Comparison of three sample size calculation methods for non-inferiority vaccine trials with multiple continuous co-primary endpoints

References

• U.S. Department of Health and Human Services, Food and Drug Administration, Center for Biologics Evaluation and Research. Guidance for industry for the evaluation of combination vaccines for preventable diseases: production, testing and clinical studies. 1997 April accessed 2017 Oct 21. https://wwwfdagov/downloads/biologicsbloodvaccines/guidancecomplianceregulatoryinformation/guidances/vaccines/ucm175909pdf 1997.
   Google Scholar
• Elsevier, Inc. “polyvalent vaccine”. Saunders comprehensive veterinary dictionary, 3 ed. 2007 accessed 2017 Nov. https://medical-dictionary.thefreedictionary.com/polyvalent+vaccine.
   Google Scholar
• Dodd D. Benefits of combination vaccines: effective vaccination on a simplified schedule. Am J Manag Care. 9;2003:S6–12.
   PubMed Web of Science ®Google Scholar
• Berger RL. Multiparameter hypothesis testing and acceptance sampling. Technometrics. 1982;24:295–300. doi:10.2307/1267823.
   Web of Science ®Google Scholar
• Chuang-Stein C, Stryszak P, Dmitrienko A, Offen W. Challenge of multiple co-primary endpoints: a new approach. Stat Med. 2007;26:1181–1192. doi:10.1002/sim.2604.
   PubMed Web of Science ®Google Scholar
• ICH Expert Working Group. ICH harmonised tripartite guideline: statistical principles for clinical trials E9. International conference on harmonisation of technical requirements for registration of pharmaceuticals for human use. 1998 February 5 [ Accessed 2017 Mar 20. http://wwwichorg/fileadmin/Public_Web_Site/ICH_Products/Guidelines/Efficacy/E9/Step4/E9_Guidelinepdf.
   Google Scholar
• Committee for Medicinal Products for Human Use. Guideline on multiplicity issues in clinical trials (Draft). London: european medicines agency. 2016 December 15 Accessed 2018 Jan 12. http://wwwemaeuropaeu/docs/en_GB/document_library/Scientific_guideline/2017/03/WC500224998pdf.
   Google Scholar
• Sozu T, Sugimoto T, Hamasaki T,et al. Sample size determination in clinical trials with multiple endpoints. New York: Springer, 2015.
   Google Scholar
• Offen W, Chuang-Stein C, Dmitrienko A, Littman G, Maca J, Meyerson L, Muirhead R, Stryszak P, Baddy A, Chen K, et al. Multiple co-primary endpoints: medical and statistical solutions: A report from the multiple endpoints expert team of the pharmaceutical research and manufacturers of America. Drug Inf J. 2007;41:31–46. doi:10.1177/009286150704100105.
   Web of Science ®Google Scholar
• Xiong C, Yu K, Gao F, Yan Y, Zhang Z. Power and sample size for clinical trials when efficacy is required in multiple endpoints: application to an Alzheimer’s treatment trial. Clin Trials. 2005;2:387–393. doi:10.1191/1740774505cn112oa.
   PubMed Web of Science ®Google Scholar
• Sozu T, Kanou T, Hamada C, Yoshimura I. Power and sample size calculations in clinical trials with multiple primary variables. Jpn J Biometrics. 2006;27:83–96. doi:10.5691/jjb.27.83.
   Google Scholar
• Sozu T, Sugimoto T, Hamasaki T. Sample size determination in superiority clinical trials with multiple co-primary correlated endpoints. J Biopharm Stat. 2011;21:650–668. doi:10.1080/10543406.2011.551329.
   PubMed Web of Science ®Google Scholar
• Sozu T, Sugimoto T, Hamasaki T. Sample size determination in clinical trials with multiple co-primary binary endpoints. Stat Med. 2010;29:2169–2179. doi:10.1002/sim.3972.
   PubMed Web of Science ®Google Scholar
• Sozu T, Sugimoto T, Hamasaki T. Sample size determination in clinical trials with multiple co‐primary endpoints including mixed continuous and binary variables. Biometrical J. 2012;54:716–729. doi:10.1002/bimj.201100221.
   PubMed Web of Science ®Google Scholar
• Sugimoto T, Sozu T, Hamasaki T. A convenient formula for sample size calculations in clinical trials with multiple co-primary continuous endpoints. Pharm Stat. 2012;11:118–128. doi:10.1002/pst.505.
   PubMed Web of Science ®Google Scholar
• Varga Z, Tsang YC, Singer J. A simple procedure to estimate the optimal sample size in case of conjunctive coprimary endpoints. Biometrical J. 2016:n/a-n/a. doi:10.1002/bimj.201500231
   PubMed Web of Science ®Google Scholar
• Julious SA, McIntyre NE. Sample sizes for trials involving multiple correlated must-win comparisons. Pharm Stat. 2012;11:177–185. doi:10.1002/pst.515.
   PubMed Web of Science ®Google Scholar
• Nauta J. 2010. Statistics in clinical vaccine trials. New York: Springer Science & Business Media, 2010.
   Google Scholar
• Chen JJ, Yuan L, Huang Z, Shi NM, Zhao YL, Xia SL, Li GH, Li RC, Li YP, Yang SY, et al. Safety and immunogenicity of a new 13-valent pneumococcal conjugate vaccine versus a licensed 7-valent pneumococcal conjugate vaccine: a study protocol of a randomised non-inferiority trial in China. BMJ Open. 2016;6:e012488. doi:10.1136/bmjopen-2016-012488.
   PubMed Web of Science ®Google Scholar
• Diez-Domingo J, Gurtman A, Bernaola E, Gimenez-Sanchez F, Martinon-Torres F, Pineda-Solas V, Delgado A, Infante-Marquez P, Liang JZ, Giardina PC, et al. Evaluation of 13-valent pneumococcal conjugate vaccine and concomitant meningococcal group C conjugate vaccine in healthy infants and toddlers in Spain. Vaccine. 2013;31:5486–5494. doi:10.1016/j.vaccine.2013.06.049.
   PubMed Web of Science ®Google Scholar
• Ofori-Anyinam O, Leroux-Roels G, Drame M, Aerssens A, Maes C, Amanullah A, Schuind A, Li P, Jain VK, Innis BL. Immunogenicity and safety of an inactivated quadrivalent influenza vaccine co-administered with a 23-valent pneumococcal polysaccharide vaccine versus separate administration, in adults ≥50 years of age: results from a phase III, randomized, non-inferiority trial. Vaccine. 2017;35:6321–6328. doi:10.1016/j.vaccine.2017.09.012.
   PubMed Web of Science ®Google Scholar
• Song JY, Cheong HJ, Hyun HJ, Seo YB, Lee J, Wie S-H, Choi MJ, Choi WS, Noh JY, Yun JW, et al. Immunogenicity and safety of a 13-valent pneumococcal conjugate vaccine and an MF59-adjuvanted influenza vaccine after concomitant vaccination in ≥60-year-old adults. Vaccine. 2017;35:313–320. doi:10.1016/j.vaccine.2016.11.047.
   PubMed Web of Science ®Google Scholar
• Julious, Steven A. Sample sizes for clinical trials. Boca Raton: Chapman and Hall/CRC, 2009.
   Google Scholar
• Julious SA. Sample sizes for clinical trials with normal data. Stat Med. 2004;23:1921–1986. doi:10.1002/sim.1783.
   PubMed Web of Science ®Google Scholar
• Senn S, Bretz F. Power and sample size when multiple endpoints are considered. Pharm Stat. 2007;6:161–170. doi:10.1002/pst.301.
   PubMed Web of Science ®Google Scholar
• Ludbrook J. Multiple comparison procedures updated. Clin Exp Pharmacol Physiol. 1998;25:1032–1037. doi:10.1111/j.1440-1681.1998.tb02179.x.
   PubMed Web of Science ®Google Scholar
• Sankoh AJ, Huque MF, Dubey SD. Some comments on frequently used multiple endpoint adjustment methods in clinical trials. Stat Med. 1997;16:2529–2542. doi:10.1002/(SICI)1097-0258(19971130)16:22<2529::AID-SIM692>3.0.CO;2-J.
   PubMed Web of Science ®Google Scholar
• Snapinn S. Some remaining challenges regarding multiple endpoints in clinical trials. Stat Med. 2017;36:4441–4445. doi:10.1002/sim.7390.
   PubMed Web of Science ®Google Scholar
• Sankoh AJ, Li H, D’Agostino RB. Composite and multicomponent end points in clinical trials. Stat Med. 2017;36:4437–4440. doi:10.1002/sim.7386.
   PubMed Web of Science ®Google Scholar
• Chuang-Stein C, Li J. Changes are still needed on multiple co-primary endpoints. Stat Med. 2017;36:4427–4436. doi:10.1002/sim.7383.
   PubMed Web of Science ®Google Scholar
• U.S. Department of Health and Human Services, Food and Drug Administration, Center for Drug Evaluation and Research (CDER), Center for biologics evaluation and research (CBER). Guidance for industry: multiple endpoints in clinical trials (draft). January 2017 Accessed 2017. https://wwwfdagov/downloads/drugs/guidancecomplianceregulatoryinformation/guidances/ucm536750pdf.
   Google Scholar
• Hamasaki T, Evans SR, Asakura K. Design, data monitoring, and analysis of clinical trials with co-primary endpoints: A review. J Biopharm Stat. 2017:1–24. doi:10.1080/10543406.2017.1378668
   PubMed Web of Science ®Google Scholar
• Jackson LA, El Sahly HM, George S, Winokur P, Edwards K, Brady RC, Rouphael N, Keitel WA, Mulligan MJ, Burton RL, et al. Randomized clinical trial of a single versus a double dose of 13-valent pneumococcal conjugate vaccine in adults 55 through 74years of age previously vaccinated with 23-valent pneumococcal polysaccharide vaccine. Vaccine. 2018;36:606–614. doi:10.1016/j.vaccine.2017.12.061.
   PubMed Web of Science ®Google Scholar
• Smith JW, Glorioso JC. Effect of cross-immunization on monotypic antibody responses to herpes simplex virus types 1 and 2. J Immunol. 116;1976:898–903.
   PubMed Web of Science ®Google Scholar
• Hung HM, Wang SJ, O’Neill R. A regulatory perspective on choice of margin and statistical inference issue in non-inferiority trials. Biometrical J Biometrische Zeitschrift. 2005;47:28–36. discussion 99-107.
   PubMed Web of Science ®Google Scholar