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

Dong, Gaohong; Huang, Bo; Verbeeck, Johan; Cui, Ying; Song, James; Gamalo, Margaret; Wang, Duolao; Hoaglin, David C.; Seifu, Yodit; Mütze, Tobias; Kolassa, John E.

doi:10.1002/pst.2251

Cited by 25 publications

(20 citation statements)

References 37 publications

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“…For the M strata, one can plug in fixed weights (

w^{((), m)})

and estimated variances and covariances of the numbers of wins for each stratum (

{\overset{truê}{σ}}_{t}^{2}^{((), m)}

{\overset{truê}{σ}}_{c}^{2}^{((), m)}

, and

{\overset{truê}{σ}}_{tc}^{((), m)}

). We show that the relations among the three win statistics and the approximate equality of their statistical tests, as presented in Dong et al, 8 also apply to the stratified win statistics. Therefore, the three stratified win statistics provide similar p ‐values and statistical powers.…”

Section: Summary and Discussionsupporting

confidence: 53%

“…The stratified win statistics defined in Section 2 have the same relations as the unstratified versions described in Dong et al 8 As indicated in Dong et al 8 and shown in Figures 1 and 2, the win odds increases (or decreases) as the net benefit increases (or decreases) regardless of ties. However, the relation between the win odds and the win ratio depends on the proportion of ties (and similarly for the net benefit):

NB = \frac{WR - 1}{WR + 1} (1 - P_{italictie})

NB = \frac{WO - 1}{WO + 1}

WO = \frac{1 + NB}{1 - NB}

WO = \frac{WR - 0.5 P_{italictie} (WR - 1)}{1 + 0.5 P_{italictie} (WR - 1)} .

Moreover, Figures 1 and 2 show the win ratio can take any positive value regardless of the proportion of ties, whereas the win odds approaches 1 and the net benefit approaches 0 as the proportion of ties increases.…”

Section: Relations Among the Stratified Win Statisticsmentioning

confidence: 75%

“…Dong et al 8 showed that the Z‐values of the statistical tests for the three unstratified win statistics are approximately equal. Using the approximate equality of

\log (x)

and

\frac{2 (x - 1)}{x + 1}

for x > 0, this approximate equivalence of statistical tests also applies to the stratified win statistics:

Z_{italicNB} = \frac{\overset{NB}{true}}{{\overset{σ}{true}}_{italicNB}} = \frac{\overset{truê}{italicWR} - 1}{\overset{truê}{italicWR} + 1} (1 - P_{italictie}) \frac{2}{{\overset{σ}{true}}_{\log (italicWR)} (1 ‐ P_{t i e})} = \frac{\overset{truê}{italicWR} - 1}{\overset{truê}{italicWR} + 1} \frac{2}{{\overset{σ}{true}}_{\log (italicWR)}} \approx \frac{\log (\overset{WR}{true})}{{\overset{σ}{true}}_{\log (italicWR)}} = Z_{\log (italicWR)},

Z_{italicNB} = \frac{\overset{NB}{true}}{{\overset{σ}{true}}_{italicNB}} = \frac{\overset{truê}{italicWO} - 1}{\overset{truê}{italicWO} + 1} \frac{1}{{\overset{σ}{true}}_{italicNB}} = \frac{\overset{truê}{italicWO} - 1}{\overset{truê}{italicWO} + 1} \frac{2}{{\overset{σ}{true}}_{\log (italicWO)}} \approx \frac{\log (\overset{truê}{italicWO})}{}

…”

Section: Approximate Equivalence Of Statistical Tests For the Stratif...mentioning

confidence: 99%

“…Dong et al 8 showed that the three win statistics can complement one another to show the strength of the treatment effect, because (1) their definitions use the same win proportions based on generalized pairwise comparisons (GPC); (2) they test the same null hypothesis of equal win probabilities between two groups; (3) for point estimates, the win odds and the net benefit are related directly to each other and are related indirectly to the win ratio through ties; (4) the estimated variances of the three win statistics are also related directly regardless of ties or indirectly related through ties (Section 3.2 gives the details); and (5) Z‐values of statistical tests of the three win statistics are approximately equal (i.e., the three win statistics provide similar p ‐values and powers). In this article, we show that the relations among the three win statistics and the approximate equivalence of their statistical tests also apply to the stratified win statistics.…”

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

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

Dong¹,

Hoaglin

Huang

et al. 2023

Pharmaceutical Statistics

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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.

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“…For the M strata, one can plug in fixed weights (

w^{((), m)})

and estimated variances and covariances of the numbers of wins for each stratum (

{\overset{truê}{σ}}_{t}^{2}^{((), m)}

{\overset{truê}{σ}}_{c}^{2}^{((), m)}

, and

{\overset{truê}{σ}}_{tc}^{((), m)}

Section: Summary and Discussionsupporting

confidence: 53%

NB = \frac{WR - 1}{WR + 1} (1 - P_{italictie})

NB = \frac{WO - 1}{WO + 1}

WO = \frac{1 + NB}{1 - NB}

WO = \frac{WR - 0.5 P_{italictie} (WR - 1)}{1 + 0.5 P_{italictie} (WR - 1)} .

Section: Relations Among the Stratified Win Statisticsmentioning

confidence: 75%

“…Dong et al 8 showed that the Z‐values of the statistical tests for the three unstratified win statistics are approximately equal. Using the approximate equality of

\log (x)

and

\frac{2 (x - 1)}{x + 1}

for x > 0, this approximate equivalence of statistical tests also applies to the stratified win statistics:

Z_{italicNB} = \frac{\overset{NB}{true}}{{\overset{σ}{true}}_{italicNB}} = \frac{\overset{truê}{italicWR} - 1}{\overset{truê}{italicWR} + 1} (1 - P_{italictie}) \frac{2}{{\overset{σ}{true}}_{\log (italicWR)} (1 ‐ P_{t i e})} = \frac{\overset{truê}{italicWR} - 1}{\overset{truê}{italicWR} + 1} \frac{2}{{\overset{σ}{true}}_{\log (italicWR)}} \approx \frac{\log (\overset{WR}{true})}{{\overset{σ}{true}}_{\log (italicWR)}} = Z_{\log (italicWR)},

Z_{italicNB} = \frac{\overset{NB}{true}}{{\overset{σ}{true}}_{italicNB}} = \frac{\overset{truê}{italicWO} - 1}{\overset{truê}{italicWO} + 1} \frac{1}{{\overset{σ}{true}}_{italicNB}} = \frac{\overset{truê}{italicWO} - 1}{\overset{truê}{italicWO} + 1} \frac{2}{{\overset{σ}{true}}_{\log (italicWO)}} \approx \frac{\log (\overset{truê}{italicWO})}{}

…”

Section: Approximate Equivalence Of Statistical Tests For the Stratif...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

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

Dong¹,

Hoaglin

Huang

et al. 2023

Pharmaceutical Statistics

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Effect of Noninvasive Airway Management of Comatose Patients With Acute Poisoning

Freund,

Viglino,

Cachanado

et al. 2023

JAMA

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ImportanceTracheal intubation is recommended for coma patients and those with severe brain injury, but its use in patients with decreased levels of consciousness from acute poisoning is uncertain.ObjectiveTo determine the effect of intubation withholding vs routine practice on clinical outcomes of comatose patients with acute poisoning and a Glasgow Coma Scale score less than 9.Design, Setting, and ParticipantsThis was a multicenter, randomized trial conducted in 20 emergency departments and 1 intensive care unit (ICU) that included comatose patients with suspected acute poisoning and a Glasgow Coma Scale score less than 9 in France between May 16, 2021, and April 12, 2023, and followed up until May 12, 2023.InterventionPatients were randomized to undergo conservative airway strategy of intubation withholding vs routine practice.Main Outcomes and MeasuresThe primary outcome was a hierarchical composite end point of in-hospital death, length of ICU stay, and length of hospital stay. Key secondary outcomes included adverse events resulting from intubation as well as pneumonia within 48 hours.ResultsAmong the 225 included patients (mean age, 33 years; 38% female), 116 were in the intervention group and 109 in the control group, with respective proportions of intubations of 16% and 58%. No patients died during the in-hospital stay. There was a significant clinical benefit for the primary end point in the intervention group, with a win ratio of 1.85 (95% CI, 1.33 to 2.58). In the intervention group, there was a lower proportion with any adverse event (6% vs 14.7%; absolute risk difference, 8.6% [95% CI, −16.6% to −0.7%]) compared with the control group, and pneumonia occurred in 8 (6.9%) and 16 (14.7%) patients, respectively (absolute risk difference, −7.8% [95% CI, −15.9% to 0.3%]).Conclusions and RelevanceAmong comatose patients with suspected acute poisoning, a conservative strategy of withholding intubation was associated with a greater clinical benefit for the composite end point of in-hospital death, length of ICU stay, and length of hospital stay.Trial RegistrationClinicalTrials.gov Identifier: NCT04653597

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