The win ratio: Impact of censoring and follow‐up time and use with nonproportional hazards

Abstract

The win ratio has been studied methodologically and applied in data analysis and in designing clinical trials. Researchers have pointed out that the results depend on follow-up time and censoring time, which are sometimes used interchangeably. In this article, we distinguish between follow-up time and censoring time, show theoretically the impact of censoring on the win ratio, and illustrate the impact of follow-up time. We then point out that, if the treatment has long-term benefit from a more important but less frequent endpoint (eg, death), the win ratio can show that benefit by following patients longer, avoiding masking by more frequent but less important outcomes, which occurs in conventional time-to-first-event analyses. For the situation of nonproportional hazards, we demonstrate that the win ratio can be a good alternative to methods such as landmark survival rate, restricted mean survival time, and weighted log-rank tests. KEYWORDS hazard ratio, landmark survival rate, log-rank test, prioritized pairwise comparisons, restricted mean survival time 1 | INTRODUCTIONMuch interest has focused on composite time-to-event endpoints when the component outcomes can be prioritized according to their clinical importance. The win ratio 1 takes into account the clinical importance order among the components, and its simple and intuitive derivation make it attractive, compared with other methods for prioritized multiple outcomes such as weighted composites and rank tests. The net benefit 2-4 (proportion in favor of treatment) is the difference in win proportion between the two groups, so the two methods are closely related.The win ratio method has received much attention in methodological research. 5-14 One possible drawback is that it depends on follow-up time and censoring. [5][6][7][8]15 To reduce the impact of censoring (or follow-up) time, Oakes 7 proposed to calculate the win ratio from the time-to-event information as of a common time, c. Further, Rauch et al 16 argued that the win ratio should not be used in the presence of censoring, and they gave an illustrative example under proportional hazards (see Section 5.2 of Rauch et al 16 ). Also, some discussions of the win ratio have used censoring time and followup time interchangeably in a broad sense.In practice, the win ratio method has been used for many retrospective analyses of clinical trials and applied in study designs. In particular, together with the Finkelstein-Schoenfeld test, 17 the win ratio was used in the primary analysis for the tafamidis Phase III transthyretin amyloid cardiomyopathy (ATTR-ACT) study. 18,19 On the composite primary endpoint of all-cause mortality and frequency of cardiovascular(CV)-related hospitalization, the (stratified) win ratio

Adjusting win statistics for dependent censoring

“…However, the unadjusted win statistics differ only slightly from the IPCW-adjusted and CovIPCW-adjusted analyses since the hazard of cardiovascular death as well as that of hospitalizations due to chronic heart failure were in general proportional between the two treatment groups. This finding is consistent with Oakes, 22 Finkelstein and Schoenfeld, 17 and Dong et al 15 on win statistics under the proportional hazards model.…”

“…Over the past decade, win statistics have been the subject of rich methodological research. [12][13][14][15][16][17][18][19][20][21][22][23][24][25] For time-to-event outcomes, censoring may introduce bias. Methods have been developed to correct for bias in the presence of independent censoring.…”

Win odds: An adaptation of the win ratio to include ties

“…For further investigations of pairwise comparisons in the time‐to‐event setting, in particular for discussions of issues related to censoring, we refer to the literature 10,36,58‐60 …”

“…Finkelstein and Schoenfeld 35 recommended to graph the win ratio over time and to be transparent about the influence of follow‐up times. Dong et al 36 see an advantage of the win ratio if patients are followed up longer.…”

The inverse-probability-of-censoring weighting (IPCW) adjusted win ratio statistic: an unbiased estimator in the presence of independent censoring

“…Since its introduction by Pocock et al in 2012, the win ratio method has received much attention in methodological research (Dong et al, 2016(Dong et al, , 2018(Dong et al, , 2019(Dong et al, and 2020Luo et al, 2015 and2017;Bebu and Lachin, 2016; Wang and Pocock, 2016;Oakes, 2016;Finkelstein and Schoenfeld, 2019;Mao, 2019), ad hoc analyses, and designs of prospective studies. In the tafamidis Phase III transthyretin amyloid cardiomyopathy study (ATTR-ACT) (Maurer et al, 2018;Pocock et al, 2019), the win ratio, as the primary analysis of the composite primary endpoint, supported the approval by the US Food and Drug Administration (FDA) of VYNDAQEL® (tafamidis meglumine) and VYNDAMAX™ (tafamidis) for treatment of cardiomyopathy to reduce cardiovascular mortality and cardiovascular-related hospitalization.…”