Use of win time for ordered composite endpoints in clinical trials

Consider the choice of outcome for overall treatment benefit in a clinical trial which measures the first time to each of several clinical events. We describe several new variants of the win ratio that incorporate the time spent in each clinical state over the common follow-up, where clinical state means the worst clinical event that has occurred by that time. One version allows restriction so that death during follow-up is most important, while time spent in other clinical states is still accounted for. Three other variants are described; one is based on the average pairwise win time, one creates a continuous outcome for each participant based on expected win times against a reference distribution and another that uses the estimated distributions of clinical state to compare the treatment arms. Finally, a combination testing approach is described to give robust power for detecting treatment benefit across a broad range of alternatives. These new methods are designed to be closer to the overall treatment benefit/harm from a patient's perspective, compared to the ordinary win ratio. The new methods are compared to the composite event approach and the ordinary win ratio. Simulations show that when overall treatment benefit on death is substantial, the variants based on either the participants' expected win times (EWTs) against a reference distribution or estimated clinical state distributions have substantially higher power than either the pairwise comparison or composite event methods. The methods are illustrated by re-analysis of the trial heart failure: a controlled trial investigating outcomes of exercise training.

Win ratio analyses of piperacillin-tazobactam versus meropenem for ceftriaxone non-susceptible Escherichia coli or Klebsiella pneumoniae bloodstream infections: Post-hoc insights from the MERINO trial

BACKGROUND

Clinical trials of treatments for serious infections commonly use the primary endpoint of all-cause mortality. However, many trial participants survive their infection and this endpoint may not truly reflect important benefits and risks of therapy. The win ratio uses a hierarchical composite endpoint that can incorporate and prioritise outcome measures by relative clinical importance.

METHODS

The win ratio methodology was applied post-hoc to outcomes observed in the MERINO trial, which compared piperacillin-tazobactam with meropenem. We quantified the win ratio with a primary hierarchical composite endpoint, including all-cause mortality, microbiological relapse and secondary infection. A win ratio of one would correspond to no difference between the two antibiotics, while a ratio less than one favors meropenem. Further analyses were performed to calculate the win odds and to introduce a continuous outcome variable in order to reduce ties.

RESULTS

With the hierarchy of all-cause mortality, microbiological relapse and secondary infection, the win ratio estimate was 0.40 (95% CI: 0.22, 0.71; p=0.002), favoring meropenem over piperacillin-tazobactam. However, 73.4% of the pairs were tied due to the small proportion of events. The win odds, a modification of the win ratio accounting for ties, was 0.79 (95% CI: 0.68, 0.92). The addition of length of stay to the primary composite, greatly minimised the number of ties (4.6%) with a win ratio estimate of 0.77 (95% CI: 0.60-0.99; p=0.04).

CONCLUSIONS

The application of the win ratio methodology to the MERINO trial data illustrates its utility and feasibility for use in antimicrobial trials.

Clinician's Approach to Advanced Statistical Methods: Win Ratios, Restricted Mean Survival Time, Responder Analyses, and Standardized Mean Differences

Novel statistical methods have emerged in recent medical literature, which clinicians must understand to properly appraise and integrate evidence into their practice. Some of these key concepts include win ratios, restricted mean survival time, responder analyses, and standardized mean difference. This article offers guidance to busy clinicians on the comprehension and practical applicability of the results to patients. Win ratios provide an alternative method to analyze composite outcomes by prioritizing individual components of the composite; prioritization of the outcomes should be evidence-based, pre-specified, and patient-centered. Restricted mean survival time presents a method to analyze Kaplan-Meier curves when assumptions required for Cox proportional hazards analysis are not met. As it only considers outcomes that occur within a specific timeframe, the duration of follow-up must be appropriately defined and based on prior epidemiologic and mechanistic evidence. Researchers can analyze continuous outcomes with responder analyses, in which participants are dichotomized into "responders" or "non-responders." While clinicians and patients may more easily grasp outcomes analyzed in this way, they should be aware of the loss of information and resulting imprecision, as well as potential to manipulate data presentation. When meta-analyzing continuous outcomes, point estimates can be converted to standardized mean differences to facilitate the combination of data utilizing various outcome measures. However, clinicians may find it challenging to grasp the clinical meaningfulness of a standardized mean difference, and may benefit from converting it to well-known outcomes. By providing the background knowledge of these statistical methods, along with practical applicability, benefits, and inevitable limitations, this article aims to provide clinicians with an approach to appraise the literature and apply the results in clinical practice.

Assessment of the DNA Mismatch Repair System Is Crucial in Colorectal Cancers Necessitating Adjuvant Treatment: A Propensity Score-Matched and Win Ratio Analysis

A deficient DNA mismatch repair (MMR) system is identified in a non-negligible part of sporadic colorectal cancers (CRCs), and its prognostic value remains controversial. High tumor mutational burden, along with a poor response to conventional chemotherapy and excellent results from immunotherapy, are the main features of this subset. The aim of this study was to evaluate the predictive value of DNA MMR system status for its best treatment. Four hundred and three CRC patients, operated on from 2014 to 2021 and not treated with immunotherapy, entered this study. Immunohistochemistry and polymerase chain reaction, as appropriate, were used to unequivocally group specimens into microsatellite stable (MSS) and instable (MSI) tumors. The win-ratio approach was utilized to compare composite outcomes. MSI tumors accounted for 12.9% of all series. The right tumor location represented the most important factor related to MSI. The status of the DNA MMR system did not appear to correlate with outcome in early-stage CRCs not requiring adjuvant treatment; in advanced stages undergoing conventional chemotherapy, MSI tumors showed significantly poorer overall and disease-free survival rates and the highest win ratio instead. The determination of DNA MMR status is crucial to recommending correct management. There is clear evidence that instable CRCs needing adjuvant therapy should undergo appropriate treatments.

Safety and Efficacy of Renal Denervation in Patients Taking Antihypertensive Medications

BACKGROUND

Renal denervation (RDN) reduces blood pressure (BP) in patients with uncontrolled hypertension in the absence of antihypertensive medications.

OBJECTIVES

This trial assessed the safety and efficacy of RDN in the presence of antihypertensive medications.

METHODS

SPYRAL HTN-ON MED is a prospective, randomized, sham-controlled, patient- and assessor-blinded trial enrolling patients from 56 clinical centers worldwide. Patients were prescribed 1 to 3 antihypertensive medications. Patients were randomized to radiofrequency RDN or sham control procedure. The primary efficacy endpoint was the baseline-adjusted change in mean 24-hour ambulatory systolic BP at 6 months between groups using a Bayesian trial design and analysis.

RESULTS

The treatment difference in the mean 24-hour ambulatory systolic BP from baseline to 6 months between the RDN group (n = 206; -6.5 ± 10.7 mm Hg) and sham control group (n = 131; -4.5 ± 10.3 mm Hg) was -1.9 mm Hg (95% CI: -4.4 to 0.5 mm Hg; P = 0.12). There was no significant difference between groups in the primary efficacy analysis with a posterior probability of superiority of 0.51 (Bayesian treatment difference: -0.03 mm Hg [95% CI: -2.82 to 2.77 mm Hg]). However, there were changes and increases in medication intensity among sham control patients. RDN was associated with a reduction in office systolic BP compared with sham control at 6 months (adjusted treatment difference: -4.9 mm Hg; P = 0.0015). Night-time BP reductions and win ratio analysis also favored RDN. There was 1 adverse safety event among 253 assessed patients.

CONCLUSIONS

There was no significant difference between groups in the primary analysis. However, multiple secondary endpoint analyses favored RDN over sham control. (SPYRAL HTN-ON MED Study [Global Clinical Study of Renal Denervation With the Symplicity Spyral Multi-electrode Renal Denervation System in Patients With Uncontrolled Hypertension in the Absence of Antihypertensive Medications]; NCT02439775).

Using the win ratio to compare laparoscopic versus open liver resection for colorectal cancer liver metastases

Background

We sought to assess the overall benefit of laparoscopic versus open hepatectomy for treatment of colorectal liver metastases (CRLMs) using the win ratio, a novel methodological approach.

Methods

CRLM patients undergoing curative-intent resection in 2001-2018 were identified from an international multi-institutional database. Patients were paired and matched based on age, number and size of lesions, lymph node status and receipt of preoperative chemotherapy. The win ratio was calculated based on margin status, severity of postoperative complications, 90-day mortality, time to recurrence, and time to death.

Results

Among 962 patients, the majority underwent open hepatectomy (n=832, 86.5%), while a minority underwent laparoscopic hepatectomy (n=130, 13.5%). Among matched patient-to-patient pairs, the odds of the patient undergoing laparoscopic resection "winning" were 1.77 [WR: 1.77, 95% confidence interval (CI): 1.42-2.34]. The win ratio favored laparoscopic hepatectomy independent of low (WR: 2.94, 95% CI: 1.20-6.39), medium (WR: 1.56, 95% CI: 1.16-2.10) or high (WR: 7.25, 95% CI: 1.13-32.0) tumor burden, as well as unilobar (WR: 1.71, 95% CI: 1.25-2.31) or bilobar (WR: 4.57, 95% CI: 2.36-8.64) disease. The odds of "winning" were particularly pronounced relative to short-term outcomes (i.e., 90-day mortality and severity of postoperative complications) (WR: 4.06, 95% CI: 2.33-7.78).

Conclusions

Patients undergoing laparoscopic hepatectomy had 77% increased odds of "winning". Laparoscopic liver resection should be strongly considered as a preferred approach to resection in CRLM patients.

Marine n-3 Fatty Acids and Prevention of Cardiovascular Disease: A Novel Analysis of the VITAL Trial Using Win Ratio and Hierarchical Composite Outcomes

This study aimed to investigate whether n-3 fatty acid supplementation reduced cardiovascular disease (CVD) events in a novel analysis using hierarchical composite CVD outcomes based on win ratio in the VITamin D and OmegA-3 TriaL (VITAL). This was a secondary analysis of our VITAL randomized trial, which assessed the effects of marine n-3 fatty acids (1 g/day) and vitamin D3 on incident CVD and cancer among healthy older adults (n = 25,871). The primary analysis estimated win ratios of a composite of major CVD outcomes prioritized as fatal coronary heart disease, other fatal CVD including stroke, non-fatal myocardial infarction (MI), and non-fatal stroke, comparing n-3 fatty acids to placebo. The primary result was a nonsignificant benefit of this supplementation for the prioritized primary CVD outcome (reciprocal win ratio [95% confidence interval]: 0.90 [0.78-1.04]), similar to the 0.92 (0.80-1.06) hazard ratio in our original time-to-first event analysis without outcome prioritization. Its benefits came from reducing MI (0.71 [0.57-0.88]) but not stroke (1.01 [0.80 to 1.28]) components. For the primary CVD outcome, participants with low fish consumption at baseline benefited (0.79 [0.65-0.96]) more than those with high consumption (1.05 [0.85-1.30]). These results are consistent with, but slightly stronger than, those without outcome prioritization.

Generalized Pairwise Comparisons to Assess Treatment Effects: JACC Review Topic of the Week

A time-to-first-event composite endpoint analysis has well-known shortcomings in evaluating a treatment effect in cardiovascular clinical trials. It does not fully describe the clinical benefit of therapy because the severity of the events, events repeated over time, and clinically relevant nonsurvival outcomes cannot be considered. The generalized pairwise comparisons (GPC) method adds flexibility in defining the primary endpoint by including any number and type of outcomes that best capture the clinical benefit of a therapy as compared with standard of care. Clinically important outcomes, including bleeding severity, number of interventions, and quality of life, can easily be integrated in a single analysis. The treatment effect in GPC can be expressed by the net treatment benefit, the success odds, or the win ratio. This review provides guidance on the use of GPC and the choice of treatment effect measures for the analysis and reporting of cardiovascular trials.

Fallacies of Using the Win Ratio in Cardiovascular Trials: Challenges and Solutions

The win ratio was introduced into cardiovascular trials as a potentially better way of analyzing composite endpoints to account for the hierarchy of clinical significance of their components and to facilitate the inclusion of recurrent events. The basic concept of the win ratio is to define a hierarchy of clinical importance within the components of the composite outcome, form all possible pairs by comparing every subject in the treatment group with every subject in the control group, and then evaluate each pair for the occurrence of the components of the composite outcome in descending order of importance, starting at the most important and progressing down the hierarchy if the outcome does not result in a win in either pair until pairs are tied for the outcome after exhaustion of all components. Although the win ratio offers a novel method of depiction of outcomes in clinical trials, its advantages may be counterbalanced by several fallacies (such as ignoring ties and weighting each hierarchal component equally) and challenges in appropriate clinical interpretation (establishing clinical meaningfulness of the observed effect size). From this perspective, we discuss these and other fallacies and provide a suggested framework to overcome such limitations to enhance utility of this statistical method across the clinical trial enterprise.

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.

The stratified win statistics (win ratio, win odds, and net benefit)

The win odds and the net benefit are related directly to each other and indirectly, through ties, to the win ratio. These three win statistics test the same null hypothesis of equal win probabilities between two groups. They provide similar p-values and powers, because the Z-values of their statistical tests are approximately equal. Thus, they can complement one another to show the strength of a treatment effect. In this article, we show that the estimated variances of the win statistics are also directly related regardless of ties or indirectly related through ties. Since its introduction in 2018, the stratified win ratio has been applied in designs and analyses of clinical trials, including Phase III and Phase IV studies. This article generalizes the stratified method to the win odds and the net benefit. As a result, the relations of the three win statistics and the approximate equivalence of their statistical tests also hold for the stratified win statistics.

The maraca plot: A novel visualization of hierarchical composite endpoints

BACKGROUND

Hierarchical composite endpoints are complex endpoints combining outcomes of different types and different clinical importance into an ordinal outcome that prioritizes the clinically most important (e.g. most severe) event of a patient. Hierarchical composite endpoint can be analysed with the win odds, an adaptation of win ratio to include ties. One of the difficulties in interpreting hierarchical composite endpoint is the lack of proper tools for visualizing the treatment effect captured by hierarchical composite endpoint, given the complex nature of the endpoint which combines events of different types.

METHODS

Hierarchical composite endpoints usually combine time-to-event outcomes and continuous outcomes into a composite; hence, it is important to capture not only the shift from more severe categories to less severe categories in the active group in comparison to the control group (as in any ordinal endpoint), but also changes occurring within each category. We introduce the novel maraca plot which combines violin plots (with nested box plots) to visualize the density of the distribution of the continuous outcome and Kaplan-Meier plots for time-to-event outcomes into a comprehensive visualization.

CONCLUSION

The novel maraca plot is suggested for visualization of hierarchical composite endpoints consisting of several time-to-event outcomes and a continuous outcome. It has a very simple structure and therefore easily communicates both the overall treatment effect and the effect on individual components.

Investigations of methods for multiple time-to-event endpoints: A chronic myeloid leukemia data analysis

BACKGROUND

In randomized controlled trials, multiple time-to-event endpoints are commonly used to determine treatment effects. However, choosing an appropriate method to address multiple endpoints, according to different purposes of clinical practice, is a challenge for researchers.

METHODS

We applied single endpoint, composite endpoint and win ratio analysis to chronic myeloid leukemia (CML) data to illustrate the distinctions with different multiple endpoints, including relapse, recovery and death after transplantation.

RESULTS

Regarding relapse and death, the hazard ratio in single endpoint analysis (HR_s ) were 1.281 (95% CI: 1.061-1.546) and hazard ratio in composite endpoint analysis (HR_c ) were 1.286 (95% CI: 1.112-1.486) and 1/WR (win ratio) was 1.292 (95% CI: 1.115-1.497) indicated a similar negative effect for non-prophylaxis patients. However, when considering recovery and death, the corresponding HR_s  = 1.280 (95% CI: 1.056-1.552) may not be enough to describe the effect on death with nonproportional hazards (p < 0.05), and for the composite endpoint analysis, the HR_c  = 0.828 (95% CI: 0.740-0.926) cannot quantify and interpret the clinical effect on the composite endpoint with the combination of recovery and death, while the 1/WR = 1.351 (95% CI: 1.207-1.513) showed an unfavourable effect for non-prophylaxis patients CONCLUSIONS: When dealing with multiple endpoints, single endpoints, researchers may choose single endpoints, composite endpoints and WR analysis due to different clinical applications and purposes. However, both single and composite endpoint analyses are hazard-based measures, and thus, the proportional hazards assumption should be considered. Moreover, composite endpoint analysis should be applied for endpoints with similar clinical meanings but not opposing implications. Win ratio analysis can be considered for different clinical importance of multiple endpoints, but the meaning of 'winner' needs to be specified for desired or undesired endpoints.

Stratified proportional win-fractions regression analysis

The recently proposed proportional win-fractions (PW) model extends the two-sample win ratio analysis of prioritized composite endpoints to regression. Its proportionality assumption ensures that the covariate-specific win ratios are invariant to the follow-up time. However, this assumption is strong and may not be satisfied by every covariate in the model. We develop a stratified PW model that adjusts for certain prognostic factors without setting them as covariates, thus bypassing the proportionality requirement. We formulate the stratified model based on pairwise comparisons within each stratum, with a common win ratio across strata modeled as a multiplicative function of the covariates. Correspondingly, we construct an estimating function for the regression coefficients in the form of an incomplete U $$ U $$ -statistic consisting of within-stratum pairs. Two types of asymptotic variance estimators are developed depending on the number of strata relative to the sample size. This in particular allows valid inference even when the strata are extremely small, such as with matched pairs. Simulation studies in realistic settings show that the stratified model outperforms the unstratified version in robustness and efficiency. Finally, real data from a major cardiovascular trial are analyzed to illustrate the potential benefits of stratification. The proposed methods are implemented in the R package WR, publicly available on the Comprehensive R Archive Network (CRAN).

Designing a longitudinal clinical trial based on a composite endpoint: Sample size, monitoring, and adaptation

Longitudinal clinical trials are often designed to compare treatments on the basis of multiple outcomes. For example in the case of cardiac trials, the outcomes of interest include mortality as well as cardiac events and hospitalization. For a COVID-19 trial, the outcomes of interest include mortality, time on ventilator, and time in hospital. Earlier work by these authors proposed a non-parametric test based on a composite of multiple endpoints referred to as the Finkelstein-Schoenfeld (FS) test (Finkelstein and Schoenfeld. Stat Med. 1999;18(11):1341-1354.). More recently, an estimate of the treatment comparison based on multiple endpoints (related to the FS test) was proposed (Pocock et al. Eur Heart J. 2011;33(2):176-182.). This estimate, which summarized the ratio of the number of patients who fared better vs worse on the experimental arm was coined the win ratio. The aim of this article is to provide guidance in the design of a trial that will use the FS test or the win ratio. The issues that will be considered are the sample size, sequential monitoring, and adaptive designs.

Win ratio approach for analyzing composite time-to-event endpoint with opposite treatment effects in its components

There is an increasing interest in the use of win ratio with composite time-to-event due to its flexibility in combining component endpoints. Exploring this flexibility further, one interesting question is in assessing the impact when there is a difference in treatment effect in the component endpoints. For example, the active treatment may prolong the time to occurrence of the negative event such as death or ventilation; meanwhile, the treatment effect may also shorten the time to achieving positive events, such as recovery or improvement. Notably, this portrays a situation where the treatment effect on time to recovery is in a different direction of benefit compared to the time to ventilation or death. Under such circumstances, if a single endpoint is used, the benefit gained for other individual outcomes is not counted and is diminished. As consequence, the study may need a larger sample size to detect a significant effect of treatment. Such a scenario can be handled by win ratio in a novel way by ranking component events, which is different from the usual composite endpoint approach such as time-to-first event. To evaluate how the different directions of treatment effect on component endpoints will impact the win ratio analysis, we use a Clayton copula-based bivariate survival simulation to investigate the correlation of component time-to-event. Through simulation, we found that compared to the marginal model using single endpoints, the win ratio analysis on composite endpoint performs better, especially when the correlation between two events is weak. Then, we applied the methodology to an infectious disease progression simulated study motivated by COVID-19. The application demonstrates that the win ratio approach offers advantages in empirical power compared to the traditional Cox proportional hazard approach when there is a difference in treatment effect in the marginal events.

Robust statistical inference for matched win statistics

As alternatives to the time-to-first-event analysis of composite endpoints, the win statistics, that is, the net benefit, the win ratio, and the win odds have been proposed to assess treatment effects, using a hierarchy of prioritized component outcomes based on clinical relevance or severity. Whether we are using paired organs of a human body or pair-matching patients by risk profiles or propensity scores, we can leverage the level of granularity of matched win statistics to assess the treatment effect. However, inference for the matched win statistics (net benefit, win ratio, and win odds)-quantities related to proportions-is either not available or unsatisfactory, especially in samples of small to moderate size or when the proportion of wins (or losses) is near 0 or 1. In this paper, we present methods to address these limitations. First, we introduce a different statistic to test for the null hypothesis of no treatment effect and provided a sample size formula. Then, we use the method of variance estimates recovery to derive reliable, boundary-respecting confidence intervals for the matched net benefit, win ratio, and win odds. Finally, a simulation study demonstrates the performance of the proposed methods. We illustrate the proposed methods with two data examples.

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

The win ratio, a recently proposed measure for comparing the benefit of two treatment groups, allows ties in the data but ignores ties in the inference. In this article, we highlight some difficulties that this can lead to, and we propose to focus on the win odds instead, a modification of the win ratio which takes ties into account. We construct hypothesis tests and confidence intervals for the win odds, and we investigate their properties through simulations and in a case study. We conclude that the win odds should be preferred over the win ratio.

Use of the Win Ratio in Cardiovascular Trials

OBJECTIVES

The purpose of this study was to compare the win ratio (WR) with the corresponding hazard ratios (HRs) and 1/HR.

BACKGROUND

The primary outcome in many cardiovascular trials is a composite that includes nonfatal and fatal events. The time-to-first event analysis gives equal statistical weighting to each component event. The WR, which takes into account the clinical importance and timing of the outcomes, has been suggested as an alternative approach.

METHODS

Cox proportional hazards models and WR.

RESULTS

In the these trials (n = 16) the WR and HR differed only slightly. For example, in the PARADIGM-HF (sacubitril/valsartan vs. enalapril), the primary outcome of time to first heart failure hospitalization (HFH) or cardiovascular death (CVD) and use of the Cox model gave a 1/HR of 1.25 (95% confidence interval [CI]: 1.12 to 1. 41; z-score = 4.8). Using WR for testing this composite in the hierarchical order of CVD and HFH gave a WR of 1.27 (95% CI: 1.15 to 1.39; z-score = 4.7), reflecting an effect similar to that of sacubitril/valsartan therapy on CVD and HFH. In the DIG (digoxin vs. placebo) trial, the outcome of time-to-first HFH or CVD using Cox gave a 1/HR of 1.18 (95% CI: 1.10 to 1.27; z-score = 4.5). Using the WR for testing this composite in the hierarchical order of CVD and HFH gave a WR of 1.14 (95% CI: 1.05 to 1.20; z-score = 3.1), reflecting a larger effect of digoxin on HFH than on CVD. Several other trials and endpoints including patient-reported measurements were studied.

CONCLUSIONS

In 16 large cardiovascular outcome trials, HR and WR provided similar estimates of treatment effects. The WR allows prioritization of fatal outcomes and the hierarchical testing of broader composite endpoints including patient-reported outcomes. In this way, the WR allows for the incorporation of patient-centered and other outcomes, while prioritizing the competing risk of death and hospital admission.

Cardio/Kidney Composite End Points: A Post Hoc Analysis of the EMPA-REG OUTCOME Trial

Background

Cardio/kidney composite end points are clinically relevant but rarely analyzed in cardiovascular trials. This post hoc analysis of the EMPA‐REG OUTCOME (Empagliflozin Cardiovascular Outcome Event Trial in Type 2 Diabetes Mellitus Patients) trial evaluated cardio/kidney composite end points by 2 statistical approaches.

Methods and Results

A total of 7020 patients with type 2 diabetes mellitus and established cardiovascular disease were treated with empagliflozin 10 or 25 mg (n=4687) or placebo (n=2333) on top of standard care. Cardio/kidney composite end points studied were: (1) cardiac or kidney death, kidney failure, hospitalization for heart failure, sustained decline in estimated glomerular filtration rate ≥40% from baseline, or sustained progression to macroalbuminuria; (2) cardiac or kidney death, kidney failure, hospitalization for heart failure, or sustained estimated glomerular filtration rate decline ≥40% from baseline; and (3) cardiac or kidney death, kidney failure, hospitalization for heart failure, or sustained doubling in serum creatinine from baseline. Cox regression using time‐to‐first‐event analysis and win ratio (WR) using hierarchical order of events were applied. Empagliflozin reduced the risk of all cardio/kidney composites. The results varied only slightly between Cox and WR (eg, composite 1: hazard ratio, 0.56 [95% CI, 0.49–0.64]; WR, 1.76 [95% CI, 1.53–2.02]. WR prioritizes events by clinical importance; in particular, all fatal events are evaluated, whereas Cox regression ignores deaths when preceded by nonfatal events. Of the 285 cardio/kidney deaths in the analysis, 44 to 56 (15%–20%), depending on the composite, occurred after a nonfatal event and were not evaluated in Cox regression but evaluated by the WR.

Conclusions

By considering the clinical relevance of different event types, the WR represents an appropriate method to complement the traditional time‐to‐first‐event analysis in cardio/kidney outcomes.

Registration

URL: https://www.clinicaltrials.gov; Unique identifier: NCT01131676.

Adjusting win statistics for dependent censoring

For composite outcomes whose components can be prioritized on clinical importance, the win ratio, the net benefit and the win odds apply that order in comparing patients pairwise to produce wins and subsequently win proportions. Because these three statistics are derived using the same win proportions and they test the same hypothesis of equal win probabilities in the two treatment groups, we refer to them as win statistics. These methods, particularly the win ratio and the net benefit, have received increasing attention in methodological research and in design and analysis of clinical trials. For time-to-event outcomes, however, censoring may introduce bias. Previous work has shown that inverse-probability-of-censoring weighting (IPCW) can correct the win ratio for bias from independent censoring. The present article uses the IPCW approach to adjust win statistics for dependent censoring that can be predicted by baseline covariates and/or time-dependent covariates (producing the CovIPCW-adjusted win statistics). Theoretically and with examples and simulations, we show that the CovIPCW-adjusted win statistics are unbiased estimators of treatment effect in the presence of dependent censoring.

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

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 two-sample 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 covariate-specific 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).

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

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.

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

The win ratio method has received much attention in methodological research, ad hoc analyses, and designs of prospective studies. As the primary analysis, it supported the approval of tafamidis for the treatment of cardiomyopathy to reduce cardiovascular mortality and cardiovascular-related hospitalization. However, its dependence on censoring is a potential shortcoming. In this article, we propose the inverse-probability-of-censoring weighting (IPCW) adjusted win ratio statistic (i.e., the IPCW-adjusted win ratio statistic) to overcome censoring issues. We consider independent censoring, common censoring across endpoints, and right censoring. We develop an asymptotic variance estimator for the logarithm of the IPCW-adjusted win ratio statistic and evaluate it via simulation. Our simulation studies show that, as the amount of censoring increases, the unadjusted win proportions may decrease greatly. Consequently, the bias of the unadjusted win ratio estimate may increase greatly, producing either an overestimate or an underestimate. We demonstrate theoretically and through simulation that the IPCW-adjusted win ratio statistic gives an unbiased estimate of treatment effect.

Analysis of ordered composite endpoints

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.

Computing Methods for Composite Clinical Endpoints in Unprotected Left Main Coronary Artery Revascularization: A Post Hoc Analysis of the DELTA Registry

OBJECTIVES

The study sought to investigate the impact of different computing methods for composite endpoints other than time-to-event (TTE) statistics in a large, multicenter registry of unprotected left main coronary artery (ULMCA) disease.

BACKGROUND

TTE statistics for composite outcome measures used in ULMCA studies consider only the first event, and all the contributory outcomes are handled as if of equal importance.

METHODS

The TTE, Andersen-Gill, win ratio (WR), competing risk, and weighted composite endpoint (WCE) computing methods were applied to ULMCA patients revascularized by percutaneous coronary intervention (PCI) or coronary artery bypass grafting (CABG) at 14 international centers.

RESULTS

At a median follow-up of 1,295 days (interquartile range: 928 to 1,713 days), all analyses showed no difference in combinations of death, myocardial infarction, and cerebrovascular accident between PCI and CABG. When target vessel revascularization was incorporated in the composite endpoint, the TTE (p = 0.03), Andersen-Gill (p = 0.04), WR (p = 0.025), and competing risk (p < 0.001) computing methods showed CABG to be significantly superior to PCI in the analysis of 1,204 propensity-matched patients, whereas incorporating the clinical relevance of the component endpoints using WCE resulted in marked attenuation of the treatment effect of CABG, with loss of significance for the difference between revascularization strategies (p = 0.10).

CONCLUSIONS

In a large study of ULMCA revascularization, incorporating the clinical relevance of the individual outcomes resulted in sensibly different findings as compared with the conventional TTE approach. In particular, using the WCE computing method, PCI and CABG were no longer significantly different with respect to the composite of death, myocardial infarction, cerebrovascular accident, or target vessel revascularization at a median of 3 years.