Analysis of ordered composite endpoints

Follmann, Dean; Hamasaki, Toshimitsu; Evans, Scott

doi:10.1002/sim.8431

Cited by 14 publications

(9 citation statements)

References 24 publications

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“…Recently, several authors have proposed methods for modelling the win-ratio as a function of covariates (e.g. Follmann et al, 2020;Mao and Wang, 2021). The estimators of the model parameters are related to the PIM parameter estimators of Thas et al (2012).…”

Section: Discussionmentioning

confidence: 99%

Semiparametric Estimation of Probabilistic Index Models: Efficiency and Bias

Vermeulen¹,

Neve²,

Amorim³

et al. 2023

STAT SINICA

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Many well known rank tests can be viewed as score tests under probabilistic index models: regression models for the conditional probability that the outcome of one randomly chosen subject exceeds the outcome of another independently chosen subject. Probabilistic index models (PIMs) provide a natural regression framework for nonparametric rank tests. In addition, PIMs supplement these tests with effect sizes and ease the development of more flexible tests e.g., tests which allow for covariate adjustment. Inference for probabilistic index models is currently based on an estimator, referred to as the standard estimator, that was heuristically derived. By appealing to semiparametric theory and a Hoeffding decomposition, we rigorously derive the class of all consistent and asymptotically normal estimators for the parameters indexing a probabilistic in-

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Section: Discussionmentioning

confidence: 99%

Semiparametric Estimation of Probabilistic Index Models: Efficiency and Bias

Vermeulen¹,

Neve²,

Amorim³

et al. 2023

STAT SINICA

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“…6 These regression approaches have different assumptions compared to ordinal logistic regression but have the advantage of the ability to deal with censoring. 7…”

Section: Methodsmentioning

confidence: 99%

Methodologies for pragmatic and efficient assessment of benefits and harms: Application to the SOCRATES trial

Evans

Knutsson

Amarenco³

et al. 2020

Clinical Trials

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Background/Aims: Standard approaches to trial design and analyses can be inefficient and non-pragmatic. Failure to consider a range of outcomes impedes evidence-based interpretation and reduces power. Traditional approaches synthesizing information obtained from separate analysis of each outcome fail to incorporate associations between outcomes and recognize the cumulative nature of outcomes in individual patients, suffer from competing risk complexities during interpretation, and since efficacy and safety analyses are often conducted on different populations, generalizability is unclear. Pragmatic and efficient approaches to trial design and analyses are needed. Methods: Approaches providing a pragmatic assessment of benefits and harms of interventions, summarizing outcomes experienced by patients, and providing sample size efficiencies are described. Ordinal outcomes recognize finer gradations of patient responses. Desirability of outcome ranking is an ordinal outcome combining benefits and harms within patients. Analysis of desirability of outcome ranking can be based on rank-based methodologies including the desirability of outcome ranking probability, the win ratio, and the proportion in favor of treatment. Partial credit analyses, involving grading the levels of the desirability of outcome ranking outcome similar to an academic test, provides an alternative approach. The methodologies are demonstrated using the acute stroke or transient ischemic attack treated with aspirin or ticagrelor and patient outcomes study (SOCRATES; NCT01994720), a randomized clinical trial. Results: Two 5-level ordinal outcomes were developed for SOCRATES. The first was based on a modified Rankin scale. The odds ratio is 0.86 (95% confidence interval = 0.75, 0.99; p = 0.04) indicating that the odds of worse stroke categorization for a trial participant assigned to ticagrelor is 0.86 times that of a trial participant assigned to aspirin. The 5-level desirability of outcome ranking outcome incorporated and prioritized survival; the number of strokes, myocardial infarction, and major bleeding events; and whether a stroke event was disabling. The desirability of outcome ranking probability and win ratio are 0.504 (95% confidence interval = 0.499, 0.508; p = 0.10) and 1.11 (95% confidence interval = 0.98, 1.26; p = 0.10), respectively, implying that the probability of a more desirable result with ticagrelor is 50.4% and that a more desirable result occurs 1.11 times more frequently on ticagrelor versus aspirin. Conclusion: Ordinal outcomes can improve efficiency through required pre-specification, careful construction, and analyses. Greater pragmatism can be obtained by composing outcomes within patients. Desirability of outcome ranking provides a global assessment of the benefits and harms that more closely reflect the experience of patients. The desirability of outcome ranking probability, the proportion in favor of treatment, the win ratio, and partial credit can more optimally inform patient treatment, enhance the understanding of the totality of intervention effects on patients, and potentially provide efficiencies over standard analyses. The methods provide the infrastructure for incorporating patient values and estimating personalized effects.

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“…The proportional win-fractions assumption is key to ensuring that the regression parameters are scientifically interpretable. Early approaches to a meaningful win ratio estimand have relied on special cases with component-wise proportional hazards structures (Kotalik et al, 2019;Follmann et al, 2020). Our model specification in terms of the time-curtailed win ratio (Oakes, 2016) allows us to directly model the covariate-specific win ratio, bypassing restrictive joint models.…”

Section: Analysis Of the Hf-action Studymentioning

confidence: 99%

A class of proportional win‐fractions regression models for composite outcomes

Mao

Wang

2020

Biometrics

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The win ratio is gaining traction as a simple and intuitive approach to analysis of prioritized composite endpoints in clinical trials. To extend it from twosample comparison to regression, we propose a novel class of semiparametric models that includes as special cases both the two-sample win ratio and the traditional Cox proportional hazards model on time to the first event. Under the assumption that the covariate-specific win and loss fractions are proportional over time, the regression coefficient is unrelated to the censoring distribution and can be interpreted as the log win ratio resulting from one-unit increase in the covariate. 𝑈-statistic estimating functions, in the form of an arbitrary covariatespecific weight process integrated by a pairwise residual process, are constructed to obtain consistent estimators for the regression parameter. The asymptotic properties of the estimators are derived using uniform weak convergence theory for 𝑈-processes. Visual inspection of a "score" process provides useful clues as to the plausibility of the proportionality assumption. Extensive numerical studies using both simulated and real data from a major cardiovascular trial show that the regression methods provide valid inference on covariate effects and outperform the two-sample win ratio in both efficiency and robustness. The proposed methodology is implemented in the R-package WR, publicly available from the Comprehensive R Archive Network (CRAN).

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Analysis of ordered composite endpoints

Cited by 14 publications

References 24 publications

Semiparametric Estimation of Probabilistic Index Models: Efficiency and Bias

Semiparametric Estimation of Probabilistic Index Models: Efficiency and Bias

Methodologies for pragmatic and efficient assessment of benefits and harms: Application to the SOCRATES trial

A class of proportional win‐fractions regression models for composite outcomes

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