Optimal Weighted Wilcoxon–Mann–Whitney Test for Prioritized Outcomes
We consider a two-group randomized clinical trial of prioritized endpoints, where mortality affects the assessment of a follow-up continuous outcome. With the continuous outcome as the principal outcome, we combine it with mortality via the worst-rank paradigm into a single composite endpoint. Then, we develop a weighted Wilcoxon–Mann–Whitney test statistic to analyze the data. We determine the optimal weights for the Wilcoxon–Mann–Whitney test statistic that maximize its power. We provide the rationale for the weights and their implications in the application of the method. In addition, we derive a formula for its power and demonstrate its accuracy in simulations. Finally, we apply the method to data from an acute ischemic stroke clinical trial of normobaric oxygen therapy.
This work was supported by grants P50-NS051343, R01-CA075971, T32 NS048005, 1RO1HL118336-01, and UL1TR001117 awarded by the National Institutes of Health. The content of this paper is solely the responsibility of the authors and does not necessarily represent the official view of the National Institutes of Health.
Conflict of Interest: None declared.
- Ahmad, Y., Nijjer, S., Cook, C. M., El-Harasis, M., Graby, J., Petraco, R., et al. (2015). A new method of applying randomised control study data to the individual patient: A novel quantitative patient-centred approach to interpreting composite end points. International Journal of Cardiology, 195, 216–224.CrossRefGoogle Scholar
- Anker, S. D., Schroeder, S., Atar, D., Bax, J. J., Ceconi, C., Cowie, M. R., et al. (2016). Traditional and new composite endpoints in heart failure clinical trials: Facilitating comprehensive efficacy assessments and improving trial efficiency. European Journal of Heart Failure, 18(5):482–489.CrossRefGoogle Scholar
- Armstrong, P. W., Westerhout, C. M., Van de Werf, F., Califf, R. M., Welsh, R. C., Wilcox, R. G., et al. (2011). Refining clinical trial composite outcomes: An application to the assessment of the safety and efficacy of a new thrombolytic–3 (assent-3) trial. American Heart Journal, 161(5), 848–854.CrossRefGoogle Scholar
- Bakal, J. A., Westerhout, C. M., & Armstrong, P. W. (2012). Impact of weighted composite compared to traditional composite endpoints for the design of randomized controlled trials. Statistical Methods in Medical Research, 24(6), 980–988. https://doi.org/10.1177/0962280211436004 MathSciNetCrossRefGoogle Scholar
- Bakal, J. A., Westerhout, C. M., Cantor, W. J., Fernández-Avilés, F., Welsh, R. C., Fitchett, D., et al. (2012). Evaluation of early percutaneous coronary intervention vs. standard therapy after fibrinolysis for st-segment elevation myocardial infarction: Contribution of weighting the composite endpoint. European Heart Journal, 34(12), 903–908.CrossRefGoogle Scholar
- Berry, J. D., Miller, R., Moore, D. H., Cudkowicz, M. E., Van Den Berg, L. H., Kerr, D. A., et al. (2013). The combined assessment of function and survival (CAFS): A new endpoint for ALS clinical trials. Amyotrophic Lateral Sclerosis and Frontotemporal Degeneration, 14(3), 162–168.CrossRefGoogle Scholar
- Braunwald, E., Antman, E. M., Beasley, J. W., Califf, R. M., Cheitlin, M. D., Hochman, J. S., et al. (2002). ACC/AHA 2002 guideline update for the management of patients with unstable angina and non–st-segment elevation myocardial infarction–summary article: A report of the American college of cardiology/American heart association task force on practice guidelines (committee on the management of patients with unstable angina). Journal of the American College of Cardiology, 40(7), 1366–1374.Google Scholar
- Campbell, D. T., & Kenny, D. A. (1999). A primer on regression artifacts. New York: Guilford Publications.Google Scholar
- Feldman, A., Baughman, K., Lee, W., Gottlieb, S., Weiss, J., Becker, L., & Strobeck, J. (1991). Usefulness of OPC-8212, a quinolinone derivative, for chronic congestive heart failure in patients with ischemic heart disease or idiopathic dilated cardiomyopathy. The American Journal of Cardiology, 68(11), 1203–1210.CrossRefGoogle Scholar
- Felker, G. M., & Maisel, A. S. (2010). A global rank end point for clinical trials in acute heart failure. Circulation: Heart Failure, 3(5), 643–646.Google Scholar
- Ferreira-González, I., Permanyer-Miralda, G., Busse, J. W., Bryant, D. M., Montori, V. M., Alonso-Coello, P., et al. (2007a). Methodologic discussions for using and interpreting composite endpoints are limited, but still identify major concerns. Journal of Clinical Epidemiology, 60(7), 651–657.CrossRefGoogle Scholar
- National Asthma Education and Prevention Program (National Heart, Lung, and Blood Institute). (2007). Third expert panel on the management of asthma. Expert panel report 3: Guidelines for the diagnosis and management of asthma. US Department of Health and Human Services, National Institutes of Health, National Heart, Lung, and Blood Institute.Google Scholar
- Pearl, J. (2014). Lord’s paradox revisited–(oh lord! kumbaya!). Tech. rep., Citeseer.Google Scholar
- Rosner, B. (2015). Fundamentals of biostatistics. Toronto: Nelson Education.Google Scholar
- Singhal, A. B. (2006). Normobaric oxygen therapy in acute ischemic stroke trial. ClinicalTrials.gov Database. http://clinicaltrials.gov/ct2/show/NCT00414726
- Sun, H., Davison, B. A., Cotter, G., Pencina, M. J., & Koch, G. G. (2012). Evaluating treatment efficacy by multiple end points in phase ii acute heart failure clinical trials analyzing data using a global method. Circulation: Heart Failure, 5(6), 742–749.Google Scholar
- Willett, J. B. (1988). Questions and answers in the measurement of change. Review of Research in Education, 15, 345–422.Google Scholar