{"id":"0cc58350-b24b-4d9d-bfb9-b96c98f85f4b","arxiv_id":"2606.24024","paper_version":1,"verdict":"UNVERDICTED","confidence":"LOW","novelty_score":6.0,"correctness_risk":"unknown","formal_verification":"none","parameter_count":0,"one_line_summary":"Pseudo-value regression allows standard GEE or OLS to estimate covariate effects on the mean cumulative function and area under the MCF for recurrent events.","lead":"The paper proposes using influence-function pseudo-values as outcomes in a regression model to estimate how covariates affect the mean cumulative function and its area for recurrent events under right-censoring. A smart generalist might read it to understand a practical way to adjust recurrent-event summaries like relapse burden for patient factors in clinical trials.","discovery_kind":"new_method","skeptic_critique":{"model":"grok-4.3","headline":"Unbiasedness of influence-function pseudo-values for MCF/AUMCF regression requires independent censoring conditional on included covariates","rationale":"The reader's weakest assumption directly isolates the condition required for the pseudo-value regression to target the correct conditional parameters; this is the point at which the argument is least secure. No other internal inconsistency (e.g., in the GEE machinery itself or the identity-link claim) is evident from the abstract or the stated central claim. The UNVERDICTED status is therefore retained.","tokens_in":1752,"tokens_out":348,"duration_ms":18991,"concrete_test":"Generate recurrent-event data under a censoring hazard that depends on an auxiliary covariate Z not included in the regression model; compute the influence-function pseudo-values for MCF at the truncation time, fit the identity-link OLS regression on the observed covariates, and verify whether the coefficient estimates remain consistent for the true conditional effects (compare bias and coverage against the oracle that includes Z).","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central construction treats influence-function pseudo-values (derived from the nonparametric MCF estimator at fixed truncation time) as regression outcomes in GEE or OLS. For the resulting estimator to be consistent for the regression parameters under an identity link, it is necessary that E[pseudo-value_i | X_i] equals the true conditional MCF given X_i. This holds only when the influence function is derived under censoring and terminal-event mechanisms that are independent of the recurrent-event process conditional on the covariates that enter the regression; dependence on additional covariates (or misspecification of the censoring law) violates the conditional unbiasedness and induces bias in the OLS/GEE coefficients.","agreement_with_reader":"agree"},"referee_report":{"model":"grok-4.3","summary":"The manuscript proposes a pseudo-value-based regression approach for estimating covariate effects on the mean cumulative function (MCF) and area under the MCF (AUMCF) at a fixed truncation time. Influence-function-based pseudo-values are constructed from the nonparametric MCF estimator and used as regression outcomes in GEE machinery (or OLS under identity link), with performance evaluated in simulations for accuracy, coverage, type I error, and power, plus an application to the ORATORIO trial.","tokens_in":1908,"tokens_out":495,"duration_ms":18474,"significance":"If the central consistency result holds, the approach supplies a straightforward, software-friendly route to covariate-adjusted inference on recurrent-event burden summaries. Credit is due for the simulation battery (accuracy, coverage, type I error, power) and the real-data demonstration on a phase-III multiple-sclerosis trial; these elements make the practical contribution concrete.","major_comments":[{"comment":"The consistency claim for the OLS/GEE estimator rests on E[pseudo-value_i | X_i] equaling the true conditional MCF given X_i. This equality holds only when the influence function is derived under censoring and terminal-event mechanisms that are independent of the recurrent process conditional on the covariates entering the regression (see abstract description of pseudo-value construction and its direct use as outcomes). The manuscript does not state this conditional-independence requirement explicitly or provide a proof/relaxation.","section":"Pseudo-value construction and consistency argument"},{"comment":"Simulation design evaluates performance only under data-generating processes that satisfy the independent-censoring assumption implicit in the influence-function derivation. Scenarios with covariate-dependent censoring or omitted censoring covariates would directly test whether bias appears in the regression coefficients when the weakest assumption is violated.","section":"Simulation studies section"}],"minor_comments":[{"comment":"Define AUMCF explicitly as the integral of the MCF up to the fixed truncation time and state whether the pseudo-value construction is applied directly to the integrated functional or obtained by integrating the MCF pseudo-values.","section":"Notation and definitions"},{"comment":"In tables reporting simulation results, add a column or footnote indicating the link function and whether GEE or OLS was used for each row.","section":"Simulation result tables"}],"recommendation":"major_revision","confidential_remarks":null},"author_rebuttal":{"model":"grok-4.3","summary":"We thank the referee for the constructive comments. We address each major comment below, indicating where we will revise the manuscript to improve clarity and completeness.","responses":[{"response":"We agree that the conditional independence of censoring and terminal events given the covariates must be stated explicitly for the consistency result to hold. In the revised manuscript we will add a dedicated paragraph in the Methods section stating this assumption and its role in ensuring E[pseudo-value_i | X_i] equals the target conditional MCF. While we do not provide a self-contained proof (as the result follows from standard properties of influence-function pseudo-values under independent censoring, as in the cited pseudo-value literature), we will include a brief justification with references to the relevant theory and note that the GEE/OLS step inherits consistency from the unbiased pseudo-values.","revision_made":"partial","referee_comment":"[Pseudo-value construction and consistency argument] The consistency claim for the OLS/GEE estimator rests on E[pseudo-value_i | X_i] equaling the true conditional MCF given X_i. This equality holds only when the influence function is derived under censoring and terminal-event mechanisms that are independent of the recurrent process conditional on the covariates entering the regression (see abstract description of pseudo-value construction and its direct use as outcomes). The manuscript does not state this conditional-independence requirement explicitly or provide a proof/relaxation."},{"response":"The referee correctly identifies that our current simulations maintain the independent-censoring assumption. We will add a new simulation scenario in which censoring depends on covariates (and an additional scenario with an omitted censoring covariate) to quantify the resulting bias in the regression coefficients. These results will be reported in a revised Table or supplementary figure, together with a short discussion of when the method remains reliable versus when the assumption is critical.","revision_made":"yes","referee_comment":"[Simulation studies section] Simulation design evaluates performance only under data-generating processes that satisfy the independent-censoring assumption implicit in the influence-function derivation. Scenarios with covariate-dependent censoring or omitted censoring covariates would directly test whether bias appears in the regression coefficients when the weakest assumption is violated."}],"tokens_in":1363,"tokens_out":468,"duration_ms":20675,"standing_objections":[]},"desk_editor":{"model":"grok-4.3","letter":"The core of the paper is taking the pseudo-value technique and pointing it at regression for the mean cumulative function and its area under the curve at a fixed time. They build the pseudo-values from the influence function of the nonparametric MCF estimator, then treat those as outcomes in GEE or OLS under an identity link.\n\nWhat the work does well is run simulations that check accuracy, coverage, type I error, and power across recurrent-event setups with censoring and terminal events, plus the ORATORIO trial example on ocrelizumab in multiple sclerosis. That gives usable evidence on how the method behaves in practice and shows it can be applied without custom software beyond standard GEE routines.\n\nThe approach stays simple and reuses existing machinery, which is a real advantage over more involved augmentation methods for covariate-adjusted summaries of recurrent burden.\n\nThe soft spot is the requirement that the influence-function pseudo-values remain unbiased for the conditional MCF given the covariates. This needs censoring and terminal events to be independent of the recurrent process conditional on the included covariates; any dependence on omitted factors or misspecification can introduce bias in the regression coefficients. The stress-test note is on target here, and the paper would be stronger with explicit checks or sensitivity results on that point.\n\nThis is aimed at applied statisticians working with recurrent-event data in trials who want an accessible regression tool for cumulative burden. A reader focused on practical methods rather than new theory would get value from the simulations and example.\n\nIt deserves peer review. The validation steps are concrete enough to justify referee time even if the theoretical step is incremental.","headline":"This adapts pseudo-value regression to MCF and AUMCF via influence functions and GEE/OLS, a practical move for recurrent-event work that stays within standard assumptions.","tokens_in":2375,"tokens_out":402,"would_cite":false,"duration_ms":19830,"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":"Pseudo-value regression estimates covariate effects on recurrent event accumulation using standard tools.","keywords":["pseudo-values","mean cumulative function","recurrent events","regression analysis","generalized estimating equations","covariate adjustment"],"falsifier":"Observing bias in the regression coefficients when the censoring mechanism depends on unobserved factors that also affect the event rate.","tokens_in":2671,"feed_emoji":"","tokens_out":523,"duration_ms":18828,"temperature":0.7,"pith_summary":"The paper develops a method that converts the mean cumulative function and its area into pseudo-values derived from influence functions. These pseudo-values then serve as outcomes in a regression model fitted by generalized estimating equations or ordinary least squares. This setup allows direct estimation of how covariates influence the total burden of recurrent events up to a fixed time, while accounting for censoring and terminal events. Simulations confirm the approach's performance, and it is applied to trial data on multiple sclerosis treatment.","feed_headline":"Pseudo-values turn recurrent counts into regression outcomes","feed_subtitle":"A new approach fits standard models to estimate how covariates change event accumulation over time.","key_machinery":"Influence-function-based pseudo-values constructed for the MCF and AUMCF, used directly as outcomes in a regression model.","core_discovery":"Influence-function-based pseudo-values can be used as regression outcomes to estimate covariate effects on the mean cumulative function and the area under the mean cumulative function at a fixed truncation time, with estimation performed via standard generalized estimating equation machinery or ordinary least squares under an identity link.","pith_inferences":["The method may extend naturally to time-varying covariates if the pseudo-value construction can be adapted.","Similar pseudo-value approaches could apply to other recurrent event summaries beyond the MCF.","Applications in other fields with recurrent events, such as reliability engineering, become more accessible with standard tools."],"forward_implications":["Standard regression software can be applied to recurrent event data without custom implementations.","Covariate effects on cumulative event burden can be estimated at any fixed time horizon.","Both the mean cumulative count and its integrated area can be modeled in the same framework.","Type I error and coverage properties hold under the assumed censoring conditions in simulations."],"fun_headline_variants":["Pseudo-values as outcomes for cumulative count regression","Covariate effects on MCF modeled with pseudo-values","Pseudo-value regression for area under the mean cumulative function","Standard GEE regression using influence-function pseudo-values for MCF","Estimating AUMCF effects via pseudo-value regression"],"cache_read_input_tokens":2112,"weakest_assumption_plain":"The influence function used to create the pseudo-values assumes censoring and terminal events are independent of the event process conditional on the covariates.","fun_headline_variants_meta":{"raw":{"variants":["Pseudo-values as outcomes for cumulative count regression","Covariate effects on MCF modeled with pseudo-values","Pseudo-value regression for area under the mean cumulative function","Standard GEE regression using influence-function pseudo-values for MCF","Estimating AUMCF effects via pseudo-value regression"]},"model":"grok-4.3","cost_usd":0.008779,"raw_usage":{"total_tokens":3931,"prompt_tokens":624,"num_sources_used":0,"completion_tokens":65,"cost_in_usd_ticks":87787000,"prompt_tokens_details":{"text_tokens":624,"audio_tokens":0,"image_tokens":0,"cached_tokens":256},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":3242,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":624,"tokens_out":65,"duration_ms":16870,"temperature":1.0,"reasoning_tokens":3242,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-06-25T23:25:52.146591+00:00","model_set":{"reader":"grok-4.3"},"falsifier":"Observing bias in the regression coefficients when the censoring mechanism depends on unobserved factors that also affect the event rate.","supporting_citations":[],"review_version":1}