﻿ ﻿Statistical Symbols and Abbreviations - Study Design and Statistics

# Statistical Symbols and AbbreviationsStudy Design and Statistics

The following may be used without expansion except where noted. For a term expanded at first mention, the abbreviation may be placed in parentheses after the expanded term and the abbreviation used thereafter (see 13.11, Clinical, Technical, and Other Common Terms). Most terms other than mathematical symbols can also be found in 19.5, Glossary of Statistical Terms.

 Symbol or abbreviation Description |x| absolute value ∑ sum > greater than ≥ greater than or equal to < less than ≤ less than or equal to ^ hat, used above a parameter to denote an estimate ANOVA analysis of variance (expand at first mention) ANCOVA analysis of covariance (expand at first mention) AR autoregression α alpha, probability of type I error 1 − α confidence coefficient β beta, probability of type II error or population regression coefficient 1 − β power of a statistical test b sample regression coefficient CI confidence interval C statistic concordance statistic (same as C index) (chi-square) χ2 test or statistic, with 3 df shown as an example CV coefficient of variation (s/x̄) × 100 (expand at first mention) d Cohen d D difference df degrees of freedom (v is the international symbol149 and also may be used if familiar to readers) D2 Mahalanobis distance, distance between the means of 2 groups Δ delta, change, difference δ delta, true sampling error ∊ epsilon, true experimental error e exponential E(x) expected value of the variable x f frequency or a function of, usually followed by an expression in parentheses, eg, f(x) F F test, ratio of 2 variances. This test can be represented by Fv1,v2(1 − α), where df = v1, v2 for numerator and denominator, respectively, and (1 − α) = confidence coefficient G2(df) likelihood ratio χ2 HR hazard ratio (expand at first mention) H0 null hypothesis H1 alternate hypothesis; specify whether 1- or 2-sided I2 test for heterogeneity κ kappa statistic λi lambda, hazard function for interval i; eigenvalue; or estimate of parameter for log-linear models Λ Wilks lambda ln natural logarithm log logarithm to base 10 (log10) MANOVA multivariate analysis of variance (expand at first mention) μ population mean n size of a subsample N total sample size n! (n) factorial OR odds ratio (expand at first mention) P statistical probability r bivariable coefficient of determination R multivariable correlation coefficient r 2 bivariable coefficient of determination R 2 multivariable coefficient of determination RR relative risk (expand at first mention) ρ rho, population correlation coefficient s2 sample variance σ2 sigma squared, population variance σ sigma, population SD SD standard deviation of a sample, can also mean standardized difference SE standard error SEM standard error of the mean t t test; specify α level, df, 1-tailed vs 2-tailed τ Kendall tau T2 Hotelling T2 statistic u Mann-Whitney U (Wilcoxon) statistic arithmetic mean z z score

Principal Author: Edward H. Livingston, MD

Acknowledgment

Thanks to the following for reviewing and providing comments to improve the manuscript: Miriam Cintron, JAMA; Trevor Lane, MA, DPhil, Edanz Group, Fukuoka, Japan; Tom Lang, MA, Tom Lang Communications, Kirkland, Washington; and Ana Marušić, MD, PhD, Journal of Global Health and University of Split School of Medicine, Croatia.

References

1.Knowles E. The Oxford Dictionary of Quotations. 5th ed. Oxford University Press; 1999.

2.Haynes RB, Mulrow CD, Huth EJ, Altman DG, Gardner MJ. More informative abstracts revisited. Ann Intern Med. 1990;113(1):69-76. doi:10.7326/0003-4819-113-1-69

3.Seymour CW, Liu VX, Iwashyna TJ, et al. Assessment of clinical criteria for sepsis: for the Third International Consensus Definitions for Sepsis and Septic Shock (Sepsis-3). JAMA. 2016;315(8):762-774. doi:10.1001/jama.2016.0288

4.The EQUATOR Network. Accessed January 26, 2019. http://www.equator-network.org/

5.CONSORT: Pilot and Feasibility Trials. Accessed August 11, 2018. http://www.consort-statement.org/extensions/overview/pilotandfeasibility

6.International Committee of Medical Journal Editors. Recommendations for the conduct, reporting, editing, and publication of scholarly work in medical journals. Updated December 2018. Accessed January 9, 2019. http://www.icmje.org/

7.Guyatt G, Rennie D, Meade MO, Cook DJ. Users’ Guides to the Medical Literature: A Manual for Evidence-Based Clinical Practice. 3rd ed. McGraw-Hill Education; 2015.

8.JAMAevidence. Accessed January 26, 2019. https://jamaevidence.mhmedical.com/

9.Calvert M, Blazeby J, Altman DG, et al. Reporting of patient-reported outcomes in randomized trials: the CONSORT PRO extension. JAMA. 2013;309(8):814-822. doi:10.1001/jama.2013.879

10.CONSORT 2010 statement: updated guidelines for reporting parallel group randomised trials. Updated January 24, 2019. Accessed January 25, 2019. http://www.equator-network.org/reporting-guidelines/consort/

11.JAMA Network Instructions for Authors. Accessed August 6, 2019. https://jamanetwork.com/journals/jama/pages/for-authors

12.Campbell MJ. Extending CONSORT to include cluster trials. BMJ. 2004;328(7441):654-655. doi:10.1136/bmj.328.7441.654

13.Detry MA, Lewis RJ. The intention-to-treat principle: how to assess the true effect of choosing a medical treatment. JAMA. 2014;312(1):85-86. doi:10.1001/jama.2014.7523

14.Weijer C, Shapiro SH, Cranley Glass K. For and against: clinical equipoise and not the uncertainty principle is the moral underpinning of the randomised controlled trial. BMJ. 2000;321(7263):756-758. doi:10.1136/bmj.321.7263.756

15.Hellman D. Evidence, belief, and action: the failure of equipoise to resolve the ethical tension in the randomized clinical trial. J Law Med Ethics. 2002;30(3):375-380.

16.Meinert CL. Clinical Trials Dictionary: Terminology and Usage Recommendations. 2nd ed. John Wiley & Sons Inc; 2012.

17.DeAngelis CD, Drazen JM, Frizelle FA, et al. Clinical trial registration: a statement from the International Committee of Medical Journal Editors. JAMA. 2004;292(11):1363-1364. doi:10.1001/jama.292.11.1363

18.CONSORT 2010 statement: extension checklist for reporting within person randomised trials. Updated January 24, 2019. Accessed January 26, 2019. http://www.equator-network.org/reporting-guidelines/consort-within-person-randomised-trials/

19.Young P, Bailey M, Beasley R, et al. Effect of a buffered crystalloid solution vs saline on acute kidney injury among patients in the intensive care unit: the split randomized clinical trial. JAMA. 2015;314(16):1701-1710. doi:10.1001/jama.2015.12334

20.Kaji AH, Lewis RJ. Noninferiority trials: is a new treatment almost as effective as another? JAMA. 2015;313(23):2371-2372. doi:10.1001/jama.2015.6645

21.Mulla SM, Scott IA, Jackevicius CA, You JJ, Guyatt GH. How to use a noninferiority trial: Users’ Guides to the Medical Literature. JAMA. 2012;308(24):2605-2611. doi:10.1001/2012.jama.11235

22.Reporting of noninferiority and equivalence randomized trials: extension of the CONSORT 2010 statement. Updated January 24, 2019. Accessed January 26, 2019. http://www.equator-network.org/reporting-guidelines/consort-non-inferiority/

23.Piaggio G, Elbourne DR, Pocock SJ, Evans SJ, Altman DG, Group C. Reporting of noninferiority and equivalence randomized trials: extension of the CONSORT 2010 statement. JAMA. 2012;308(24):2594-2604. doi:10.1001/jama.2012.87802

24.Moher D, Schulz KF, Altman D, Group C. The CONSORT statement: revised recommendations for improving the quality of reports of parallel-group randomized trials. JAMA. 2001;285(15):1987-1991. doi:10.1001/jama.298.7.776

25.Curley MQ, Wypij D, Watson R, et al. Protocolized sedation vs usual care in pediatric patients mechanically ventilated for acute respiratory failure: a randomized clinical trial. JAMA. 2015;313(4):379-389. doi:10.1001/jama.2014.18399

26.Meurer WJ, Lewis RJ. Cluster randomized trials: evaluating treatments applied to groups. JAMA. 2015;313(20):2068-2069. doi:10.1001/jama.2015.5199

27.CONSORT 2010 statement: extension to cluster randomised trials. Updated January 24, 2019. Accessed January 26, 2019. http://www.equator-network.org/reporting-guidelines/consort-cluster/

28.Ellenberg SS. The stepped-wedge clinical trial: evaluation by rolling deployment. JAMA. 2018;319(6):607-608. doi:10.1001/jama.2017.21993

29.Hemming K, Haines TP, Chilton PJ, Girling AJ, Lilford RJ. The stepped wedge cluster randomised trial: rationale, design, analysis, and reporting. BMJ. 2015;350:h391. doi:10.1136/bmj.h391

30.Transparent Reporting of Evaluations with Nonrandomized Designs (TREND). CDC website. Updated September 26, 2018. Accessed January 25, 2019. https://www.cdc.gov/trendstatement/

31.Rossouw JE, Anderson GL, Prentice RL, et al. Risks and benefits of estrogen plus progestin in healthy postmenopausal women: principal results from the Women’s Health Initiative randomized controlled trial. JAMA. 2002;288(3):321-333. doi:10.1001/jama.288.3.321

32.The Strengthening the Reporting of Observational Studies in Epidemiology (STROBE) Statement: guidelines for reporting observational studies. Updated November 15, 2018. Accessed January 26, 2019. http://www.equator-network.org/reporting-guidelines/strobe/

33.Kempen JH. Appropriate use and reporting of uncontrolled case series in the medical literature. Am J Ophthalmol. 2011;151(1):7-10. doi:10.1016/j.ajo.2010.08.047

34.Good research practices for comparative effectiveness research: defining, reporting and interpreting nonrandomized studies of treatment effects using secondary data sources. Updated October 23, 2013. Accessed March 27, 2018. http://www.equator-network.org/reporting-guidelines/good-research-practices-for-comparative-effectiveness-research-defining-reporting-and-interpreting-nonrandomized-studies-of-treatment-effects-using-secondary-data-sources-the-ispor-good-research-pr/

35.Good research practices for cost-effectiveness analysis alongside clinical trials: the ISPOR RCT-CEA Task Force report. Accessed March 29, 2018. http://www.equator-network.org/reporting-guidelines/good-research-practices-for-cost-effectiveness-analysis-alongside-clinical-trials-the-ispor-rct-cea-task-force-report/

36.STARD 2015: An Updated List of Essential Items for Reporting Diagnostic Accuracy Studies. Updated November 1, 2018. Accessed January 26, 2019. http://www.equator-network.org/reporting-guidelines/stard/

37.Transparent reporting of a multivariable prediction model for individual prognosis or diagnosis (TRIPOD): the TRIPOD statement. Accessed March 16, 2018. http://www.equator-network.org/reporting-guidelines/tripod-statement/

38.The Reporting of studies Conducted using Observational Routinely-collected health Data (RECORD) Statement. Accessed March 29, 2018. http://www.equator-network.org/reporting-guidelines/record/

39.Preferred Reporting Items for Systematic Reviews and Meta-Analyses: The PRISMA Statement. Updated September 6, 2018. Accessed January 26, 2019. http://www.equator-network.org/reporting-guidelines/prisma/

40.Meta-analysis of Observational Studies in Epidemiology: a proposal for reporting. Accessed January 27, 2019. http://www.equator-network.org/reporting-guidelines/meta-analysis-of-observational-studies-in-epidemiology-a-proposal-for-reporting-meta-analysis-of-observational-studies-in-epidemiology-moose-group/

41.Standards for Reporting Qualitative Research: a synthesis of recommendations. Accessed March 16, 2018. http://www.equator-network.org/reporting-guidelines/srqr/

42.Consolidated Criteria for Reporting Qualitative Research (COREQ): a 32-item checklist for interviews and focus groups. Accessed March 16, 2018. http://www.equator-network.org/reporting-guidelines/coreq/

43.SQUIRE 2.0 (Standards for Quality Improvement Reporting Excellence): revised publication guidelines from a detailed consensus process. Updated February 1, 2017. Accessed January 26, 2019. http://www.equator-network.org/reporting-guidelines/squire/

44.American Association for Public Opinion Research (AAPOR). Standard Definitions. Accessed August 6, 2019. https://aapor.org/Publications-Media/AAPOR-Journals/Standard-Definitions.aspx

45.Good practice in the conduct and reporting of survey research. Accessed January 27, 2019. http://www.equator-network.org/reporting-guidelines/good-practice-in-the-conduct-and-reporting-of-survey-research/

46.Rothman KJ, Greenland S, Lash TL. Modern Epidemiology. 3rd ed. Wolters Kluwer Health/Lippincott Williams & Wilkins; 2008.

47.Dekkers OM, Egger M, Altman DG, Vandenbroucke JP. Distinguishing case series from cohort studies. Ann Intern Med. 2012;156(1):37-40. doi:10.7326/0003-4819- 156-1-201201030-00006

48.Concato J. Is it time for medicine-based evidence? JAMA. 2012;307(15):1641-1643. doi:10.1001/jama.2012.482

49.Golub RM, Fontanarosa PB. Comparative effectiveness research: relative successes. JAMA. 2012;307(15):1643-1645. doi:10.1001/jama.2012.490

50.Moher D, Olkin I. Meta-analysis of randomized controlled trials: a concern for standards. JAMA. 1995;274(24):1962-1964. doi:10.1001/jama.1995.03530240072044

51.Murad M, Montori VM, Ioannidis JA, et al. How to read a systematic review and meta-analysis and apply the results to patient care: Users’ Guides to the Medical Literature. JAMA. 2014;312(2):171-179. doi:10.1001/jama.2014.5559

52.Bailar JC III. The practice of meta-analysis. J Clin Epidemiol. 1995;48(1):149-157. doi:10.1016/0895-4356(94)00149-K

53.Shapiro S. Meta-analysis/shmeta-analysis. Am J Epidemiol. 1994;140(9):771-778.

54.Petitti DB. Of babies and bathwater. Am J Epidemiol. 1994;140(9):779-782.

55.Greenland S. Can meta-analysis be salvaged? Am J Epidemiol. 1994;140(9):783-787.

56.Chalmers TC, Lau J. Meta-analytic stimulus for changes in clinical trials. Stat Methods Med Res. 1993;2(2):161-172. doi:10.1177/096228029300200204

57.Jadad AR, McQuay HJ. Meta-analyses to evaluate analgesic interventions: a systematic qualitative review of their methodology. J Clin Epidemiol. 1996;49(2):235-243. doi:10.1016/0895-4356(95)00062-3

58.Sampson M, Barrowman NJ, Moher D, et al. Should meta-analysts search Embase in addition to Medline? J Clin Epidemiol. 2003;56(10):943-955. doi:10.1016/S0895-4356(03)00110-0

59.Rethlefsen ML, Murad M, Livingston EH. Engaging medical librarians to improve the quality of review articles. JAMA. 2014;312(10):999-1000. doi:10.1001/jama.2014.9263

60.Berlin JA, Golub RM. Meta-analysis as evidence: building a better pyramid. JAMA. 2014;312(6):603-606. doi:10.1001/jama.2014.8167

61.Shaw P. Quantifying the benefits and risks of methylphenidate as treatment for childhood attention-deficit/hyperactivity disorder. JAMA. 2016;315(18):1953-1955. doi:10.1001/jama.2016.3427

62.Stewart LA, Clarke M, Rovers M, et al. Preferred Reporting Items for a Systematic Review and Meta-analysis of individual participant data: the PRISMA-IPD statement. JAMA. 2015;313(16):1657-1665. doi:10.1001/jama.2015.3656

63.Golub RM, Fontanarosa PB. Researchers, readers, and reporting guidelines: writing between the lines. JAMA. 2015;313(16):1625-1626. doi:10.1001/jama.2015.3837

64.Easterbrook PJ, Berlin JA, Gopalan R, Matthews DR. Publication bias in clinical research. Lancet. 1991;337(8746):867-872. doi:10.1371/annotation/a65c0f61-eb99-42f0-828b-5a8662bce4f7

65.Dickersin K, Scherer R, Lefebvre C. Identifying relevant studies for systematic reviews. BMJ. 1994;309(6964):1286-1291. doi:10.1136/bmj.309.6964.1286

66.Higgins JPT, Green S. Cochrane Handbook for Systematic Reviews of Interventions. Version 5.1.0. Updated March 2011. Cochrane Collaboration; 2011. https://www.handbook.cochrane.org

67.Gerbarg ZB, Horwitz RI. Resolving conflicting clinical trials: guidelines for meta-analysis. J Clin Epidemiol. 1988;41(5):503-509. doi:10.1016/0895-4356(88)90053-4

68.Murad MH, Montori VM, Ioannidis JPA, et al. Understanding and applying the results of a systematic review and meta-analysis. In: Guyatt G, Rennie D, Meade MO, Cook DJ, eds. Users’ Guides to the Medical Literature: A Manual for Evidence-Based Clinical Practice. 3rd ed. McGraw-Hill Education; 2015.

69.Thompson SG. Why sources of heterogeneity in meta-analysis should be investigated. BMJ. 1994;309(6965):1351-1355. doi:10.1136/bmj.309.6965.1351

70.Mills EJ, Ioannidis JPA, Thorlund K, Schünemann HJ, Puhan MA, Guyatt G. Network meta-analysis. In: Guyatt G, Rennie D, Meade MO, Cook DJ, eds. Users’ Guides to the Medical Literature: A Manual for Evidence-Based Clinical Practice. 3rd ed. McGraw-Hill Education; 2015.

71.Bero L, Rennie D. The Cochrane Collaboration. Preparing, maintaining, and disseminating systematic reviews of the effects of health care. JAMA. 1995;274(24):1935-1938. doi:10.1001/jama.1995.03530240045039

72.Bauchner H, Fontanarosa PB, Golub RM. JAMA welcomes the US Preventive Services Task Force. JAMA. 2016;315(4):351-352. doi:10.1001/jama.2015.18448

73.Mark DH. Visualizing cost-effectiveness analysis. JAMA. 2002;287(18):2428-2429. doi:10.1001/jama.287.18.2428

74.Saha S, Hoerger TJ, Pignone MP, et al. The art and science of incorporating cost effectiveness into evidence-based recommendations for clinical preventive services. Am J Prev Med. 2001;20(3):36-43. doi:10.1016/S0749-3797(01)00260-4

75.Udvarhelyi I, Colditz GA, Rai A, Epstein AM. Cost-effectiveness and cost-benefit analyses in the medical literature: are the methods being used correctly? Ann Intern Med. 1992;116(3):238-244. doi:10.7326/0003-4819-116-3-238

76.Kassirer JP, Angell M. The journal’s policy on cost-effectiveness analyses. N Engl J Med. 1994;331(10):669-670. doi:10.1056/NEJM199409083311009

77.Hill SR, Mitchell AS, Henry DA. Problems with the interpretation of pharmacoeconomic analyses: a review of submissions to the Australian Pharmaceutical Benefits Scheme. JAMA. 2000;283(16):2116-2121. doi:10.1001/jama.283.16.2116

78.Russell LB, Gold MR, Siegel JE, Daniels N, Weinstein MC. The role of cost-effectiveness analysis in health and medicine. JAMA. 1996;276(14):1172-1177. doi:10.1001/jama.1996.03540140060028

79.Siegel JE, Weinstein MC, Russell LB, Gold MR. Recommendations for reporting cost-effectiveness analyses. JAMA. 1996;276(16):1339-1341. doi:10.1001/jama.1996.03540160061034

80.Drummond M, Jefferson T. Guidelines for authors and peer reviewers of economic submissions to the BMJ. BMJ. 1996;313(7052):275-283. doi:10.1136/bmj.313.7052.275

81.Drummond MF, Richardson WS, O'Brien BJ, Levine M, Heyland D. Users’ Guides to the Medical Literature, XIII: how to use an article on economic analysis of clinical practice, A: are the results of the study valid? JAMA. 1997;277(19):1552-1557. doi:10.1001/jama.1997.03540430064035

82.Consolidated Health Economic Evaluation Reporting Standards (CHEERS) statement. Updated February 1, 2017. Accessed January 26, 2019. http://www.equator-network.org/reporting-guidelines/cheers/

83.Bossuyt PM, Reitsma JB, Bruns DE, et al. Towards complete and accurate reporting of studies of diagnostic accuracy: the STARD initiative. BMJ. 2003;326(7379):41-44. doi:10.1136/bmj.326.7379.41

84.Simel DL, Rennie D. A primer on the precision and accuracy of the clinical examination. In: The Rational Clinical Examination: Evidence-Based Clinical Diagnosis. McGraw-Hill Education; 2016.

85.Ebell MH, Call M, Shinholser J, Gardner J. Does this patient have infectious mononucleosis? the Rational Clinical Examination systematic review. JAMA. 2016;315(14):1502-1509. doi:10.1001/jama.2016.2111

86.Alba A, Agoritsas T, Walsh M, et al. Discrimination and calibration of clinical prediction models: Users’ Guides to the Medical Literature. JAMA. 2017;318(14):1377-1384. doi:10.1001/jama.2017.12126

87.Johnson TP, Wislar JS. Response rates and nonresponse errors in surveys. JAMA. 2012;307(17):1805-1806. doi:10.1001/jama.2012.3532

88.Livingston EH, Wislar JS. Minimum response rates for survey research. Arch Surg. 2012;147(2):110-110. doi:10.1001/archsurg.2011.2169

89.Lee H, Herbert RD, McAuley JH. Mediation analysis. JAMA. 2019;321(7):697-698. doi:10.1001/jama.2018.21973

90.Emdin CA, Khera AV, Kathiresan S. Mendelian randomization. JAMA. 2017;318(19):1925-1926. doi:10.1001/jama.2017.17219

91.Davey Smith G, Paternoster L, Relton C. When will mendelian randomization become relevant for clinical practice and public health? JAMA. 2017;317(6):589-591. doi:10.1001/jama.2016.21189

92.Bailar JC, Mosteller F. Medical Uses of Statistics. 2nd ed. NEJM Books; 1992.

93.Marriott FHC, Kendall MG, International Statistical Institute. A Dictionary of Statistical Terms. 5th ed. Longman Publishing Group; 1990.

94.Glantz SA. Primer of Biostatistics. McGraw-Hill; 1981.

95.Riegelman RK, Riegelman RK. Studying a Study & Testing a Test: Reading Evidence-Based Health Research. 6th ed. Wolters Kluwer/Lippincott Williams & Wilkins Health; 2013.

96.Eisenhart C. Realistic evaluation of the precision and accuracy of instrument calibration systems. J Res Natl Bur Stand. 1963;67C:161-187.

97.Bland JM, Altman D. Statistical methods for assessing agreement between two methods of clinical measurement. Lancet. 1986;327(8476):307-310. doi:10.1016/S0140-6736(86)90837-8

98.Last JM, Abramson JH, International Epidemiological Association. A Dictionary of Epidemiology. 3rd ed. Oxford University Press; 1995.

99.Vickers AJ, Altman DG. Statistics notes: analysing controlled trials with baseline and follow up measurements. BMJ. 2001;323(7321):1123-1124. doi:10.1136/bmj.323.7321.1123

100.Lang TA, Secic M. How to Report Statistics in Medicine: Annotated Guidelines for Authors, Editors, and Reviewers. 2nd ed. American College of Physicians; 2006.

101.Ansari AR, Bradley RA. Rank-sum tests for dispersions. Ann Math Statist. 1960;31(4):1174-1189. https://projecteuclid.org/euclid.aoms/1177705688

102.Watters JK, Bluthenthal RN, Kral AH. HIV seroprevalence in injection drug users. JAMA. 1995;273(15):1178-1178. doi:10.1001/jama.1995.03520390036028

103.Cutter GR, Mutti DO, Zadnik K. Optometric care and undetected eye disease: a case of Berkson’s bias? Arch Intern Med. 1995;155(4):427-429. doi:10.1001/archinte.1995.00430040102015

104.Everitt B. The Cambridge Dictionary of Statistics in the Medical Sciences. Cambridge University Press; 1995.

105.Hoffmann MK, Shi H, Schmitz BL, et al. Noninvasive coronary angiography with multislice computed tomography. JAMA. 2005;293(20):2471-2478. doi:10.1001/jama.293.20.2471

106.Pencina MJ, D’Agostino RB Sr. Evaluating discrimination of risk prediction models: the C statistic. JAMA. 2015;314(10):1063-1064. doi:10.1001/jama.2015.11082

107.Meurer WJ, Tolles J. Logistic regression diagnostics: understanding how well a model predicts outcomes. JAMA. 2017;317(10):1068-1069. doi:10.1001/jama.2016.20441

108.Livingston EH. The mean and standard deviation: what does it all mean? J Surg Res. 2004;119(2):117-123. doi:10.1016/j.jss.2004.02.008

109.Riegelman RK, Hirsch RP. Studying a Study and Testing a Test: How to Read the Medical Literature. 2nd ed. Little Brown; 1989.

110.Dimick JB, Nicholas LH, Ryan AM, Thumma JR, Birkmeyer JD. Bariatric surgery complications before vs after implementation of a national policy restricting coverage to centers of excellence. JAMA. 2013;309(8):792-799. doi:10.1001/jama.2013.755

111.Dimick JB, Ryan AM. Methods for evaluating changes in health care policy: the difference-in-differences approach. JAMA. 2014;312(22):2401-2402. doi:10.1001/jama.2014.16153

112.The disability-adjusted life year (DALY) definition, measurement and potential use. Accessed November 30, 2018. https://documents.worldbank.org/curated/en/482351468764408897/The-disability-adjusted-life-year-DALY-definition-measurement-and-potential-use

113.Robinson WS. Ecological correlations and the behavior of individuals. Int J Epidemiol. 2009;38(2):337-341. doi:10.1093/ije/dyn357

114.Livingston EH, Elliot A, Hynan L, Cao J. Effect size estimation: a necessary component of statistical analysis. Arch Surg. 2009;144(8):706-712. doi:10.1001/archsurg.2009.150

115.Ingelfinger JA. Biostatistics in Clinical Medicine. 3rd ed. McGraw-Hill; 1994.

116.Haukoos JS, Lewis RJ. The propensity score. JAMA. 2015;314(15):1637-1638. doi:10.1001/jama.2015.13480

117.Tolles J, Lewis RJ. Time-to-event analysis. JAMA. 2016;315(10):1046-1047. doi:10.1001/jama.2016.1825

118.Allison PD. Survival Analysis Using SAS: A Practical Guide. 2nd ed. SAS Institute; 2010.

119.Hosmer DW, Lemeshow S, Sturdivant RX. Applied Logistic Regression. 3rd ed. Wiley; 2013.

120.Livingston EH. Who was student and why do we care so much about his t-test? J Surg Res. 2004;118(1):58-65. doi:10.1016/j.jss.2004.02.003

121.Li P, Stuart EA, Allison DB. Multiple imputation: a flexible tool for handling missing data. JAMA. 2015;314(18):1966-1967. doi:10.1001/jama.2015.15281

122.Newgard CD, Lewis RJ. Missing data: how to best account for what is not known. JAMA. 2015;314(9):940-941. doi:10.1001/jama.2015.10516

123.Everitt B, Everitt B. Statistical Methods in Medical Investigations. 2nd ed. Halsted Press; 1994.

124.Elliott AC, Woodward WA. Statistical Analysis Quick Reference Guidebook: With SPSS Examples. Sage Publications; 2007.

125.Cohen J, Cohen P, West SG, Aiken LS. Applied Multiple Regression/Correlation Analysis for the Behavioral Sciences. 3rd ed. Lawrence Erlbaum Associates; 2003.

126.Cleveland WS, Devlin SJ. Locally weighted regression: an approach to regression analysis by local fitting. J Am Stat Assoc. 1988;83(403):596-610.

127.Krumholz HM, Nuti SV, Downing NS, Normand ST, Wang Y. Mortality, hospitalizations, and expenditures for the Medicare population aged 65 years or older, 1999-2013. JAMA. 2015;314(4):355-365. doi:10.1001/jama.2015.8035

128.Harrell FE. Regression Modeling Strategies: With Applications to Linear Models, Logistic Regression, and Survival Analysis. Springer; 2001.

129.Stukel TA, Fisher ES, Wennberg DE, Alter DA, Gottlieb DJ, Vermeulen MJ. Analysis of observational studies in the presence of treatment selection bias: effects of invasive cardiac management on AMI survival using propensity score and instrumental variable methods. JAMA. 2007;297(3):278-285. doi:10.1001/jama.297.3.278

130.Colton T. Statistics in Medicine. Little Brown; 1974.

131.Detry MA, Ma Y. Analyzing repeated measurements using mixed models. JAMA. 2016;315(4):407-408. doi:10.1001/jama.2015.19394

132.Cao J, Zhang S. Multiple comparison procedures. JAMA. 2014;312(5):543-544. doi:10.1001/jama.2014.9440.

133.Elashoff JD. Down with multiple t-tests. Gastroenterology. 1981;80(3):615-620.

134.Guyatt G, Sackett D, Taylor DW, Chong J, Roberts R, Pugsley S. Determining optimal therapy--randomized trials in individual patients. N Engl J Med. 1986;314(14):889-892. doi:10.1056/NEJM198604033141406

135.Bingel U; for the Placebo Competence Team. Avoiding nocebo effects to optimize treatment outcome. JAMA. 2014;312(7):693-694. doi:10.1001/jama.2014.8342

136.Agoritsas T, Merglen A, Shah ND, O’Donnell M, Guyatt GH. Adjusted analyses in studies addressing therapy and harm: Users’ Guides to the Medical Literature. JAMA. 2017;317(7):748-759. doi:10.1001/jama.2016.20029

137.Zhang J, Yu KF. What’s the relative risk? a method of correcting the odds ratio in cohort studies of common outcomes. JAMA. 1998;280(19):1690-1691. doi:10.1001/jama.280.19.1690

138.Livingston EH, Cassidy L. Statistical power and estimation of the number of required subjects for a study based on the t-test: a surgeon's primer. J Surg Res. 2005;126(2):149-159. doi:10.1016/j.jss.2004.12.013

139.Deslée G, Mal H, Dutau H, et al. Lung volume reduction coil treatment vs usual care in patients with severe emphysema: the REVOLENS randomized clinical trial. JAMA. 2016;315(2):175-184. doi:10.1001/jama.2015.17821

140.Scherer RW, Dickersin K, Langenberg P. Full publication of results initially presented in abstracts: a meta-analysis. JAMA. 1994;272(2):158-162. doi:10.1001/jama.1994.03520020084025

141.Stein MB, Chen C-Y, Ursano RJ, et al. Genome-wide association studies of posttraumatic stress disorder in 2 cohorts of US Army soldiers. JAMA Psychiatry. 2016;73(7):695-704. doi:10.1001/jamapsychiatry.2016.0350

142.Kypri K, Vater T, Bowe SJ, et al. Web-based alcohol screening and brief intervention for university students: a randomized trial. JAMA. 2014;311(12):1218-1224. doi:10.1001/jama.2014.2138

143.Pope C, Mays N. Reaching the parts other methods cannot reach: an introduction to qualitative methods in health and health services research. BMJ. 1995;311(6996):42-45. doi:10.1136/bmj.311.6996.42

144.Murad MH, Montori VM, Ioannidis JPA, Prasad K, Cook DJ, Guyatt G. Fixed-effects and random-effects models. In: Guyatt G, Rennie D, Meade MO, Cook DJ, eds. Users’ Guides to the Medical Literature. 3rd ed. McGraw-Hill; 2015.

145.Schomer DL, Lewis RJ. Stopping seizures early and the surgical epilepsy trial that stopped even earlier. JAMA. 2012;307(9):966-968. doi:10.1001/jama.2012.251

146.Bassler D, Briel M, Montori VM, et al. Stopping randomized trials early for benefit and estimation of treatment effects: systematic review and meta-regression analysis. JAMA. 2010;303(12):1180-1187. doi:10.1001/jama.2010.310

147.Viele K, McGlothlin A, Broglio K. Interpretation of clinical trials that stopped early. JAMA. 2016;315(15):1646-1647. doi:10.1001/jama.2016.2628

148.Kaji AH, Lewis RJ. Are we looking for superiority, equivalence, or noninferiority? asking the right question and answering it correctly. Ann Emerg Med. 2010;55(5):408-411. doi:10.1016/j.annemergmed.2010.01.024

149.Halperin M, Hartley HO, Hoel PG; COPSS Committee on Symbols and Notation. Recommended standards for statistical symbols and notation. Am Stat. 1965;19(3):12-14. doi:10.2307/2681417

Elliott AC, Woodward WA. Statistical Analysis Quick Reference Guidebook: With SPSS Examples. Sage Publications; 2007.

Guyatt G, Rennie D, Meade M, Cook D, American Medical Association. Users’ Guides to the Medical Literature: A Manual for Evidence-Based Clinical Practice. 3rd ed. McGraw-Hill Education Medical; 2015.

Livingston EH, Lewis RJ. JAMA Guide to Statistics and methods. McGraw-Hill Education; 2020.

JAMAevidence. Accessed November 9, 2019. https://jamaevidence.mhmedical.com

Motulsky H. Intuitive Biostatistics: A Nonmathematical Guide to Statistical Thinking. 3rd ed. Oxford University Press; 2014.

Riegelman RK, Riegelman RK. Studying a Study & Testing a Test: Reading Evidence-Based Health Research. 6th ed. Wolters Kluwer/Lippincott Williams & Wilkins Heath; 2013.

Rothman KJ, Greenland S, Lash TL. Modern Epidemiology. 3rd ed. Wolters Kluwer Health/Lippincott Williams & Wilkins; 2008.

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