Hajime Uno, PhD (*); Janet Wittes, PhD (*); Haoda Fu, PhD (*); Scott D. Solomon, MD; Brian Claggett, PhD; Lu Tian, ScD; Tianxi Cai, ScD; Marc A. Pfeffer, MD, PhD; Scott R. Evans, PhD; Lee-Jen Wei, PhD
Acknowledgment: The authors thank Dr. Robert O'Neill, 2 referees, and the editors.
Grant Support: Partially supported by the National Institute of Health (grant UM1AI104681 [Dr. Evans]) and contracts.
Disclosures: Dr. Wittes reports consulting fees paid to her employer from Astra-Zeneca, Bristol-Myers Squibb, Merck, Amgen, Reata, Relypsa, Acerta, and Janssen outside the submitted work. Dr. Pfeffer reports both grants and personal fees from Amgen; grants alone from Celladon, Hamilton Health Sciences, Novartis, and Sanofi Aventis; and personal fees alone from Aastrom, Abbot Vascular, Cleveland Clinic, FibroGen, GlaxoSmithKline, Medtronic, Merck, Roche, Servier, Teva, Daiichi Sankyo, Genzyme, Novo Nordisk, Salix, and Sanderling outside the submitted work. In addition, the Brigham and Women's Hospital has patents for the use of inhibitors of the ras genes in selected survivors of myocardial infarction with Novartis; Dr. Pfeffer is a co-inventor, and his share of the licensing agreement is irrevocably transferred to charity. Dr. Evans reports grants from the National Institute of Allergy and Infectious Diseases of the National Institutes of Health during the conduct of the study and personal fees from Millennium: The Takeda Oncology Company, Pfizer, Roche, Novartis, Achaogen, personal fees from MGH, Taris, Boston University, Huntington's Study Group, Auspex, Alcon, Merck, Chelsea, MannKind, QRx Pharma, IMMPACT (Initiative on Methods, Measurement, and Pain Assessment in Clinical Trials), Genentech, Affymax, FzioMed, Amgen, GlaxoSmithKline, Sunovion, Boehringer-Ingelheim, American Statistical Association, U.S. Food and Drug Administration, Osaka University, City of Hope, National Cerebral and Cardiovascular Center of Japan, National Institutes of Health, Muscle Study Group, Society for Clinical Trials, Dug Information Association, University of Rhode Island, Rutgers New Jersey Medical School, PPRECISE (Preclinical Pain Research Consortium for Investigating Safety and Efficacy), and Statistical Communications in Infectious Diseases outside the submitted work. Authors not named here have disclosed no conflicts of interest. Disclosures can also be viewed at www.acponline.org/authors/icmje/ConflictOfInterestForms.do?msNum=M14-1741.
Editors' Disclosures: Christine Laine, MD, MPH, Editor in Chief, reports that she has no financial relationships or interests to disclose. Darren B. Taichman, MD, PhD, Executive Deputy Editor, reports that he has no financial relationships or interests to disclose. Cynthia D. Mulrow, MD, MSc, Senior Deputy Editor, reports that she has no relationships or interests to disclose. Deborah Cotton, MD, MPH, Deputy Editor, reports that she has no financial relationships or interest to disclose. Jaya K. Rao, MD, MHS, Deputy Editor, reports that she has stock holdings/options in Eli Lilly and Pfizer. Sankey V. Williams, MD, Deputy Editor, reports that he has no financial relationships or interests to disclose. Catharine B. Stack, PhD, MS, Deputy Editor for Statistics, reports that she has stock holdings in Pfizer.
Requests for Single Reprints: Lee-Jen Wei, PhD, Department of Biostatistics, Harvard School of Public Health, 655 Huntington Avenue, Boston, MA 02115; e-mail, email@example.com.
Current Author Addresses: Dr. Uno: Department of Medical Oncology, Dana-Farber Cancer Institute, 450 Brookline Avenue, Boston, MA 02215.
Dr. Wittes: Statistics Collaborative, 1625 Massachusetts Avenue, Northwest, Suite 600, Washington, DC 20036.
Dr. Fu: Eli Lilly and Company, 893 South Delaware Street, Indianapolis, IN 46285.
Drs. Solomon, Claggett, and Pfeffer: Division of Cardiovascular Medicine, Brigham and Women's Hospital, 75 Francis Street, Boston, MA 02115.
Dr. Tian: Department of Health Research and Policy, Stanford University School of Medicine, Palo Alto, CA 94305.
Drs. Cai, Evans, and Wei: Department of Biostatistics, Harvard School of Public Health, 655 Huntington Avenue, Boston, MA 02115.
Author Contributions: Conception and design: H. Uno, J. Wittes, H. Fu, L. Tian, S.R. Evans, L. Wei.
Analysis and interpretation of the data: H. Uno, H. Fu, B. Claggett, L. Wei.
Drafting of the article: H. Uno, J. Wittes, H. Fu, B. Claggett, L. Tian, S.R. Evans, L. Wei.
Critical revision of the article for important intellectual content: H. Uno, J. Wittes, H. Fu, S.D. Solomon, B. Claggett, L. Tian, M.A. Pfeffer, S.R. Evans, L. Wei.
Final approval of the article: H. Uno, J. Wittes, H. Fu, S.D. Solomon, B. Claggett, L. Tian, S.R. Evans, T. Cai, M.A. Pfeffer, L. Wei.
Statistical expertise: H. Uno, J. Wittes, H. Fu, B. Claggett, L. Tian, T. Cai, S.R. Evans, L. Wei.
Obtaining of funding: S.D. Solomon.
Administrative, technical, or logistic support: H. Fu.
Collection and assembly of data: H. Uno, S.D. Solomon.
A noninferiority study is often used to investigate whether a treatment's efficacy or safety profile is acceptable compared with an alternative therapy regarding the time to a clinical event. The empirical quantification of the treatment difference for such a study is routinely based on the hazard ratio (HR) estimate. The HR, which is not a relative risk, may be difficult to interpret clinically, especially when the underlying proportional hazards assumption is violated. The precision of the HR estimate depends primarily on the number of observed events but not directly on exposure times or sample size of the study population. If the event rate is low, the study may require an impractically large number of events to ensure that the prespecified noninferiority criterion for the HR is attainable. This article discusses deficiencies in the current approach for the design and analysis of a noninferiority study. Alternative procedures are provided, which do not depend on any model assumption, to compare 2 treatments. For a noninferiority safety study, the patients' exposure times are more clinically important than the observed number of events. If the patients' exposure times are long enough to evaluate safety reliably, then these alternative procedures can effectively provide clinically interpretable evidence on safety, even with relatively few observed events. These procedures are illustrated with data from 2 studies. One explores the cardiovascular safety of a pain medicine; the second examines the cardiovascular safety of a new treatment for diabetes. These alternative strategies to evaluate safety or efficacy of an intervention lead to more meaningful interpretations of the analysis results than the conventional strategy that uses the HR estimate.
Uno H, Wittes J, Fu H, Solomon SD, Claggett B, Tian L, et al. Alternatives to Hazard Ratios for Comparing the Efficacy or Safety of Therapies in Noninferiority Studies. Ann Intern Med. 2015;163:127–134. doi: 10.7326/M14-1741
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Published: Ann Intern Med. 2015;163(2):127-134.
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