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An IPCW Adjusted Win Statistics Approach in Clinical Trials Incorporating Equivalence Margins to Define Ties

T0 review · 4 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read The paper claims that win statistics with clinical equivalence margins can be estimated without censoring-induced bias.

desk verdict A genuinely useful extension of win statistics to equivalence margins; the common-censoring theory holds up, but the sign error and the unproven induced-censoring workaround need fixing before this is used confirmatorily. read the letter →

arxiv 2506.03050 v1 pith:RFVS4YOI submitted 2025-06-03 stat.ME stat.AP

Ying Cui , Bo Huang , Gaohong Dong , Ryuji Uozumi , Lu Tian This is my paper
classification stat.MEstat.AP MSC 62N0162P10
keywords winstatisticsratioequivalencemarginright-censoringIPCWrandomizedclinicaltrialstime-to-eventendpointsmultiple
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper proposes a class of win statistics for clinical trials in which several time-to-event endpoints of different priorities are compared pairwise, and two patients count as tied on an endpoint when their event times differ by no more than a user-specified equivalence margin $\zeta_l$. The central claim is that, after truncating all event times at a pre-specified horizon $\tau$ and weighting each pairwise comparison by inverse probabilities of censoring survival, the treatment and control win probabilities $\pi_t$ and $\pi_c$ are consistently estimable under independent common right-censoring. This matters because win ratio, net benefit, and win odds are then free of censoring-induced bias, which prior IPCW-style estimators did not achieve for the component win probabilities, and because no previous win-statistic formulation allowed clinical equivalence margins to define ties. Finite-sample simulations under exponential and Weibull settings, and an application to a renal-cell carcinoma trial, are presented as evidence that the estimators and their confidence intervals behave well in practice.

What carries the argument

The central object is the pair of win probabilities $\pi_t$ and $\pi_c$ built from endpoint-wise win contributions, where the comparison of a treatment patient with a control patient proceeds through endpoints in priority order, and a tie on endpoint $l$ is defined by the equivalence margin $\zeta_l$: $|T^{(t)}_l \wedge \tau - T^{(c)}_l \wedge \tau| \le \zeta_l$. The mechanism that carries the argument is inverse-probability-of-censoring weighting: each pairwise indicator is divided by the product of estimated censoring-survival probabilities evaluated at the largest shifted event time involved in the comparison. For endpoints beyond the first, the inclusion-exclusion principle turns the tie region into a signed combination of simple win regions, which is what makes the estimator tractable and consistent under common censoring.

What would settle it

Simulate a two-endpoint trial where overall survival is censored at last follow-up and progression-free survival at the last radiological assessment, with sparse and discretized assessment times, and check whether the induced-common-censoring IPCW estimate of the win ratio converges to the known true value as the sample size grows; a persistent bias would falsify the endpoint-specific-censoring extension.

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Extended reading notes

Core claim

The paper's core claim is that the win probabilities defined on truncated event times $T^{(t)}_l \wedge \tau$ and $T^{(c)}_l \wedge \tau$, with ties declared when $|T^{(t)}_l \wedge \tau - T^{(c)}_l \wedge \tau| \le \zeta_l$, are identifiable under right-censoring, and that the proposed IPCW estimators $\hat\pi_t$ and $\hat\pi_c$ are consistent for them. The estimators are U-statistics formed from all treatment-control patient pairs, with each indicator of winning on endpoint $l$ reweighted by Kaplan-Meier estimates of the probability that both patients' censoring times exceed the relevant comparison time; for $l \ge 2$, an inclusion-exclusion expansion decomposes the tie region on the higher-priority endpoints into signed half-space events. The censoring weights cancel the nuisance censoring distribution, so the estimands do not depend on how the trial is followed up. The win ratio, net benefit, and win odds are then estimated by plug-in, and inference uses a bivariate normal approximation with a consistently estimated covariance matrix.

Load-bearing premise

The consistency proof assumes that each patient has a single censoring time shared by all endpoints, independent of all outcomes, with positive probability of exceeding $\tau$; when endpoints such as overall survival and progression-free survival have different censoring times, the induced-common-censoring version is supported by simulation, not by a proof.

Editorial extensions

If this is right

  • Win statistics with equivalence margins become estimable without being tied to the censoring distribution, aligning with the regulatory estimand principle that treatment-effect measures should not depend on follow-up timing.
  • Tests based on win ratio, win odds, and net benefit are asymptotically equivalent, so a trial can pre-specify any of the three contrasts without changing the large-sample operating characteristics.
  • Because the win statistics pool information across all prioritized endpoints, they can be substantially more powerful than a log-rank test on time-to-first-event, as the simulations show.
  • With a sufficiently large time horizon $\tau$, type I error and power are largely insensitive to the equivalence margin $\zeta$; with small $\tau$, larger margins can reduce power.
  • In the single-endpoint proportional-hazards case, the win ratio retains its established relationship to the hazard ratio, so the method specializes gracefully to existing practice.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If the consistency argument is right, the same inclusion-exclusion weighting should extend to endpoint-specific censoring by replacing the common censoring survival function with an estimate of the joint censoring survival function; the paper's induced-common-censoring shortcut would then be a special case rather than a necessity.
  • Because the three test statistics are asymptotically equivalent, design choices among win ratio, win odds, and net benefit matter mainly for interpretation and tie definition, not for asymptotic power; a formal equivalence-testing framework on the margin $\zeta$ is not developed and could be a natural next step.
  • The method invites sensitivity analyses reporting win statistics across a grid of margins, as in the paper's example; extending that to a pre-specified rule for choosing $\zeta$ from the assessment schedule for progression-free survival is a concrete practical extension.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 5 minor

Summary. The paper proposes a class of win statistics for multiple prioritized time-to-event endpoints in which ties are defined via user-specified equivalence margins ζ_l, and develops inverse-probability-of-censoring-weighted (IPCW) estimators of the win probabilities π_t and π_c under a common, independent censoring mechanism. The estimators are defined with a pre-specified time horizon τ, and the paper claims consistency and asymptotic normality, with a variance estimator and corresponding tests for the win ratio, net benefit, and win odds. The manuscript includes an extensive simulation study, a real-data illustration using the JAVELIN Renal 101 trial, and a supplementary file with derivations and additional simulations.

Significance. If the consistency and inference results hold, the paper addresses a real gap in the win-statistics literature: it provides a censoring-robust approach that explicitly incorporates equivalence margins, allowing non-informative ties due to both incomplete follow-up and clinically negligible differences. The paper's strengths include a detailed supplementary derivation of the zero-margin estimator, a first-order U-statistic representation for the variance, extensive simulations covering several survival distributions and sample sizes, a real-data example, and a publicly available R package. However, the manuscript currently contains a concrete sign error in the tie-probability estimator, an unproven extension to endpoint-specific censoring, and a missing proof for positive equivalence margins, all of which need to be addressed before the central claims can be accepted.

major comments (4)
  1. [Section 2.2, Remark 3] The estimator \hatπ_tie for P(∩_{k=1}^L U_k) uses the coefficient (-1)^{L+1} multiplied by ∏_{k=1}^L s_k. For L=1, with B_1={T^t_1∧τ > T^c_1∧τ - ζ_1} and A_1={T^t_1∧τ > T^c_1∧τ + ζ_1}, the target is P(B_1)-P(A_1). The formula, however, assigns coefficients -1 and +1 to B_1 and A_1, respectively, because (-1)^2=+1 and ∏s_k=-1 when s=-1. Thus the estimator equals the negative of the target. The correct inclusion-exclusion coefficient is (-1)^L, not (-1)^{L+1}; with (-1)^L the signs become + and - as required. This error propagates into the normalized estimates \hatπ_t/(\hatπ_t+\hatπ_c+\hatπ_tie) and \hatπ_c/(\hatπ_t+\hatπ_c+\hatπ_tie) and into the null variance formula in Section 3 that uses \hatπ_tie. The formula should be corrected and the simulations and real-data analysis checked for whether the adjustment was actually used.
  2. [Section 2.1, endpoint-specific censoring paragraph] The proposed 'induced common censoring' workaround replaces endpoint-specific censoring times by their minimum and then applies the IPCW estimator designed for a single common censoring time. No conditions are given under which the induced censoring time C_min is independent of the endpoint times, which is the key assumption needed for the IPCW identity in Section S1. The simulation in Section S5.2 generates (C_1,C_2) independently of (T_1,T_2), so it does not cover the realistic oncology setting in which PFS censoring is tied to the assessment process and can be informative. The real-data analysis in Section 5 with OS and PFS relies on this unproven step. The authors should either prove consistency under explicit sufficient conditions, provide a concrete counterexample where the estimator is biased, or explicitly restrict the claims and the application to settings where the induced censoring is known to be independent of the endpoints.
  3. [Section 2.2 and Supplementary Material S1] The consistency proof in Section S1 is carried out only for the zero-margin case ζ=0. For positive equivalence margins, the main text states 'it can be shown' and gives an inclusion-exclusion expression, but no unbiasedness or consistency calculation is provided for the positive-margin estimators. Since the incorporation of equivalence margins is a central contribution, the authors should add a rigorous proof that the estimator with positive ζ_l is unbiased, including verification that the denominators involving max{(X^c_{k,j}+s_k ζ_k)} and max{X^c_{k,j}} correctly cancel the joint censoring probabilities for each term in the inclusion-exclusion, and that the U-statistic representation in the supplement extends to this case.
  4. [Remark 3, final sentence] The statement 'As the sample size increases, the probability of the need for such an adjustment converges to zero' is false when ζ=0 and the endpoint distributions are continuous. In that case the tie probability P(U_1)=0, so π_t+π_c=1; the estimators \hatπ_t and \hatπ_c fluctuate around these values, and P(\hatπ_t+\hatπ_c>1) tends to approximately 0.5, not 0. This does not invalidate the main consistency results, but the claimed asymptotic rationale for the finite-sample adjustment is incorrect and should be stated more carefully.
minor comments (5)
  1. [Remark 3] The text says 'adjust the estimators for πt and πt by'; the second occurrence should be π_c.
  2. [Section 2.1] In the definition of \tilde δ^{(c)}_{C,j}, the notation uses C^{(t)}_j and \tilde X^{(t)}_j; these should be C^{(c)}_j and \tilde X^{(c)}_j.
  3. [Remark 1] The claim that the data-driven choice of τ based on censoring quantiles 'can be shown' to work is not supported by a proof or reference; the authors should either provide a rigorous statement or soften this claim to a conjecture.
  4. [Supplementary Material S4] Several displayed formulas have unbalanced parentheses, for example g^{(2)}_1(X^c_j) = (X^c_{2,j}+ζ_2) ∨ (X^c_{1,j}-ζ_1) is missing a closing parenthesis. These typos should be corrected.
  5. [Section 3] The text refers to 'Appendices B and C' for the U-statistic representation, but the corresponding material appears only in the supplementary file; the reference should be aligned.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the IPCW estimators are derived from explicit unbiasedness identities and checked against external benchmarks; the unproven induced-common-censoring extension is a limitation, not a circular reduction.

full rationale

Walking the derivation chain, the win probabilities are defined as explicit functionals of the joint distribution of truncated event times (Section 2), and the proposed estimators are explicit IPCW averages (Sections 2.1 and 2.2) whose unbiasedness is derived in Supplementary Section S1 by conditioning on T and using independence of the common censoring time C; no parameter is fitted to force the identity. The positive-margin estimator follows the same inclusion-exclusion structure (Section 2.2 and Figure S1), and the finite-sample normalization in Remark 3 is ancillary. The user-specified tau and zeta define the estimand rather than being tuned to the data, so no fitted input is renamed as a prediction. Although the paper cites prior work by its own authors ([14,15,16]), the load-bearing consistency claim is proved in the supplement, not imported from those citations; external checks (log-rank, Cox, RMST, and simulations against a no-censoring Monte Carlo truth) support the estimator's behavior. The genuine weaknesses are non-circular: (i) the induced-common-censoring extension for endpoint-specific censoring is heuristic, and the paper states 'This conversion is feasible only when the minimum censoring time is always known, even when the clinical event of interest occurs first' while validating it only by simulation (S5.2), not by proof; (ii) the positive-margin consistency proof is asserted ('it can be shown') and only the zero-margin case is fully written out in S1. These are completeness and assumption issues, not cases where a prediction reduces by construction to its inputs. Hence score 0.

Assumptions & free parameters 2 free parameters · 6 assumptions · 0 invented entities

The method rests on standard statistical assumptions (independent and common censoring, positive follow-up probability) plus user-chosen tau and zeta that define the estimand. No new physical or mathematical entities are postulated.

free parameters (2)
  • time horizon tau = user-specified, e.g., 24 months in the JAVELIN example; data-driven quantile rule in Remark 1
    Defines the truncated event times T and tau in the estimand; the estimator and its consistency require P(C_t and C_c > tau) > 0.
  • equivalence margins zeta_l = user-specified per endpoint, e.g., 0, 2, 4 months in the example; 0 to 6 in simulations
    Define the tie regions U_k; the estimand itself changes with zeta, and no data-driven rule is given.
assumptions (6)
  • domain assumption A single common censoring time C per patient applies to all endpoints.
    Stated in Section 2 and used throughout the IPCW derivation and the supplementary consistency proof.
  • domain assumption Censoring time C is independent of all endpoints of interest.
    Required for the IPCW argument in Section S1 to factor the conditional expectation into G(t) and G(c).
  • domain assumption P(C_t and C_c > tau) > 0, with follow-up beyond the relevant comparison thresholds.
    Assumed in Section 2; positive margins may require censoring support beyond tau, a case the paper does not explicitly handle.
  • standard math Kaplan-Meier estimators of the censoring survival functions are consistent.
    Used in Section 2.1 and the supplement to replace G with consistent estimates.
  • standard math Two-sample U-statistic asymptotic normality and the delta method apply to the win probability contrasts.
    Invoked in Section 3 and Section S2-S3 for variance estimation and z-tests.
  • standard math Event times are continuous and samples are i.i.d. within treatment arms.
    Assumed implicitly throughout; needed to avoid ties at observed uncensored event times.

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Cite this review

Pith. "Pith review of An IPCW Adjusted Win Statistics Approach in Clinical Trials Incorporating Equivalence Margins to Define Ties." pith.science (2026). https://pith.science/paper/RFVS4YOI

@misc{pith2026250603050,
  author       = {Pith},
  title        = {Pith review of: An IPCW Adjusted Win Statistics Approach in Clinical Trials Incorporating Equivalence Margins to Define Ties},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/RFVS4YOI}},
  note         = {Machine review of arXiv:2506.03050}
}
read the original abstract

In clinical trials, multiple outcomes of different priorities commonly occur as the patient's response may not be adequately characterized by a single outcome. Win statistics are appealing summary measures for between-group difference at more than one endpoint. When defining the result of pairwise comparisons of a time-to-event endpoint, it is desirable to allow ties to account for incomplete follow-up and not clinically meaningful difference in endpoints of interest. In this paper, we propose a class of win statistics for time-to-event endpoints with a user-specified equivalence margin. These win statistics are identifiable in the presence of right-censoring and do not depend on the censoring distribution. We then develop estimation and inference procedures for the proposed win statistics based on inverse-probability-of-censoring {weighting} (IPCW) adjustment to handle right-censoring. We conduct extensive simulations to investigate the operational characteristics of the proposed procedure in the finite sample setting. A real oncology trial is used to illustrate the proposed approach.

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