Large sample inference for a win ratio analysis of a composite outcome based on prioritized components

Bebu, Ionut; Lachin, John M.

doi:10.1093/biostatistics/kxv032

Cited by 93 publications

(114 citation statements)

References 22 publications

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“…A closed form variance estimate for the WR was developed in the work of Bebu and Lachin. 12 A related estimand that counts such "tied" subjects is the MW parameter given by 13 which was mentioned in the work of Evans and Follmann 10 as a natural metric for the DOOR ranking approach. A form that allows for covariates with uncensored data is known as the probabilistic index.…”

Section: Methodsmentioning

confidence: 99%

Analysis of ordered composite endpoints

Follmann

Hamasaki

Evans

2019

Statistics in Medicine

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Composite endpoints are frequently used in clinical trials, but simple approaches, such as the time to first event, do not reflect any ordering among the endpoints. However, some endpoints, such as mortality, are worse than others. A variety of procedures have been proposed to reflect the severity of the individual endpoints such as pairwise ranking approaches, the win ratio, and the desirability of outcome ranking. When patients have different lengths of follow-up, however, ranking can be difficult and proposed methods do not naturally lead to regression approaches and require specialized software. This paper defines an ordering score O to operationalize the patient ranking implied by hierarchical endpoints. We show how differential right censoring of follow-up corresponds to multiple interval censoring of the ordering score allowing standard software for survival models to be used to calculate the nonparametric maximum likelihood estimators (NPMLEs) of different measures. Additionally, if one assumes that the ordering score is transformable to an exponential random variable, a semiparametric regression is obtained, which is equivalent to the proportional hazards model subject to multiple interval censoring. Standard software can be used for estimation. We show that the NPMLE can be poorly behaved compared to the simple estimators in staggered entry trials. We also show that the semiparametric estimator can be more efficient than simple estimators and explore how standard Cox regression maneuvers can be used to assess model fit, allow for flexible generalizations, and assess interactions of covariates with treatment. We analyze a trial of short versus long-term antiplatelet therapy using our methods. KEYWORDScomposite endpoints, DOOR, pairwise regression, probabilistic index model, win ratio INTRODUCTIONComposite endpoints are frequently used in clinical trials to provide a more comprehensive characterization of clinical outcomes than can be achieved by a single endpoint. In cardiovascular disease, the composite endpoint might include death, stroke, myocardial infarction (MI), major bleed, or revascularization. In trials of infections with drug resistant pathogens, death and kidney failure might be used while in trials of multiple sclerosis, death, relapse, or "substantial progression" might be used. Often, components of the endpoint are treated equally, for example, by using the time to occurrence of the first of any constituent endpoints.

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Section: Methodsmentioning

confidence: 99%

Analysis of ordered composite endpoints

Follmann

Hamasaki

Evans

2019

Statistics in Medicine

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“…The function "wwratio", based on Luo et al [4], provides calculation of the weighted win loss statistics and their corresponding asymptotic variances under the same setting. And the function "genwr", based on the idea of Bebu and Lachin [5], provides calculation of the (un-weighted) win loss statistics and their corresponding asymptotic variances for general types of outcomes. Note that, instead of using n 1 -1 and n 0 -1 in the calculation of estimated variances as Bebu and Lachin [5], we use n 1 and n 0 in the calculation which is consistent with the variance estimation in "winratio" and "wwratio".…”

Section: Package Overview and Usagementioning

confidence: 99%

“…And the function "genwr", based on the idea of Bebu and Lachin [5], provides calculation of the (un-weighted) win loss statistics and their corresponding asymptotic variances for general types of outcomes. Note that, instead of using n 1 -1 and n 0 -1 in the calculation of estimated variances as Bebu and Lachin [5], we use n 1 and n 0 in the calculation which is consistent with the variance estimation in "winratio" and "wwratio". We expect the difference is small between these two versions of variance calculation when the sample size is moderate to large.…”

Section: Package Overview and Usagementioning

confidence: 99%

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WWR: An R package for analyzing prioritized outcomes

Qiu¹,

Luo²,

Bai³

et al. 2017

J Med Stat Inform

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Background: In analyzing survival trials, time-to-first-event analysis is commonly used without considering clinical importance of different events. The recently proposed win loss approach can take into account the order of clinical importance of clinical events. The weighted win loss approach improves the efficiency of the original win loss approach with optimal weights. The general win loss approach can be used to handle all types of outcomes. A publically available tool to implement these approaches is on demand. Methods: We developed an R package, WWR, to implement the win loss approaches in analyzing prioritized outcomes. Results:We illustrate the use of this package with a real data example. Conclusions:The WWR package provides an efficient way to calculate the win loss statistics (ratio, difference and product) and their asymptotic variances along with the contribution indexes.

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“…Thus, in order to take ties appropriately into account, we use a more general definition of the Mann-Whitney effect: p " P pT 1 ą T 2 q`1 2 P pT 1 " T 2 q, (1.1) also known as ordinal effect size measure in case of completely observed data (Ryu and Agresti 2008;Konietschke et al 2012). Recently, a related effect measure, the so called win ratio (for prioritized outcomes), has been investigated considerably by several authors (Pocock et al 2012, Rauch et al 2014, Luo et al 2015, Abdalla et al 2016Bebu and Lachin 2016 as well as Wang and Pocock 2016). It is the odds of the Mann-Whitney effect p in (1.1), i.e.…”

Section: Introductionmentioning

confidence: 99%

Bootstrap- and permutation-based inference for the Mann–Whitney effect for right-censored and tied data

Dobler¹,

Pauly²

2017

TEST

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The Mann-Whitney effect is an intuitive measure for discriminating two survival distributions.Here we analyze various inference techniques for this parameter in a two-sample survival setting with independent right-censoring, where the survival times are even allowed to be discretely distributed. This allows for ties in the data and requires the introduction of normalized versions of Kaplan-Meier estimators from which adequate point estimates are deduced. Asymptotically exact inference procedures based on standard normal, bootstrap-and permutation-quantiles are developed and compared in simulations. Here, the asymptotically robust and -under exchangeable data -even finitely exact permutation procedure turned out to be the best. Finally, all procedures are illustrated using a real data set.

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Large sample inference for a win ratio analysis of a composite outcome based on prioritized components

Cited by 93 publications

References 22 publications

Analysis of ordered composite endpoints

Analysis of ordered composite endpoints

WWR: An R package for analyzing prioritized outcomes

Bootstrap- and permutation-based inference for the Mann–Whitney effect for right-censored and tied data

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