The Effect of the Number of Matched Data Pairs on the Win Ratio Statistic and Confidence Intervals: A Simulation Study

Year 2026, Volume: 28 Issue: 1 , 3 - 10 , 25.04.2026

İsmet Doğan

https://doi.org/10.18678/dtfd.1778178

https://izlik.org/JA46AG29TT

Abstract

Aim: The aim of this study was to demonstrate the effect of paired data numbers on the win ratio statistic and its 95% confidence intervals for two composite endpoints. Material and Methods: This is a simulation study. Data was generated for 35 different scenarios of matched data pairs within the range 10≤𝑛≤1000 using the Python random library. A total of 34101 different data sets (286 for 𝑛=10, 815 for 𝑛=15, and 1000 data sets for each of the other 33 cases with 𝑛≥20) were used in the study. Results: As the number of paired data increases, the win ratio increases, although not regularly. The number of cases where the value of the win ratio statistic is greater than one is not affected by the number of paired data, and the win ratio numbers considered important increase as the number of paired data increases. As the number of paired data increases, the lower and upper limits of the win ratio approach each other, although not regularly, and the differences between the upper and lower limits also decrease. Conclusion: When evaluating the results of the study in general, it can be said that the increase in the number of paired data affects the number of significant win ratio and the maximum win ratio, and the confidence interval of the win ratio is more affected by the data structure than the size of the number of paired data.

Keywords

Treatment efficacy , composite outcomes , win ratio , matched data pairs , confidence interval

References

• Palileo-Villanueva LM, Dans AL. Composite endpoints. J Clin Epidemiol. 2020;128:157-8. doi:10.1016/j.jclinepi.2020.07.017.
• Huque MF, Alosh M, Bhore R. Addressing multiplicity issues of a composite endpoint and its components in clinical trials. J Biopharm Stat. 2011;21(4):610-34. doi:10.1080/10543406.2011.551327.
• Baracaldo-Santamaría D, Feliciano-Alfonso JE, Ramirez-Grueso R, Rojas-Rodríguez LC, Dominguez-Dominguez CA, Calderon-Ospina CA. Making sense of composite endpoints in clinical research. J Clin Med. 2023;12(13):4371. doi:10.3390/jcm12134371.
• Peng L. The use of the win odds in the design of non-inferiority clinical trials. J Biopharm Stat. 2020;30(5): 941-6. doi:10.1080/10543406.2020.1757690.
• Monzo L, Levy B, Duarte K, Baudry G, Combes A, Ouattara A, et al. Use of the win ratio analysis in critical care trials. Am J Respir Crit Care Med. 2024;209(7):798-804. doi:10.1164/rccm.202309-1644CP.
• Mao L, Kim K, Li Y. On recurrent-event win ratio. Stat Methods Med Res. 2022;31(6):1120-34. doi:10.1177/09622802221084134.
• Ajufo E, Nayak A, Mehra MR. Fallacies of using the win ratio in cardiovascular trials: challenges and solutions. JACC Basic Transl Sci. 2023;8(6):720-7. doi:10.1016/j.jacbts.2023.05.004.
• Pocock SJ, Ariti CA, Collier TJ, Wang D. The win ratio: a new approach to the analysis of composite endpoints in clinical trials based on clinical priorities. Eur Heart J. 2012;33(2):176-82. doi:10.1093/eurheartj/ehr352.
• Wang B, Zhou D, Zhang J, Kim Y, Chen LW, Dunnmon P, et al. Statistical power considerations in the use of win ratio in cardiovascular outcome trials. Contemp Clin Trials. 2023;124:107040. doi:10.1016/j.cct.2022.107040.
• Redfors B, Gregson J, Crowley A, McAndrew T, Ben-Yehuda O, Stone GW, et al. The win ratio approach for composite endpoints: practical guidance based on previous experience. Eur Heart J. 2020;41(46):4391-9. doi:10.1093/eurheartj/ehaa665.
• Song J, Verbeeck J, Huang B, Hoaglin DC, Gamalo-Siebers M, Seifu Y, et al. The win odds: statistical inference and regression. J Biopharm Stat. 2023;33(2):140-50. doi:10.1080/10543406.2022.2089156.
• Luo X, Tian H, Mohanty S, Tsai WY. An alternative approach to confidence interval estimation for the win ratio statistic. Biometrics. 2015;71(1):139-45. doi:10.1111/biom.12225.
• Dong G, Li D, Ballerstedt S, Vandemeulebroecke M. A generalized analytic solution to the win ratio to analyze a composite endpoint considering the clinical importance order among components. Pharm Stat. 2016;15(5):430-7. doi:10.1002/pst.1763.
• Oakes D. On the win-ratio statistic in clinical trials with multiple types of event. Biometrika. 2016;103(3):742-5. doi:10.1093/biomet/asw026.
• Bebu I, Lachin JM. Large sample inference for a win ratio analysis of a composite outcome based on prioritized components. Biostatistics. 2016;17(1):178-87. doi:10.1093/biostatistics/kxv032.
• Luo X, Qiu J, Baid S, Tian H. Weighted win loss approach for analyzing prioritized outcomes. Stat Med. 2017;36(15):2452-65. doi:10.1002/sim.7284.
• Wang D, Pocock S. A win ratio approach to comparing continuous non-normal outcomes in clinical trials. Pharm Stat. 2016;15(3):238-45. doi:10.1002/pst.1743.
• Dong G, Hoaglin DC, Qiu J, Matsouaka RA, Chang YW, Wang J, et al. The win ratio: on interpretation and handling of ties. Stat Biopharm Res. 2020;12(1):99-106. doi:10.1080/19466315.2019.1575279.
• Finkelstein DM, Schoenfeld DA. Graphing the win ratio and its components over time. Stat Med. 2019;38(1):53-61. doi:10.1002/sim.7895.
• Dong G, Qiu J, Wang D, Vandemeulebroecke M. The stratified win ratio. J Biopharm Stat. 2018;28(4):778-96. doi:10.1080/10543406.2017.1397007.
• Mao L. On the alternative hypotheses for the win ratio. Biometrics. 2019;75(1):347-51. doi:10.1111/biom.12954.
• Finkelstein DM, Schoenfeld DA. Combining mortality and longitudinal measures in clinical trials. Stat Med. 1999;18(11):1341-54. doi:10.1002/(sici)1097-0258(19990615)18:11<1341::aid-sim129>3.0.co;2-7.
• Hara H, van Klaveren D, Kogame N, Chichareon P, Modolo R, Tomaniak M, et al. Statistical methods for composite endpoints. EuroIntervention. 2021;16(18):e1484-95. doi:10.4244/EIJ-D-19-00953.
• Wang H, Peng J, Zheng JZ, Wang B, Lu X, Chen C, et al. Win ratio -an intuitive and easy-to-interpret composite outcome in medical studies. Shanghai Arch Psychiatry. 2017;29(1):55-60. doi:10.11919/j.issn.1002-0829.217011.
• Chiaruttini MV, Lorenzoni G, Spolverato G, Gregori D. Win statistics in observational cancer research: integrating clinical and quality-of-life outcomes. J Clin Med. 2024;13(11):3272. doi:10.3390/jcm13113272.
• Brunner E, Vandemeulebroecke M, Mütze T. Win odds: an adaptation of the win ratio to include ties. Stat Med. 2021;40(14):3367-84. doi:10.1002/sim.8967.