{"id":"2c5c7cfb-d584-43b5-92be-d515a1b05da4","arxiv_id":"2605.27085","paper_version":1,"verdict":"UNVERDICTED","confidence":"LOW","novelty_score":6.0,"correctness_risk":"unknown","formal_verification":"none","parameter_count":1,"one_line_summary":"Develops and validates IPW and AIPW estimators for win measures with missing hierarchical ordinal endpoints, including variance estimation via influence functions.","lead":"The paper develops IPW and AIPW estimators to correct bias in win measures for clinical trials with missing ordinal endpoints. These methods reweight observed pairs and add outcome modeling for better efficiency and robustness.","discovery_kind":"new_method","skeptic_critique":{"model":"grok-4.3","headline":"IPW consistency requires correct specification of the joint non-missingness model (MAR given treatment + baselines)","rationale":"The reader's weakest_assumption directly identifies the same modeling requirement that determines whether the consistency and coverage claims hold. Full-text access does not reveal an internal inconsistency or stronger supporting evidence (e.g., machine-checked proof) that would override this assumption.","tokens_in":1779,"tokens_out":285,"duration_ms":29457,"concrete_test":"Simulate data under MAR but with an additional unobserved covariate that affects both missingness and the ordinal outcomes; re-fit the IPW estimator using only the observed covariates as in the paper; check whether the win-ratio bias exceeds 5% relative error while AIPW remains closer to truth.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"The IPW estimator reweights observed pairs by the inverse of the estimated P(both endpoints observed | treatment, covariates) to recover the joint cell probabilities that define the win measures. This step is unbiased only if the missingness model is correctly specified and the probability is consistently estimated. AIPW adds outcome regression for double robustness, but the paper's consistency claim for IPW (and the efficiency comparison) still rests on this modeling assumption. No derivation or simulation detail in the provided text shows robustness to misspecification of the missingness mechanism beyond the stated covariates.","agreement_with_reader":"agree"},"referee_report":{"model":"grok-4.3","summary":"The manuscript develops IPW and AIPW estimators for win measures (win ratio, win odds, net benefit, and DOOR) defined via pairwise comparisons of multiple hierarchical ordinal endpoints when some endpoints are missing. Missingness is allowed to depend on treatment assignment and baseline covariates under a MAR assumption. The IPW reweights observed pairs by the inverse of the estimated joint non-missingness probability to recover the cell probabilities that define the win measures; AIPW augments this with outcome regression for double robustness and efficiency. Closed-form variance estimators are derived from influence functions. Simulations show the standard approach (treating incomplete pairs as ties) is biased while the proposed estimators are consistent with near-nominal coverage, AIPW being more efficient; applications to SCOUT-CAP and ACTT-1 trials are presented along with the R package WinMO.","tokens_in":1901,"tokens_out":594,"duration_ms":28459,"significance":"If the derivations and simulation results hold, the work fills a clear methodological gap by extending standard IPW/AIPW theory to win measures with missing hierarchical ordinal data, a setting common in clinical trials. The double-robustness property of AIPW, the closed-form variances, and the provision of an R package for implementation are concrete strengths that support usability and reproducibility. The simulation evidence for consistency and coverage under the stated missingness mechanism is a positive feature.","major_comments":[{"comment":"Methods section (IPW construction): consistency of the IPW estimator for the joint cell probabilities requires correct specification and consistent estimation of the joint non-missingness probability P(both endpoints observed | treatment, covariates). The manuscript states this assumption but does not report any sensitivity analyses or additional simulations under misspecification of the missingness model, which is load-bearing for the practical claim that the IPW estimator remains consistent when applied to real data.","section":"Methods"},{"comment":"Simulation studies: all reported scenarios assume the missingness model is correctly specified with the same covariates used in estimation. This leaves open whether the reported near-nominal coverage and efficiency advantage of AIPW persist when the missingness mechanism is misspecified, which directly affects the strength of evidence for the central consistency and efficiency claims.","section":"Simulations"}],"minor_comments":[{"comment":"The abstract and introduction could more explicitly note that the double robustness of AIPW holds only if at least one of the missingness or outcome models is correctly specified, to avoid overstatement of robustness.","section":"Abstract"},{"comment":"Notation for the joint non-missingness probability and the cell-probability estimators could be clarified with an explicit equation linking the reweighting step to the win-measure definitions.","section":"Methods"}],"recommendation":"minor_revision","confidential_remarks":null},"author_rebuttal":{"model":"grok-4.3","summary":"We thank the referee for the constructive comments and positive overall assessment. We address each major comment below.","responses":[{"response":"We agree that the consistency of the IPW estimator relies on correct specification of the missingness model, as stated in the manuscript. Sensitivity analyses under misspecification would strengthen the practical claims. We will add such simulations (including cases where the missingness model omits key covariates or uses an incorrect functional form) to the revised manuscript. Note that the AIPW estimator retains double robustness, providing protection against misspecification of either the missingness or outcome model.","revision_made":"yes","referee_comment":"[Methods] Methods section (IPW construction): consistency of the IPW estimator for the joint cell probabilities requires correct specification and consistent estimation of the joint non-missingness probability P(both endpoints observed | treatment, covariates). The manuscript states this assumption but does not report any sensitivity analyses or additional simulations under misspecification of the missingness model, which is load-bearing for the practical claim that the IPW estimator remains consistent when applied to real data."},{"response":"We acknowledge that the reported simulations assume correct specification of the missingness model. To directly address this, we will expand the simulation section in revision to include misspecified missingness scenarios. These will evaluate bias, coverage, and relative efficiency of IPW versus AIPW, allowing assessment of whether the efficiency advantage and near-nominal coverage persist. We anticipate AIPW will demonstrate greater robustness due to double robustness.","revision_made":"yes","referee_comment":"[Simulations] Simulation studies: all reported scenarios assume the missingness model is correctly specified with the same covariates used in estimation. This leaves open whether the reported near-nominal coverage and efficiency advantage of AIPW persist when the missingness mechanism is misspecified, which directly affects the strength of evidence for the central consistency and efficiency claims."}],"tokens_in":1545,"tokens_out":419,"duration_ms":27894,"standing_objections":[]},"desk_editor":{"model":"grok-4.3","letter":"The core contribution is extending inverse probability weighting to win measures (win ratio, net benefit, etc.) when multiple ordinal endpoints have missing values that can depend on treatment and baselines. The standard pairwise approach treats incomplete pairs as ties and can bias results even under MCAR; the new IPW reweights complete pairs by the inverse of estimated joint non-missingness probabilities, and AIPW adds outcome regression for efficiency and double robustness. They derive influence-function variances and show in simulations that the usual method is biased while the proposed estimators stay consistent with near-nominal coverage, AIPW being more efficient. Applications to SCOUT-CAP and ACTT-1 plus the WinMO R package make it immediately usable.\n\nThe main limitation is the modeling assumption: IPW is unbiased only if the joint non-missingness probability is correctly specified given treatment and covariates. The stress-test note is on target here; the paper does not report simulations under misspecification of that model, so the robustness claim rests on the usual IPW theory rather than extra evidence. AIPW offers partial protection but still needs at least one model right. The applications are illustrative rather than a strong external validation.\n\nThis is targeted at biostatisticians handling win measures in trials with incomplete ordinal data. The methods are grounded in standard theory, the simulations are relevant, and the package lowers the barrier. It deserves peer review.","headline":"The paper fills a practical gap with IPW and AIPW estimators for win measures under missing hierarchical ordinal endpoints, backed by simulations and an R package, but consistency still requires correct specification of the joint missingness model.","tokens_in":2351,"tokens_out":369,"would_cite":false,"duration_ms":18219,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"grok-4.3","headline":"IPW and AIPW estimators yield consistent win measures for ordinal endpoints with missing data","keywords":["win ratio","win measures","missing data","inverse probability weighting","augmented IPW","ordinal endpoints","clinical trials","estimation"],"falsifier":"Simulation results or trial data where the missingness probability model is misspecified, leading to biased IPW estimates despite known true win measures.","tokens_in":2708,"feed_emoji":"📊","tokens_out":619,"duration_ms":45341,"temperature":0.7,"pith_summary":"This paper develops methods to estimate win measures such as the win ratio when multiple ordinal endpoints have missing values that may depend on treatment and covariates. The standard method of treating incomplete pairs as ties can bias results even when data are missing completely at random. The authors propose inverse probability weighting (IPW) that reweights observed pairs by their probability of being fully observed, and an augmented version (AIPW) that adds outcome modeling for better efficiency and double robustness. They derive closed-form variance estimators and demonstrate through simulations that the new estimators are consistent with good coverage, while the standard approach is not. The methods are applied to two clinical trials to show practical use.","feed_headline":"Weighting fixes bias in win measures with missing endpoints","feed_subtitle":"IPW and AIPW estimators stay consistent when treating missing pairs as ties does not, even under random missingness.","key_machinery":"IPW estimator that reweights pairwise comparisons using estimated joint non-missingness probabilities, and its augmented version that combines with outcome regression for double robustness.","core_discovery":"We develop inverse probability weighting (IPW) and augmented IPW (AIPW) estimators for win measures with hierarchical ordinal endpoints subject to missing data, allowing missingness to depend on treatment assignment and baseline covariates. The IPW estimator corrects bias by reweighting complete observed outcomes using joint non-missingness probabilities involved in estimating the joint cell probabilities that define the win measures. The AIPW estimator additionally incorporates outcome modeling, improving efficiency and achieving double robustness. For inference, we derive closed-form variance estimators for both methods based on influence functions.","pith_inferences":["The double robustness property of AIPW protects against misspecification of either the missingness or outcome model.","These estimators could be extended to settings with more complex missingness patterns or additional covariates.","Adoption of these methods may lead to more reliable conclusions in clinical trials with incomplete ordinal data."],"forward_implications":["The standard pairwise-comparison approach produces biased estimates even under MCAR.","IPW and AIPW estimators are consistent for the true win measures.","AIPW estimator is more efficient than IPW.","Variance estimators for IPW and AIPW achieve near-nominal coverage in simulations."],"fun_headline_variants":["IPW and AIPW correct bias in win measures with missing ordinal endpoints","IPW AIPW methods yield consistent win measures despite missing data","AIPW boosts efficiency over IPW for missing ordinal win measures","Double robust AIPW for win measures with covariate dependent missingness","Closed form variance for IPW AIPW win measures under missing endpoints"],"cache_read_input_tokens":2112,"weakest_assumption_plain":"The probability of joint non-missingness for pairs can be correctly estimated from treatment assignment and baseline covariates, and the missingness mechanism is correctly specified for the IPW to be unbiased.","fun_headline_variants_meta":{"raw":{"variants":["IPW and AIPW correct bias in win measures with missing ordinal endpoints","IPW AIPW methods yield consistent win measures despite missing data","AIPW boosts efficiency over IPW for missing ordinal win measures","Double robust AIPW for win measures with covariate dependent missingness","Closed form variance for IPW AIPW win measures under missing endpoints"]},"model":"grok-4.3","cost_usd":0.007359,"raw_usage":{"total_tokens":3439,"prompt_tokens":776,"num_sources_used":0,"completion_tokens":88,"cost_in_usd_ticks":73587000,"prompt_tokens_details":{"text_tokens":776,"audio_tokens":0,"image_tokens":0,"cached_tokens":256},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":2575,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":776,"tokens_out":88,"duration_ms":26510,"temperature":1.0,"reasoning_tokens":2575,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-06-29T15:38:57.474704+00:00","model_set":{"reader":"grok-4.3"},"falsifier":"Simulation results or trial data where the missingness probability model is misspecified, leading to biased IPW estimates despite known true win measures.","supporting_citations":[],"review_version":1}