{"id":"e5a1fdbc-5f0b-4931-9b5c-2e8cbdc25c88","arxiv_id":"2411.17533","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"Pseudo-value regression extends mediation analysis to time-to-event estimands, giving additive direct and indirect effects on survival probability, RMST, and cumulative incidence scales.","lead":"This paper shows that pseudo-values, a known survival-analysis tool, can turn censored time-to-event outcomes into ordinary continuous numbers for mediation analysis, so standard software can estimate direct and indirect treatment effects. The method covers survival probabilities, restricted mean survival time, and cumulative incidence with competing risks, and is tested in simulations and a multiple sclerosis trial.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Linear pseudo-value outcome model is misspecified in the simulations themselves, so the claimed unbiasedness of the product-method estimates is not supported by the presented evidence.","rationale":"The reader's weakest_assumption correctly identifies the linearity/no-interaction form of Eqs. 13–14 as load-bearing, but frames the simulations as testing exactly that structure ('linear/exponential structure'). In fact, the simulation's exponential hazard induces a conditional survival probability that is strongly nonlinear in the mediator on the pseudo-value scale, so the linear outcome model is misspecified even in the 'correct' scenarios. This makes the unbiasedness claim suspect: the product-method formulas are only guaranteed under correct linear specification, and no evidence is given that the small-bias approximation persists outside the narrow simulation grid. The proposed concrete test directly challenges the claim by using a more extreme but still fully specified version of the paper's own generative model; if bias appears, the paper would need to present the method as an approximation with quantified error, or adopt flexible outcome models (e.g., link functions or interactions). The reader's additional concern about pseudo-value correlation for inference is valid and complementary, but the point-estimation misspecification is more fundamental because it undermines the primary simulation evidence. Verdict remains CONDITIONAL rather than REJECT because the method may still be a useful approximation in many settings, but the claim of unbiasedness as stated is not supported and requires either empirical demonstration of negligible bias or a corrected claim.","tokens_in":103,"tokens_out":12215,"duration_ms":292739,"concrete_test":"Rerun the Section 4.1 scenario with no censoring, β0=ln(1/3), βA=0 (indirect-effect-only case), βM=ln(5), and τ=4, with N=1000 per arm. Compute the pseudo-value product-method NIE (α_A·β_M from the two lm() fits) and compare it with the Gauss-Hermite quadrature truth for E[S(τ;0,M1)]−E[S(τ;0,M0)]. If the relative bias exceeds 5%, the linear outcome model is not unbiased under the paper's own generative family, and the central claim must be revised.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"The central claim is that pseudo-values turn survival endpoints into continuous outcomes that can be plugged into standard linear mediation software, so that NDE=β_A, NIE=α_A·β_M, and TE=β_A+α_A·β_M (Eqs. 15–17) are unbiased. This identification requires E[pseudo-value | A,M,C] to be linear in A and M with no A×M interaction (Eq. 14). The simulation generates T|A,M ~ Exp(exp(β0 + AβA + MβM)). Under this model, the conditional survival probability S(τ|A,M) = exp(−τ exp(β0+AβA+MβM)) is not linear in M, and the conditional expectation of the pseudo-value inherits this nonlinearity. Even without censoring, the pseudo-value equals I(T>τ), whose conditional mean is the nonlinear S(τ|A,M). Thus Eq. 14 is misspecified in exactly the scenarios used for validation. The reported 'unbiased' results cannot be exact; at best they are small-bias approximations on a narrow parameter grid (k=3, τ∈{2,3,4}, moderate effects). No scenario with stronger nonlinearity, an interaction, or a non-normal mediator is tested. The paper should either quantify the bias and qualify 'unbiased' or demonstrate robustness under misspecification. A related gap is that the reported delta-method inference from lm() treats pseudo-values as independent, which they are not; the paper mentions bootstrap recalculation but does not use it as the primary simulation inference.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes using pseudo-values to transform survival outcomes into continuous outcomes that can be analyzed with standard linear mediation models, thereby estimating natural direct, indirect, and total effects on survival probability, restricted mean survival time, and cumulative incidence. The method is illustrated with simulations across 324 scenarios and an application to the PARADIGMS multiple sclerosis trial. The central claim is that after constructing pseudo-values, the product-method formulas (NDE = β_A, NIE = α_A β_M, TE = β_A + α_A β_M) yield unbiased estimates and valid inference.","tokens_in":17278,"tokens_out":5049,"duration_ms":57464,"significance":"If the central claim were fully established, the paper would offer a practical simplification: applied analysts could use familiar software (e.g., CMAverse) for mediation analysis of time-to-event outcomes, with interpretable additive decompositions. The paper also contributes a computationally efficient influence-function approximation for pseudo-values and validates it thoroughly (R² = 1.00; reduced runtime). However, the load-bearing assumptions of linearity and independence of the pseudo-value outcome model are not adequately examined, and the simulation evidence does not support the claim of exact unbiasedness as stated. The method is potentially useful but needs substantial additional validation and more careful qualifiers.","major_comments":[{"comment":"The data-generating process T|A,M ~ Exp(exp(β0 + AβA + MβM)) yields a conditional survival probability S(τ|A,M) = exp(−τ exp(β0 + AβA + MβM)) that is not linear in M, and the same holds for the conditional mean of the pseudo-values. Equation (14) is therefore misspecified in the very scenarios used to validate the method. The product-method formulas (15)–(17) are exact only when the pseudo-value outcome model is correctly specified, so the claim in §4.3.1 that the approach is 'unbiased for the true NIE, NDE, and TE' cannot hold exactly under this generative model. The reported results likely reflect small bias on a narrow parameter grid (k=3, τ∈{2,3,4}) rather than exact unbiasedness. The paper should either provide a theoretical argument for why the linear pseudo-value model yields consistent natural effects under this nonlinear data-generating process, or substantially expand the simulations to include stronger nonlinearity, A×M interactions, and non-normal mediators, and qualify the 'unbiased' wording accordingly.","section":"§4.1–4.3.1, Eq. (20)"},{"comment":"The inference in the simulation studies is based on the multivariate delta method applied to standard linear-model output from lm(), which treats pseudo-values as independent observations. Pseudo-values are correlated by construction because each leave-one-out estimate shares the full-sample estimate (Eq. 6). The standard errors from lm() are therefore not valid for pseudo-value regression, and the reported type I error and coverage results do not provide reliable evidence of valid inference. The paper mentions that bootstrap should recalculate pseudo-values, but the simulations do not use this approach as the primary inference. The authors should either use a variance estimator that accounts for the pseudo-value dependence (e.g., bootstrap with recalculation, or a sandwich estimator) or explicitly state that the reported type I error/coverage results are for an ad hoc procedure whose repeated-sampling properties are not guaranteed.","section":"§4.2, §4.3.2, Fig. 3"},{"comment":"The paper's robustness suggestion—comparing TE from the model-based decomposition with an independent estimate—is not reported in the simulations. Given that the pseudo-value outcome model is misspecified in the simulated scenarios, the degree of agreement between the product-method TE and the direct difference of estimands would directly quantify the bias induced by the linearity assumption. Adding this diagnostic to the simulation results would help readers assess whether the product method is acceptable in practice under realistic misspecification.","section":"§3.1, Step 4 and §6"}],"minor_comments":[{"comment":"The text says 'casual graph' in the caption; should be 'causal graph'.","section":"§2.1, Fig. 1 caption"},{"comment":"The outcome model includes confounders C but Eq. (1) in the background does not; this is fine but should be noted explicitly to avoid confusion about whether the earlier equations are unadjusted.","section":"§3.1, Eq. (14)"},{"comment":"The notation 'TTE' is used once and then 'T'; please define consistently.","section":"§4.1, Eq. (19)–(20)"},{"comment":"The figure caption says 'Bias was evaluated across 10,000 simulation replicates', but the text states N ∈ {50,100,200} per arm; it would help to state the total number of replicates for each N and τ.","section":"§4.3.1, Fig. 2"},{"comment":"The sentence 'the empirical type I error was 0.05 ... and 0.04 ... averaged across all cases considered' is vague; specify the estimands, time points, and sample sizes included in the average.","section":"§4.3.2"},{"comment":"The table reports 'Proportion Mediated' with confidence intervals, but the method for obtaining the CI for the proportion is not described; clarify whether it is from the bootstrap or delta method.","section":"§5, Table 1"}],"recommendation":"major_revision","confidential_remarks":"The stress-test concern is valid and should be addressed before publication. The paper's core contribution is a practical simplification, but the current simulation evidence overclaims exact unbiasedness under a model that is actually misspecified. The inference section also needs to correct the handling of pseudo-value dependence. I recommend major revision rather than rejection because the approach may be salvageable by reframing the claims, adding misspecification simulations, and using appropriate inference."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The paper does something genuinely useful: it takes the pseudo-value mediation idea from Chernofsky's RMST work and extends it to survival probability and cumulative incidence with competing risks, then packages it into a simple workflow (pseudo()/SurvUtils + lm/CMAverse). The PARADIGMS example is a nice, honest illustration, and the validation of the influence-function approximation is solid. I'd send this to a serious referee—applied biostatisticians will want to use it, and the presentation is clear enough for them to try.\n\nThe main soft spot is the linearity assumption. The simulations generate T|A,M as exponential with log-hazard linear in A and M. That makes the true survival probability S(τ|A,M) = exp(-τ exp(β0 + AβA + MβM)) nonlinear in M (and A), so fitting the linear pseudo-value outcome model (14) is a misspecification. The product method then targets the best linear projection, not the true NDE/NIE, unless the approximation is very good. The results show bias near zero, which is reassuring, but calling that 'unbiased' overstates it. The paper should either quantify the bias and say 'negligible bias under these simulation settings,' or add robustness scenarios (stronger effects, interactions, non-normal mediators) before making a general claim. The stress-test note is correct on this point.\n\nThe second issue is inference. The simulations use the delta method with lm() standard errors, which treats pseudo-values as independent. They are not, since each pseudo-value depends on the full sample. The paper mentions bootstrapping with pseudo-value recalculation, but doesn't use it as the primary simulation inference. That leaves the type-I error results arguably based on an incorrect variance assumption. A sandwich estimator or a comparison against the bootstrap would settle it. Minor, but worth fixing.\n\nThe mediator measured after conditioning on survival to year 1 is acknowledged and not resolved—fair enough for recurrent events, but it limits the method's applicability to mortality outcomes.\n\nOverall: a practical, well-written paper with a real audience, but the theoretical claims need tempering and the inference validation needs tightening. I'd accept it for review, but expect a revision that addresses the linearity and independence issues.","headline":"Useful applied extension of pseudo-value mediation to survival probability and competing risks, but the 'unbiased' claim rests on simulations where the linear outcome model is misspecified.","tokens_in":17809,"tokens_out":3312,"would_cite":false,"duration_ms":33848,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["62N01","62N02","62P10"],"pacs":[],"model":"deepseek-v4-flash","headline":"Pseudo-values transform censored survival outcomes into continuous-like responses, so the familiar product-method mediation formulas apply to survival probability, restricted mean survival time, and cumulative incidence.","keywords":["pseudo-values","causal mediation","survival analysis","restricted mean survival time","cumulative incidence","competing risks","time-to-event outcomes","product method"],"falsifier":"Generate data with a treatment-by-mediator interaction, for example a hazard $\\lambda = \\exp(\\beta_0 + A\\beta_A + A\\beta_{AM}M + M\\beta_M)$, compute the true natural indirect effect by numerical integration over the mediator, and compare it with the product $\\alpha_A\\beta_M$ from the paper's pipeline. A systematic discrepancy would show that the linear no-interaction models are load-bearing rather than a convenience.","tokens_in":16832,"feed_emoji":"📊","tokens_out":5376,"duration_ms":49546,"temperature":0.7,"pith_summary":"The paper argues that pseudo-values—jackknife-style transformations that turn censored survival data into values that behave like continuous outcomes—let researchers run causal mediation analysis on time-to-event endpoints with the same simple product formulas used for linear outcomes. The central claim is that natural direct, indirect, and total effects on survival probability, restricted mean survival time, and cumulative incidence (with competing risks) can be estimated by fitting an ordinary linear model to pseudo-values and multiplying coefficients from a mediator regression. If right, this makes mediation for survival data accessible to standard software and gives an additive, interpretable decomposition instead of decomposing hazard ratios. The simulations across 324 estimands are offered as evidence: the pseudo-value estimates are reported unbiased and type-I error is controlled at the nominal level under the null.","feed_headline":"Pseudo-values make survival mediation as simple as linear regression","feed_subtitle":"Decompose effects on survival probability, restricted mean time, and cumulative incidence into direct and mediated parts.","key_machinery":"The central object is the pseudo-value $Y_i = n\\hat{\\theta} - (n-1)\\hat{\\theta}_{(-i)}$, where $\\hat{\\theta}$ is the full-sample estimate of the survival functional and $\\hat{\\theta}_{(-i)}$ is the leave-one-out estimate. When the influence function of the estimator is known, the pseudo-value is approximated by $\\hat{\\theta} + \\varphi(X_i)$, which the paper validates as nearly identical to the jackknife version and much faster to compute. This machinery converts censored-data estimation into a continuous-outcome regression problem, so the causal estimands are identified by the coefficients of two linear models and combined by the product-method formulas.","core_discovery":"The paper's central discovery is a simplification: once survival data are converted into pseudo-values for an expectation-type estimand, censoring is accounted for inside those values, and the outcome model can be fit as a linear regression. Combining this with a linear mediator model yields the classical product-method decomposition: the natural direct effect is the treatment coefficient in the pseudo-value outcome model, the natural indirect effect is the product of the treatment coefficient in the mediator model and the mediator coefficient in the outcome model, and the total effect is their sum. The paper claims this pipeline is unbiased for all three estimands across sample sizes, time points, and the presence or absence of direct or indirect effects, and that p-values are uniformly distributed under the null of no mediation.","pith_inferences":["If the linearity assumptions hold even approximately, the same pseudo-value pipeline could extend to other expectation-type estimands such as years of life lost or event-free survival at multiple horizons, but the paper does not test those extensions.","The requirement that the mediator is measured after treatment and before the outcome makes the method most defensible for non-terminal recurrent events or early biomarkers; applying it to terminal events where mediator values are observed only among survivors would require additional missing-data assumptions.","One could benchmark the pseudo-value product method against nonparametric natural-effect estimates on real trial data to see whether the proportion mediated is stable across modeling choices."],"forward_implications":["Analysts can apply existing continuous-outcome mediation software to survival endpoints without writing specialized survival mediation routines.","Effects can be reported as differences in probabilities or restricted mean survival time, with an additive total effect that makes the proportion mediated easy to state.","The same procedure covers cumulative incidence in the presence of competing risks, an estimand rarely handled in earlier survival mediation work.","Influence-function approximations make bootstrap inference for pseudo-value mediation computationally practical in large samples.","The approach sidesteps the non-collapsibility of hazard ratios and the incompatibility of proportional hazards models with and without the mediator."],"supporting_citations":[{"why":"Introduces pseudo-value regression, the foundation for treating censored survival functionals as continuous outcomes.","marker":"[17]"},{"why":"Extends pseudo-values to causal inference, the lineage the paper builds on for mediation.","marker":"[18]"},{"why":"Prior thesis work applying pseudo-values to mediation of restricted mean survival time, which this paper extends to survival probabilities and cumulative incidence.","marker":"[21]"},{"why":"Supplies the product-method direct and indirect effect decomposition that the pseudo-value pipeline reuses.","marker":"[24]"},{"why":"Provides the general pseudo-observation framework connecting jackknife values to regression models.","marker":"[27]"},{"why":"Gives the counting-process estimators (Kaplan-Meier and Aalen-Johansen) used to construct the pseudo-values.","marker":"[28]"},{"why":"Documents the mediation software that accepts the pseudo-values as a linear outcome, enabling the simplified workflow.","marker":"[45]"}],"fun_headline_variants":["Pseudo-values turn survival mediation into linear regression","Survival mediation simplified: use pseudo-values","Linear regression for survival mediation via pseudo-values","Skip the hazard ratio: pseudo-values for survival mediation","Pseudo-values: a simpler path to survival mediation"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The approach assumes the mediator model and the pseudo-value outcome model are both correctly specified as linear with no treatment–mediator interaction, and that every mediator–outcome confounder is measured and included; the simulations only exercise this exact structure.","fun_headline_variants_meta":{"raw":{"variants":["Pseudo-values turn survival mediation into linear regression","Survival mediation simplified: use pseudo-values","Linear regression for survival mediation via pseudo-values","Skip the hazard ratio: pseudo-values for survival mediation","Pseudo-values: a simpler path to survival mediation"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000718,"raw_usage":{"total_tokens":3251,"prompt_tokens":1000,"completion_tokens":2251,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":616,"completion_tokens_details":{"reasoning_tokens":2180}},"tokens_in":616,"tokens_out":2251,"duration_ms":16119,"temperature":1.0,"reasoning_tokens":2180,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-12T12:00:05.762484+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Generate data with a treatment-by-mediator interaction, for example a hazard $\\lambda = \\exp(\\beta_0 + A\\beta_A + A\\beta_{AM}M + M\\beta_M)$, compute the true natural indirect effect by numerical integration over the mediator, and compare it with the product $\\alpha_A\\beta_M$ from the paper's pipeline. A systematic discrepancy would show that the linear no-interaction models are load-bearing rather than a convenience.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Introduces pseudo-value regression, the foundation for treating censored survival functionals as continuous outcomes."},{"cited_title":"K., Syriopoulou, E","cited_arxiv_id":null,"evidence_quote":"Extends pseudo-values to causal inference, the lineage the paper builds on for mediation."},{"cited_title":"Methods for causal mediation analysis with applications in HIV and cardiores- piratory fitnessPhD thesis (2022)","cited_arxiv_id":null,"evidence_quote":"Prior thesis work applying pseudo-values to mediation of restricted mean survival time, which this paper extends to survival probabilities and cumulative incidence."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the product-method direct and indirect effect decomposition that the pseudo-value pipeline reuses."},{"cited_title":"& Perme, M","cited_arxiv_id":null,"evidence_quote":"Provides the general pseudo-observation framework connecting jackknife values to regression models."},{"cited_title":"& Keiding, N.Statistical Models Based on Counting Pro- cesses 1st ed","cited_arxiv_id":null,"evidence_quote":"Gives the counting-process estimators (Kaplan-Meier and Aalen-Johansen) used to construct the pseudo-values."},{"cited_title":"A., VanderWeele, T","cited_arxiv_id":null,"evidence_quote":"Documents the mediation software that accepts the pseudo-values as a linear outcome, enabling the simplified workflow."}],"review_version":1}