{"id":"91945b06-aeb9-4a30-b078-a713da8a9e4a","arxiv_id":"2606.25749","paper_version":1,"verdict":"UNVERDICTED","confidence":"LOW","novelty_score":7.0,"correctness_risk":"unknown","formal_verification":"none","parameter_count":1,"one_line_summary":"A Bayesian nonparametric model for nonignorable dropout in bivariate longitudinal outcomes uses sensitivity parameters and identifying restrictions to handle missing data complexities, demonstrated on a trial of intellectual disability treatment.","lead":"The paper introduces a Bayesian nonparametric method to jointly model nonignorable dropout processes for each outcome in bivariate longitudinal data while using sensitivity parameters to explore missingness assumptions. Smart generalists might read it because it targets cost-effectiveness analyses in clinical trials, where missing data can bias policy-relevant conclusions about treatment value.","discovery_kind":"new_method","skeptic_critique":{"model":"grok-4.3","headline":"Partial identification via identifying restrictions may fail to hold when dropout times differ across the two responses","rationale":"The reader's weakest_assumption directly identifies the identification step as the least secure part of the argument; the staggered-dropout feature makes that step even more delicate, but the abstract supplies no further technical detail that would allow a stronger objection.","tokens_in":1753,"tokens_out":308,"duration_ms":12246,"concrete_test":"Generate bivariate longitudinal data under a known nonignorable mechanism with staggered dropout times (e.g., one outcome observed up to t=4, the other up to t=3 for the same subject); fit the proposed model under the stated identifying restrictions and sensitivity-parameter priors; verify whether the posterior credible intervals for the joint mean or cost-effectiveness ratio contain the true values at nominal coverage.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim rests on jointly modeling two dropout processes while partially identifying the missing bivariate outcomes through identifying restrictions that condition on the observed dropout indicators and sensitivity parameters. When individuals can drop out at different times for each response (explicitly noted in the abstract), these restrictions implicitly require that the conditional distribution of the unobserved outcomes given the observed history and the two dropout indicators can be expressed without additional cross-response dependence that is not captured by the nonparametric model on the observed data. If that factorization does not hold, varying the priors on the sensitivity parameters will not correctly bound the range of possible biases in the cost-effectiveness parameters.","agreement_with_reader":"agree"},"referee_report":{"model":"grok-4.3","summary":"The paper proposes a Bayesian nonparametric approach to handle nonignorable dropout in bivariate longitudinal data (e.g., effectiveness and cost measures in clinical trials). It jointly models the two dropout processes, specifies a flexible nonparametric model for the observed data, and partially identifies the missing data distribution using identifying restrictions that condition on the dropout indicators and sensitivity parameters, with alternative nonignorable scenarios explored via priors on those parameters. The method is motivated by and applied to trial data on treatment for intellectual disability and challenging behaviour.","tokens_in":1852,"tokens_out":545,"duration_ms":16078,"significance":"If the partial identification strategy is valid, the work provides a flexible, nonparametric framework for sensitivity analysis under nonignorable missingness in bivariate longitudinal settings with possibly differing dropout times per response. This addresses a practical gap in trial-based economic evaluations where standard parametric models struggle with skewness, spikes, and multivariate dropout, potentially leading to more robust cost-effectiveness inferences.","major_comments":[{"comment":"Abstract and modeling section on identifying restrictions: the claim that the distribution of the missing bivariate outcomes is partially identified via restrictions conditional on the two dropout indicators and sensitivity parameters does not address the case (explicitly noted in the abstract) where individuals drop out at different times for each response. When dropout times differ, the required conditional distribution of the unobserved outcomes given observed history and the pair of dropout indicators may involve cross-response dependence not captured by the nonparametric model fitted only to observed data; varying priors on the sensitivity parameters would then fail to correctly bound bias in the cost-effectiveness parameters.","section":"Abstract / identifying restrictions"},{"comment":"Section describing the joint dropout model: no derivation or explicit factorization is provided showing how the bivariate dropout process is specified when the two responses have misaligned observation times, which is load-bearing for the claim that the approach jointly models both dropout processes while remaining computationally tractable.","section":"Joint dropout model"}],"minor_comments":[{"comment":"Abstract contains a repeated word: 'The modelling task may be also be complicated'.","section":"Abstract"},{"comment":"Notation for the sensitivity parameters and the nonparametric components should be introduced with explicit definitions and distinguished from standard MNAR parameters in the literature.","section":"Notation"}],"recommendation":"major_revision","confidential_remarks":"The manuscript appears to be a methodological proposal without simulation studies or empirical validation results in the provided text; this limits assessment of finite-sample performance. The citation pattern does not reference recent work on bivariate MNAR models with staggered dropout, which may affect perceived novelty."},"author_rebuttal":{"model":"grok-4.3","summary":"We thank the referee for the constructive and detailed comments, which highlight important aspects of our approach to nonignorable dropout in bivariate longitudinal settings. We address each major comment below and indicate the revisions planned for the manuscript.","responses":[{"response":"We appreciate the referee's point on the challenges posed by misaligned dropout times. Our nonparametric model for the observed data is specified jointly across both responses, capturing dependence up to the last observed time for each. The identifying restrictions are formulated conditionally on the pair of dropout indicators to permit the sensitivity parameters to encode cross-response associations in the unobserved data. That said, we acknowledge that the original manuscript did not provide a sufficiently explicit derivation showing how this conditional distribution preserves or bounds the relevant dependence when observation times differ. We will revise the modeling section to include this derivation and clarify how the sensitivity analysis correctly informs bounds on bias for the cost-effectiveness parameters.","revision_made":"yes","referee_comment":"[Abstract / identifying restrictions] Abstract and modeling section on identifying restrictions: the claim that the distribution of the missing bivariate outcomes is partially identified via restrictions conditional on the two dropout indicators and sensitivity parameters does not address the case (explicitly noted in the abstract) where individuals drop out at different times for each response. When dropout times differ, the required conditional distribution of the unobserved outcomes given observed history and the pair of dropout indicators may involve cross-response dependence not captured by the nonparametric model fitted only to observed data; varying priors on the sensitivity parameters would then fail to correctly bound bias in the cost-effectiveness parameters."},{"response":"We agree that an explicit factorization of the bivariate dropout process under misaligned observation times is necessary to substantiate the claim of joint modeling and computational tractability. Although the model construction relies on a joint specification that factors through the observed data likelihood and appropriate priors for the dropout indicators, the manuscript did not include the full derivation. In the revision we will add this factorization, along with details on how the joint process is implemented in the MCMC algorithm to maintain tractability.","revision_made":"yes","referee_comment":"[Joint dropout model] Section describing the joint dropout model: no derivation or explicit factorization is provided showing how the bivariate dropout process is specified when the two responses have misaligned observation times, which is load-bearing for the claim that the approach jointly models both dropout processes while remaining computationally tractable."}],"tokens_in":1447,"tokens_out":508,"duration_ms":21415,"standing_objections":[]},"desk_editor":{"model":"grok-4.3","letter":"This paper proposes a Bayesian nonparametric joint model for bivariate longitudinal outcomes with nonignorable dropout at different times plus sensitivity parameters.\n\nIt handles a genuine practical problem in trial-based economic evaluations, where costs and effectiveness measures are often skewed or spiked and dropout is not random. The nonparametric specification for the observed data plus the joint dropout modeling gives a flexible way to avoid strong parametric assumptions, and the sensitivity parameters let users explore different nonignorable scenarios. That combination is not standard in the literature they cite.\n\nThe soft spot is the partial identification step. The approach relies on identifying restrictions conditioned on the two dropout indicators and the sensitivity parameters. When individuals drop out at different times for each response, it is not obvious that the conditional distribution of the unobserved parts factors cleanly without extra cross-response dependence that the nonparametric model on the observed data might miss. The stress-test note flags this, and it lands as a real concern rather than a minor one; the abstract does not show derivations or checks that would settle it.\n\nThe work is aimed at statisticians and health economists who need tools for sensitivity analysis in bivariate longitudinal settings with missingness. A reader working on cost-effectiveness models would find the setup relevant.\n\nIt deserves peer review to examine the identification assumptions and any simulation or real-data validation that the full manuscript provides.","headline":"The paper proposes a Bayesian nonparametric joint model for bivariate longitudinal outcomes with nonignorable dropout at different times plus sensitivity parameters, but the identification step needs scrutiny when dropout patterns diverge.","tokens_in":2317,"tokens_out":346,"would_cite":false,"duration_ms":12217,"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":"A Bayesian nonparametric model jointly handles nonignorable dropout for each of two longitudinal outcomes while allowing sensitivity analysis on the missingness assumptions.","keywords":["nonignorable dropout","bivariate longitudinal data","Bayesian nonparametric","sensitivity analysis","missing data","cost-effectiveness","identifying restrictions"],"falsifier":"Collect a new trial dataset in which all participants complete every scheduled assessment and then compare the model's posterior predictions for the would-be missing values (under each prior on the sensitivity parameters) against the actually observed values.","tokens_in":2639,"feed_emoji":"","tokens_out":621,"duration_ms":11798,"temperature":0.7,"pith_summary":"The paper develops a method for analyzing incomplete bivariate longitudinal data, such as paired measures of effectiveness and costs in clinical trials, where participants drop out at different times for each outcome. It models the observed data flexibly with a nonparametric Bayesian approach and then uses restrictions tied to the dropout indicators plus sensitivity parameters to partially identify the distribution of the missing values. Different priors on those sensitivity parameters let the analyst explore a range of nonignorable missingness scenarios without assuming the dropout is unrelated to the unseen outcomes. This setup directly addresses the identification problems that arise when the outcome is multivariate and the data show skewness or point masses.","feed_headline":"Bayesian model identifies missing bivariate outcomes under nonignorable dropout","feed_subtitle":"Joint nonparametric specification plus sensitivity parameters let analysts explore how different dropout mechanisms affect paired longitudin","key_machinery":"Joint Bayesian nonparametric model for the observed data together with identifying restrictions conditional on dropout indicators and sensitivity parameters.","core_discovery":"The central claim is that a flexible nonparametric Bayesian specification for the observed bivariate longitudinal responses, combined with identifying restrictions that condition on the observed dropout indicators and on chosen sensitivity parameters, permits joint modeling of the two dropout processes and supports exploration of nonignorable missingness through alternative priors on the sensitivity parameters.","pith_inferences":["The same structure could be used to handle trivariate or higher-dimensional longitudinal outcomes if the identifying restrictions are extended accordingly.","Policy conclusions drawn from cost-effectiveness trials may shift when the sensitivity parameters are allowed to differ across treatment arms.","The method suggests a route for sensitivity analysis in other settings where dropout times differ across multiple correlated endpoints."],"forward_implications":["Different dropout times for the two response types can be accommodated without forcing a common dropout process.","Skewness and point masses in the data are captured without parametric assumptions on the outcome distributions.","Multiple nonignorable missingness scenarios can be examined by varying the priors placed on the sensitivity parameters.","The approach supplies cost-effectiveness estimates that incorporate uncertainty arising from the dropout mechanism."],"fun_headline_variants":["Bayesian nonparametric approach for nonignorable dropout in bivariate models","Nonparametric Bayesian jointly models paired dropout in longitudinal data","Sensitivity analysis of nonignorable dropout using Bayesian bivariate models","Flexible Bayesian model explores nonignorable missingness in bivariate outcomes"],"cache_read_input_tokens":2112,"weakest_assumption_plain":"The distribution of the missing data can be partially identified through restrictions that depend on the dropout indicators and on the chosen values of the sensitivity parameters.","fun_headline_variants_meta":{"raw":{"variants":["Bayesian nonparametric approach for nonignorable dropout in bivariate models","Nonparametric Bayesian jointly models paired dropout in longitudinal data","Sensitivity analysis of nonignorable dropout using Bayesian bivariate models","Flexible Bayesian model explores nonignorable missingness in bivariate outcomes"]},"model":"grok-4.3","cost_usd":0.004949,"raw_usage":{"total_tokens":2430,"prompt_tokens":686,"num_sources_used":0,"completion_tokens":66,"cost_in_usd_ticks":49487000,"prompt_tokens_details":{"text_tokens":686,"audio_tokens":0,"image_tokens":0,"cached_tokens":256},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":1678,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":686,"tokens_out":66,"duration_ms":14381,"temperature":1.0,"reasoning_tokens":1678,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-06-25T20:15:43.822364+00:00","model_set":{"reader":"grok-4.3"},"falsifier":"Collect a new trial dataset in which all participants complete every scheduled assessment and then compare the model's posterior predictions for the would-be missing values (under each prior on the sensitivity parameters) against the actually observed values.","supporting_citations":[],"review_version":1}