., 23 and Wan et al .”
Serpa, F., Rivera, A., Fernandes, J. M., Braga, M. A. P., Araújo¹, B. D. S. G., Félix, I. F., Ferro, E. G., ZIMETBAUM, P. J., d’Ávila, A., & Kramer, D. B. (2024) · Heart Rhythm · doi:10.1016/j.hrthm.2024.08.027 · Cited by 29
Liao, Y., Chiu, H., Huang, F., Chang, Y., Huang, Y., Wei, P., Wang, W., Hung, C., & Tung, H. (2025) · Journal of the American Geriatrics Society · doi:10.1111/jgs.19425 · Cited by 34
Zhang, G., Zhang, K., Cui, W., Hong, Y., & Zhang, Z. (2018) · Journal of Clinical Anesthesia · doi:10.1016/j.jclinane.2018.08.008 · Cited by 30
Ryan, O. K., Ryan, É. J., Creavin, B., Boland, M. R., Kelly, M. E., & Winter, D. C. (2020) · Techniques in Coloproctology · doi:10.1007/s10151-020-02172-2 · Cited by 29
Prognostic value of liver biochemical parameters for COVID-19 mortality
Lin, Y., Chen, B., Wang, Y., Yang, Y., Zeng, J., Deng, G., Deng, Y., & Zeng, F. (2020) · Annals of Hepatology · doi:10.1016/j.aohep.2020.10.007 · Cited by 29
Peng, R., Li, H., Yang, L., Zeng, L., Yi, Q., Xu, P., Pan, X., & Zhang, L. (2021) · PLoS ONE · doi:10.1371/journal.pone.0245317 · Cited by 33
Gastric dysrhythmia in gastroesophageal reflux disease: a systematic review and meta-analysis
Bhat, S., Varghese, C., Carson, D. A., Hayes, T. C. L., Gharibans, A. A., Andrews, C. N., & O’Grady, G. (2021) · Esophagus · doi:10.1007/s10388-021-00820-6 · Cited by 27
Zhang, Y., Zhang, Y., Zhang, Y., Ye, W., & Korivi, M. (2021) · International Journal of Environmental Research and Public Health · doi:10.3390/ijerph18136723 · Cited by 29
“If no response was received from the author, standard errors (SE) were converted to SD, and the quartile data were converted to mean and SD [38,39].”
MethodRobotic Esophagectomy. A Systematic Review with Meta-Analysis of Clinical Outcomes
Manigrasso, M., Vertaldi, S., Marello, A., Antoniou, S. A., Francis, N. K., Palma, G. D. D., & Milone, M. (2021) · Journal of Personalized Medicine · doi:10.3390/jpm11070640 · Cited by 29
Steroids use in non-oxygen requiring COVID-19 patients: a systematic review and meta-analysis
Sahu, A. K., Mathew, R., Bhat, R., Malhotra, C., Nayer, J., Aggarwal, P., & Galwankar, S. C. (2021) · QJM · doi:10.1093/qjmed/hcab212 · Cited by 29
Shorey, S., Downe, S. M., Chua, J. Y. X., Byrne, S. O., Fobelets, M., & Lalor, J. (2021) · Trauma Violence & Abuse · doi:10.1177/15248380211060808 · Cited by 30
Len, P., Iskakova, G., Sautbayeva, Z., Kussanova, A., Tauekelova, A., Sugralimova, M., Dautbaeva, A. S., Abdieva, M. M., Ponomarev, E. D., Tikhonov, A., et al. (2022) · Frontiers in Cardiovascular Medicine · doi:10.3389/fcvm.2022.794092 · Cited by 29
Deng, J., Heybati, K., Ramaraju, H. B., Zhou, F., Rayner, D. G., & Heybati, S. (2022) · Infection · doi:10.1007/s15010-022-01825-8 · Cited by 29
Mashhadi, N. S., Darand, M., Rouhani, M. H., Yahay, M., Feltham, B. A., & Saraf‐Bank, S. (2022) · Behavioural Brain Research · doi:10.1016/j.bbr.2022.114083 · Cited by 31
O'Donnell, J. P., Gasior, S. A., Davey, M. G., O'Malley, E., Lowery, A., McGarry, J., O'Connell, A. M., Kerin, M. J., & McCarthy, P. (2022) · European Journal of Radiology · doi:10.1016/j.ejrad.2022.110561 · Cited by 29
Dorsch, S., Carling, C., Cao, Z., Fanayan, E., Graham, P. L., McCluskey, A., Schurr, K., Scrivener, K., & Tyson, S. F. (2022) · Journal of physiotherapy · doi:10.1016/j.jphys.2022.11.008 · Cited by 29
Zawiah, M., Khan, A. H., Farha, R. K. A., Abubakar, U., & Bitar, A. N. (2023) · Current Medical Research and Opinion · doi:10.1080/03007995.2023.2174327 · Cited by 29
Liu, H., Zhu, J., Wen, J., & Fu, Q. (2023) · Medicine · doi:10.1097/md.0000000000032981 · Cited by 29
“If the data were shown as median, minimum to maximum or inter-quartile ranges, we converted them to mean and standard deviation.[18,19] When data were presented as a graph, we extracted the information with digitizing software (GetData Graph Digitizer 2.”
MethodDiagnostic value of IL-6 for patients with asthma: a meta-analysis
Pan, R., Kuai, S., Li, Q., Zhu, X., Wang, T., & Cui, Y. (2023) · Allergy Asthma and Clinical Immunology · doi:10.1186/s13223-023-00794-3 · Cited by 28
“reported median and interquartile range, we analyzed the mean and standard deviation mathematically [16, 17].”
MethodRadiographic Outcomes of Robot-Assisted Versus Conventional Total Knee Arthroplasty
Riantho, A., Butarbutar, J. C. P., Fidiasrianto, K., Elson, E., Irvan, I., Haryono, H., & Prasetio, J. N. (2023) · JBJS Open Access · doi:10.2106/jbjs.oa.23.00010 · Cited by 28
Davergne, T., Meidinger, P., Dechartres, A., & Gossec, L. (2023) · Journal of Medical Internet Research · doi:10.2196/45207 · Cited by 38
Lin, J.-W., Chen, C.-T., Hsieh, M., Lee, I.-H., Yen, D. H.-T., Cheng, H., & Hsu, T. (2023) · BMJ Open · doi:10.1136/bmjopen-2023-072736 · Cited by 28
Circulating Surfactant Protein D: A Biomarker for Acute Lung Injury?
Elmore, A., Almuntashiri, A., Wang, X., Almuntashiri, S., & Zhang, D. (2023) · Biomedicines · doi:10.3390/biomedicines11092517 · Cited by 28
Drug-Induced Progressive Multifocal Leukoencephalopathy (PML): A Systematic Review and Meta-Analysis
Rindi, L. V., Zaçe, D., Braccialarghe, N., Massa, B., Barchi, V., Iannazzo, R., Fato, I., Maria, F. D., Kontogiannis, D., Malagnino, V., et al. (2024) · Drug Safety · doi:10.1007/s40264-023-01383-4 · Cited by 31
“When median (interquartile range, IQR) of treatment duration was given, we calculated mean and standard deviation (SD) in order to be able to include the studies in the same meta-analysis [14, 15].”
The role of the NLRP3 inflammasome in atherosclerotic disease: Systematic review and meta-analysis
Khair, M., Khair, M., Vangaveti, V., & Malabu, U. H. (2024) · Journal of Cardiology · doi:10.1016/j.jjcc.2024.03.003 · Cited by 28
Chen, X., Zhi, H., Wang, X., Zhou, Z., Luo, H., Li, J., Sehmi, R., O’Byrne, P. M., & Chen, R. (2024) · Lung · doi:10.1007/s00408-024-00717-y · Cited by 28
“[36–39] There was no dispute after two reviewers consulted with the statistician.”
Xu, Y., Ji, T., Li, X., Yang, Y., Zheng, L., Qiu, Y., Chen, L., & Li, G. (2024) · International Journal of Nursing Studies · doi:10.1016/j.ijnurstu.2024.104849 · Cited by 32
Jones, P. A. T., Moolyk, A. N., Ruchat, S.-M., Ali, M. U., Fleming, K., Meyer, S., Sjwed, T. N., Wowdzia, J. B., Maier, L. E., Mottola, M. F., et al. (2024) · British Journal of Sports Medicine · doi:10.1136/bjsports-2024-108483 · Cited by 33
Reitano, G., Tumminello, A., Ghaffar, U., Saggionetto, G., Taverna, A., Mangiacavallo, F., Ahmed, M. E., Basourakos, S. P., Carletti, F., Minardi, D., et al. (2025) · European Urology Open Science · doi:10.1016/j.euros.2025.02.003 · Cited by 30
“Mean and SD were estimated when these were not available using the methods of Luo et al [12] and Wan et al [13].”
Aeschlimann, F. A., Chong, S., Lyons, T. W., Beinvogl, B. C., Góez-Mogollón, L. M., Tan, S., & Laxer, R. M. (2018) · The Journal of Pediatrics · doi:10.1016/j.jpeds.2018.08.065 · Cited by 28
“The systemic review and meta-analyses were performed according to the Cochrane Handbook for Systematic Reviews of Interventions and the PRISMA statement.18 Means were estimated from median and IQR.19,20 Statistical analysis was performed using STATA v 14.2 (StataCorp, College Station, Texas).”
MethodInfluentialZhao, D., Khawaja, A. T., Jin, L., Chan, K. W., Tonetti, M. S., Tang, S. C. W., & Pelekos, G. (2019) · Clinical Oral Investigations · doi:10.1007/s00784-019-03066-w · Cited by 28
Goldsworthy, S., Palmer, S., Latour, J. M., McNair, H. A., & Cramp, M. (2020) · Radiography · doi:10.1016/j.radi.2020.03.002 · Cited by 30
Wang, Y., Zhang, X., Xie, X., Chen, W., Li, M., Diao, D., & Dang, C. (2020) · Cancer Biology & Therapy · doi:10.1080/15384047.2020.1838032 · Cited by 30
“The difference between groups was compared by the sample sizes, medians, and mid-quartile ranges, and the P value was calculated using Luo’s methods.(20) P values less than 0.”
MethodYan, W. S., Chen, D., Bigambo, F. M., Wei, H., Wang, X., & Xia, Y. (2021) · BMC Infectious Diseases · doi:10.1186/s12879-021-05847-9 · Cited by 28
“The converter considered the sample size and proved to be the closest to the actual estimation method [27, 28].”
BackgroundMarasini, S., Britten‐Jones, A. C., Dean, S. J., Swift, S., & Craig, J. P. (2021) · The Ocular Surface · doi:10.1016/j.jtos.2021.03.002 · Cited by 28
Zhou, Y., Feng, H., Li, G., Xu, C., Wu, Y., & Li, H. (2021) · International Journal of Nursing Practice · doi:10.1111/ijn.12966 · Cited by 28
Miller, C. T., Owen, P. J., Than, C. A., Ball, J., Sadler, K., Piedimonte, A., Benedetti, F., & Belavý, D. L. (2021) · Sports Medicine · doi:10.1007/s40279-021-01526-6 · Cited by 29
“Where post-intervention SD was unavailable, pre-intervention SD was utilised based on Cochrane guidelines [36, 37].”
MethodThong, D., Halim, Z., Chia, J., Chua, F., & Wong, A. (2021) · Journal of Parenteral and Enteral Nutrition · doi:10.1002/jpen.2324 · Cited by 28
Comparison of Different Anti-Demodex Strategies: A Systematic Review and Meta-Analysis
Li, J., Wei, E., Reisinger, A., French, L. E., Clanner-Engelshofen, B. M., & Reinholz, M. (2022) · Dermatology · doi:10.1159/000526296 · Cited by 28
Jayedi, A., Zeraattalab-Motlagh, S., Shahinfar, H., Gregg, E. W., & Shab‐Bidar, S. (2023) · American Journal of Clinical Nutrition · doi:10.1016/j.ajcnut.2023.03.018 · Cited by 35
Aliseda, D., Sapisochín, G., Martí‐Cruchaga, P., Zozaya, G., Blanco, N., Goh, B. K. P., & Rotellar, F. (2023) · Annals of Surgical Oncology · doi:10.1245/s10434-023-13498-0 · Cited by 28
Tsakos, E., Xydias, E. M., Ziogas, A. C., Sorrentino, F., Nappi, L., Vlachos, N., & Daniilidis, A. (2023) · Journal of Clinical Medicine · doi:10.3390/jcm12124134 · Cited by 32
Machado, M. F., Felix, N. S., Melo, P., Gauza, M. D. M., Calomeni, P. A.-K. B., Generoso, G., Khatri, S., Altmayer, S., Blankstein, R., Bittencourt, M. S., et al. (2023) · Circulation Cardiovascular Imaging · doi:10.1161/circimaging.123.015800 · Cited by 30
Hughes, S. M., Levy, C., Katz, R., Lokken, E. M., Anahtar, M. N., Hall, M. B., Bradley, F., Castle, P. E., Cortez, V. A., Doncel, G. F., et al. (2022) · BMC Medicine · doi:10.1186/s12916-022-02532-9 · Cited by 27
Jensen, C. F. (2022) · Nutrition Reviews · doi:10.1093/nutrit/nuac096 · Cited by 27
Quantitative impact of frenotomy on breastfeeding: a systematic review and meta-analysis
Cordray, H., Raol, N., Mahendran, G. N., Tey, C. S., Nemeth, J. K., Sutcliffe, A. G., Ingram, J. C., & Sharp, W. G. (2023) · Pediatric Research · doi:10.1038/s41390-023-02784-y · Cited by 30
“For studies that reported summary statistics as median (IQR), the Luo 32 and Shi 33 derivation methods were used to estimate the mean (SD).”
Panunzio, A., Labate, C., Zacheo, F., Orlando, R., Rizzo, F. L., Porcaro, A. B., Migliorini, F., Pagliarulo, V., & Tafuri, A. (2023) · International Journal of Impotence Research · doi:10.1038/s41443-023-00798-y · Cited by 28
Czyż, S. H., Wójcik, A. M., Solarská, P., & Kiper, P. (2024) · Scientific Reports · doi:10.1038/s41598-024-65753-3 · Cited by 38
“If SEM (standard error of the mean) was available, we converted it into SD. Similarly, if quartiles were available, we converted these with Mean Variance calculator 30–33 .”
MethodDereje, D., Abessa, T. G., Lamba, D., Triccas, L. T., & Bonnechère, B. (2025) · Journal of NeuroEngineering and Rehabilitation · doi:10.1186/s12984-025-01603-1 · Cited by 34
“If the median and range were reported instead of the mean and standard deviation, these values were estimated using the methods developed by Luo et al. and Wan et al. [41, 43].”
Cai, B., Luo, X., Zhang, P., Luan, Y., Cai, X., & He, X. (2021) · Nutrition Metabolism and Cardiovascular Diseases · doi:10.1016/j.numecd.2021.06.013 · Cited by 27
Gravier, F., Smondack, P., Boujibar, F., Prieur, G., Médrinal, C., Combret, Y., Muir, J., Baste, J. M., Cuvelier, A., Debeaumont, D., et al. (2021) · Journal of physiotherapy · doi:10.1016/j.jphys.2021.12.010 · Cited by 27
Kow, C. S., Lee, L., Ramachandram, D. S., Hasan, S. S., Ming, L. C., & Goh, H. P. (2021) · Immunity Inflammation and Disease · doi:10.1002/iid3.562 · Cited by 27
“When the duration of hospital stay was not reported in mean and standard deviation, we first estimated the skewness of the data distribution using median and interquartile range with the method developed by Shi et al.8; if the distribution of data was significantly skewed from normality, the trial was excluded for ana…”
MethodRademacher, J., Glaubitz, S., Zechel, S., Oettler, M., Tampe, B., Schmidt, J., & Korsten, P. (2022) · Clinical and Experimental Rheumatology · doi:10.55563/clinexprheumatol/2ao5ze · Cited by 27
Outcomes of enhanced recovery after surgery in lung cancer: A systematic review and meta-analysis
Zhang, W., Zhang, Y., Qin, Y., & Shi, J. (2022) · Asia-Pacific Journal of Oncology Nursing · doi:10.1016/j.apjon.2022.100110 · Cited by 27
Sarcopenic obesity and therapeutic outcomes in gastrointestinal surgical oncology: A meta-analysis
Wang, P., Wang, S., Ma, Y., Li, H., Liu, Z., Lin, G., Li, X., Yang, F., & Qiu, M. (2022) · Frontiers in Nutrition · doi:10.3389/fnut.2022.921817 · Cited by 29
The Status of Oxidative Stress in Patients with Alcohol Dependence: A Meta-Analysis
Yang, M., Zhou, X., Tan, X., Huang, X., Lu, Y., Zhang, Z., Yang, Y., Xu, M., Wan, Y., & Li, Z. (2022) · Antioxidants · doi:10.3390/antiox11101919 · Cited by 29
Fu, Y., Qiu, J., Yu, Y., Wu, D., & Zhang, T. (2022) · Frontiers in Surgery · doi:10.3389/fsurg.2022.989065 · Cited by 27
“The inclusion criteria were as followed: (1) comparative study of RPD and OPD; (2) papers written in English; (3) papers published in or after 2016.”
BackgroundClinical Indicators for Asthma-COPD Overlap: A Systematic Review and Meta-Analysis
Peng, J., Wang, M., Wu, Y., Shen, Y., & Chen, L. (2022) · International Journal of COPD · doi:10.2147/copd.s374079 · Cited by 27
“…were offered only in a study, we converted the data into approximate means with standard deviations (SDs) according to the validated statistical method, 13,14 and if there were two or more subgroups in a study, we calculated the combined means and SDs according to the Cochrane Handbook guidelines.”
Liang, S., Mijatovic, J., Li, A., Koemel, N. A., Nasir, R., Toniutti, C., Bell-Anderson, K. S., Skilton, M. R., & O’Leary, F. (2022) · Nutrients · doi:10.3390/nu15010076 · Cited by 28
Steinkamp, M. P., Lagutina, I. V., Brayer, K. J., Schultz, F. A., Burke, D., Pankratz, V. S., Adams, S. F., Hudson, L. G., Ness, S. A., & Wandinger‐Ness, A. (2023) · Cancer Research Communications · doi:10.1158/2767-9764.crc-22-0300 · Cited by 27
“For uniformity, average and SEM for MDC levels were estimated from the listed median and interquartile range using an online estimator (31).”
Tian, Y., Ran, H., Wen, X., Fu, G., Zhou, X., Liu, R., & Pan, T. (2023) · Frontiers in Nutrition · doi:10.3389/fnut.2023.1179432 · Cited by 27
Luan, J., Wu, M., Wang, X., Qiao, L., Guo, G., & Zhang, C. (2020) · Radiation Oncology · doi:10.1186/s13014-020-01643-y · Cited by 27
Metadata
- 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
