Restricted accessResearch articleFirst published online 2023-3
Generalised pairwise comparisons for trend: An extension to the win ratio and win odds for dose-response and prognostic variable analysis with arbitrary statements of outcome preference
The win ratio is a novel approach for handling complex patient outcomes that have seen considerable interest in the medical statistics literature, and operates by considering all-to-all pairwise statements of preference on outcomes. Recent extensions to the method have focused on the two-group case, with few developments made for considering the impact of a well-ordered explanatory variable, which would allow for dose-response analysis or the analysis of links between complex patient outcomes and prognostic variables. Where such methods have been developed, they are semiparametric methods that can only be applied to survival outcomes. In this article, we introduce the generalised pairwise comparison for trend, a modified form of Agresti’s generalised odds ratio. This approach is capable of considering arbitrary statements of preference, thus enabling its use across all types of outcome data. We provide a simulation study validating the approach and illustrate it with three clinical applications in stroke research.
PeacockJPeacockP. Oxford handbook of medical statistics. New York: Oxford University Press, 2011.
2.
GómezGLagakosSW. Statistical considerations when using a composite endpoint for comparing treatment groups. Stat Med2013; 32: 719–738.
3.
JerathAAustinPCWijeysunderaDN. Days alive and out of hospital: Validation of a patient-centered outcome for perioperative medicine. Anesthesiology2019; 131: 84–93.
4.
AngusDCDerdeLAl-BeidhF, et al. Effect of hydrocortisone on mortality and organ support in patients with severe covid-19: The remap-cap covid-19 corticosteroid domain randomized clinical trial. JAMA2020; 324: 1317–1329.
5.
BollenKA. Latent variables in psychology and the social sciences. Annu Rev Psychol2002; 53: 605–634.
6.
RethnamVBernhardtJDeweyH, et al. Utility-weighted modified Rankin scale: Still too crude to be a truly patient-centric primary outcome measure?Int J Stroke2020; 15: 268–277.
7.
BuyseM. Generalized pairwise comparisons of prioritized outcomes in the two-sample problem. Stat Med2010; 29: 3245–3257.
8.
PocockSJAritiCACollierTJ, et al. The win ratio: A new approach to the analysis of composite endpoints in clinical trials based on clinical priorities. Eur Heart J2012; 33: 176–182.
9.
JohnsHBernhardtJChurilovL. Distance-based classification and regression trees for the analysis of complex predictors in health and medical research. Stat Methods Med Res2021; 30: 2085–2104.
10.
DongGLiDBallerstedtS, et al. A generalized analytic solution to the win ratio to analyze a composite endpoint considering the clinical importance order among components. Pharm Stat2016; 15: 430–437.
11.
MaoLKimKMiaoX. Sample size formula for general win ratio analysis. Biometrics 2022; 78: 1257–1268.
12.
RauchGKunzmannKKieserM, et al. A weighted combined effect measure for the analysis of a composite time-to-first-event endpoint with components of different clinical relevance. Stat Med2018; 37: 749–767.
13.
RauchGJahn-EimermacherABrannathW, et al. Opportunities and challenges of combined effect measures based on prioritized outcomes. Stat Med2014; 33: 1104–1120.
14.
ZimmermannGBrunnerEBrannathW, et al. Pseudo-ranks: The better way of ranking?Am Stat 2022; 76: 124–130.
15.
BrunnerEVandemeulebroeckeMMützeT. Win odds: An adaptation of the win ratio to include ties. Stat Med 2021; 40: 3367–3384.
16.
LuoXTianHMohantyS, et al. An alternative approach to confidence interval estimation for the win ratio statistic. Biometrics2015; 71: 139–145.
17.
BebuILachinJM. Large sample inference for a win ratio analysis of a composite outcome based on prioritized components. Biostatistics2016; 17: 178–187.
18.
DongGQiuJWangD, et al. The stratified win ratio. J Biopharm Stat2018; 28: 778–796.
19.
GasparyanSBFolkvaljonFBengtssonO, et al. Adjusted win ratio with stratification: Calculation methods and interpretation. Stat Methods Med Res2021; 30: 580–611.
20.
DongGHoaglinDCQiuJ, et al. The win ratio: On interpretation and handling of ties. Stat Biopharm Res 2020: 12; 99–106.
21.
DongGMaoLHuangB, et al. The inverse-probability-of-censoring weighting (IPCW) adjusted win ratio statistic: An unbiased estimator in the presence of independent censoring. J Biopharm Stat2020; 30: 882–899.
22.
DongGHuangBWangD, et al. Adjusting win statistics for dependent censoring. Pharm Stat 2021; 20: 440–450.
23.
MaoLWangT. A class of proportional win-fractions regression models for composite outcomes. Biometrics2021; 77: 1265–1275.
24.
MackMJLeonMBThouraniVH, et al. Transcatheter aortic-valve replacement with a balloon-expandable valve in low-risk patients. N Engl J Med2019; 380: 1695–1705.
25.
MaurerMSSchwartzJHGundapaneniB, et al. Tafamidis treatment for patients with transthyretin amyloid cardiomyopathy. N Engl J Med2018; 379: 1007–1016.
26.
RogersJKPocockSJMcMurrayJJ, et al. Analysing recurrent hospitalizations in heart failure: A review of statistical methodology, with application to charm-preserved. Eur J Heart Fail2014; 16: 33–40.
27.
BenatarMWuuJAndersenPM, et al. Randomized, double-blind, placebo-controlled trial of arimoclomol in rapidly progressive SOD1 ALS. Neurology2018; 90: e565–e574.
28.
NovackVBeitlerJRYitshak-SadeM, et al. Alive and ventilator-free: A hierarchical, composite outcome for clinical trials in the acute respiratory distress syndrome. Crit Care Med2020; 48: 158.
29.
AgrestiA. Generalized odds ratios for ordinal data. Biometrics1980; 36: 59–67.
30.
KendallM. Rank correlation methods, 4th ed. High Wycombe, Bucks.: Charles Griffin, 1970.
31.
GoodmanLAKruskalWH. Measures of association for cross classifications. J Am Stat Assoc1954; 49: 732–764.
32.
CheungLCPanQHyunN, et al. Prioritized concordance index for hierarchical survival outcomes. Stat Med2019; 38: 2868–2882.
33.
O'Brien RG and Castelloe J. Exploiting the link between the Wilcoxon-Mann–Whitney test and a simple odds statistic. In Proceedings of the 2005 American Statistical Association conference. San Francisco, America, March 26–29 2006, paper no 209-31. Cary, NC: SAS Institute. https://support.sas.com/resources/papers/proceedings/proceedings/sugi31/toc.html#st.
34.
CampbellBCMitchellPJChurilovL, et al. Tenecteplase versus alteplase before thrombectomy for ischemic stroke. N Engl J Med2018; 378: 1573–1582.
35.
CampbellBCMitchellPJChurilovL, et al. Effect of intravenous tenecteplase dose on cerebral reperfusion before thrombectomy in patients with large vessel occlusion ischemic stroke: The Extend-IA TNK part 2 randomized clinical trial. JAMA2020; 323: 1257–1265.
36.
BanksJLMarottaCA. Outcomes validity and reliability of the modified Rankin scale: implications for stroke clinical trials: A literature review and synthesis. Stroke2007; 38: 1091–1096.
37.
BrottTAdams JrHPOlingerCP, et al. Measurements of acute cerebral infarction: A clinical examination scale. Stroke1989; 20: 864–870.
38.
NagarajaNForderJRWarachS, et al. Reversible diffusion-weighted imaging lesions in acute ischemic stroke: A systematic review. Neurology2020; 94: 571–587.
39.
WoutersANystenCThijsV, et al. Prediction of outcome in patients with acute ischemic stroke based on initial severity and improvement in the first 24 h. Front Neurol2018; 308. DOI: 10.3389/fneur.2018.00308
40.
BernhardtJLanghornePLindleyRI, et al. Efficacy and safety of very early mobilisation within 24 h of stroke onset (avert): A randomised controlled trial. Lancet2015; 386: 46–55.
41.
HawthorneGRichardsonJOsborneR. The assessment of quality of life (AQoL) instrument: A psychometric measure of health-related quality of life. Qual Life Res1999; 8: 209–224.
42.
CouparFPollockARoweP, et al. Predictors of upper limb recovery after stroke: A systematic review and meta-analysis. Clin Rehabil2012; 26: 291–313.
43.
WesterlindEPerssonHCSunnerhagenKS. Return to work after a stroke in working age persons; a six-year follow up. PLoS ONE2017; 12: e0169759.
44.
WaltersRCollierJMCarvalhoLB, et al. Exploring post acute rehabilitation service use and outcomes for working age stroke survivors ( 65 years) in Australia, UK and South East Asia: Data from the international avert trial. BMJ Open2020; 10: e035850.
45.
ZannadFMcMurrayJJKrumH, et al. Eplerenone in patients with systolic heart failure and mild symptoms. N Engl J Med2011; 364: 11–21.
46.
BrillemanSLWolfeRMoreno-BetancurM, et al. Simulating survival data using the simsurv R package. J Stat Softw2021; 97: 1–27.
47.
RedforsBGregsonJCrowleyA, et al. The win ratio approach for composite endpoints: Practical guidance based on previous experience. Eur Heart J2020; 41: 4391–4399.
48.
DongGHuangBVerbeeckJ, et al. Win statistics (win ratio, win odds, and net benefit) can complement one another to show the strength of the treatment effect on time-to-event outcomes. Pharm Stat2022. DOI: 10.1002/pst.2251
49.
VerbeeckJOzenneBAndersonWN. Evaluation of inferential methods for the net benefit and win ratio statistics. J Biopharm Stat2020; 30: 765–782.
50.
ThasONeveJDClementL, et al. Probabilistic index models. J R Stat Soc: Ser B (Stat Methodol)2012; 74: 623–671.
Supplementary Material
Please find the following supplemental material available below.
For Open Access articles published under a Creative Commons License, all supplemental material carries the same license as the article it is associated with.
For non-Open Access articles published, all supplemental material carries a non-exclusive license, and permission requests for re-use of supplemental material or any part of supplemental material shall be sent directly to the copyright owner as specified in the copyright notice associated with the article.
