{"id":"c2e8a338-76e2-4904-addb-8e68a6267172","arxiv_id":"2412.09786","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":2,"one_line_summary":"A new nonparametric testing procedure uses linear contrasts and one-step bias correction to test whether counterfactual survival probabilities are constant across a continuous exposure under right censoring.","lead":"The authors propose a class of nonparametric tests for whether a continuous dose or biomarker changes the chance of surviving past a set time when outcomes are right-censored. The tests adjust for confounders with machine learning and are applied to HIV prevention trial data.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The EIF in Theorem 2 and the EIF derived in the supplementary proof differ by a non-negligible constant term, and the supplementary version is not mean-zero; because the one-step estimator and Monte Carlo null distribution inherit D_P, the proof of Theorem 3 is internally inconsistent until this…","rationale":"I read the main text and supplement. The reader's weakest_assumption was B1, but I see a more fundamental and more easily checkable problem: the influence function that Theorem 3's expansion is built on is stated one way in Theorem 2 and derived differently in the supplement. This makes the proof of the central claim non-self-consistent. If a corrected derivation reproduces Theorem 2, the remaining B1-B3 verification for the recommended machine-learning nuisance estimators is still needed and the CONDITIONAL verdict stands. If the derivation instead supports the supplementary formula, then D_n and the Gaussian process covariance are wrong and Theorem 3 is not proved for the implemented estimator. In either case the reader's conditional acceptance is appropriate; my concern sharpens the condition rather than moving the verdict.","tokens_in":20585,"tokens_out":15369,"duration_ms":172041,"concrete_test":"Implement a small parametric submodel (e.g., A|W ~ Normal, T|A,W ~ Exponential with linear log-hazard, independent censoring), and use finite differences to estimate the Gateaux derivative of ψ_P,t(h) along several score directions s. Compute E[D_Thm2 s] and E[D_supp s] and also E[D_Thm2], E[D_supp]. If E[D_supp]≠0 or E[D_supp s] fails to match the numerical derivative, the supplementary EIF is invalid; if E[D_Thm2]≠0 or fails to match, Theorem 2 itself must be corrected. Re-running this check would settle which D_P should appear in Theorem 3 and in the implemented D_n.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Theorem 3 is the load-bearing result: it supplies the uniform expansion ψ†_n,t(h)−ψ_P,t(h)=n^{-1}Σ D_P(O_i;h)+r_n(h), sup_h|r_n|=o_p(n^{-1/2}), and the weak convergence that justifies the Monte Carlo p-values. Therefore D_P must be the true efficient influence function. Comparing Theorem 2 with the supplementary proof, the displayed D_P differs in the final constant term: Theorem 2 has −2 E_P{h(A)θbar_A(t)}, while the supplementary derivation ends with −E_P[h(A)]E_P[θ_A(t)]. These are not generally equal. More seriously, taking the expectation of the supplementary expression gives 2 Cov_P(h(A),θ_A(t))−E_P[h(A)]E_P[θ_A(t)], which is not zero in general, so that expression cannot be an influence function. Theorem 2's version does have mean zero. At least one of the two formulas is wrong, and the one-step estimator D_n in Eq. (5), the covariance estimator in §5.3, and the proof of Theorem 3 are tied to these objects. The reader's B1 concern is also valid, but it is secondary: if D_P is not pinned down correctly, the Donsker and rate conditions cannot even be stated unambiguously.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper develops a nonparametric hypothesis-testing framework for whether the counterfactual survival probability at a fixed time point varies with a continuous exposure when the outcome is right-censored. The approach reformulates the null in terms of linear contrasts ψ_P,t(h) of the centered dose–response curve, establishes pathwise differentiability of these contrasts, constructs a one-step estimator with a uniform asymptotic linear representation over a function class H, and derives a Gaussian-process null distribution used for Monte Carlo p-values. The methodology is illustrated with simulations and an application to the AMP HIV prevention trials. The paper is an extension of the authors' earlier work on continuous exposures with uncensored outcomes to the censored-data setting.","tokens_in":20801,"tokens_out":10887,"duration_ms":99651,"significance":"If the central theorem is correct, the paper offers a principled way to test for exposure effects on survival across a continuum without parametric assumptions, which is valuable for infectious-disease biomarker studies. The paper provides a clear target estimand, an explicit influence-function construction, a careful discussion of function classes H, and simulation evidence. The proof strategy follows the one-step estimation route, and the application to AMP data is relevant. However, the manuscript currently has a serious inconsistency in the influence-function derivation and relies on unverified regularity conditions for machine-learning nuisance estimators; these must be resolved before the theoretical claims can be accepted.","major_comments":[{"comment":"The efficient influence function D_P stated in Theorem 2 differs from the expression derived in the supplementary proof by a constant term: Theorem 2 contains −2E_P{h(A)θ̄_A^P(t)}, whereas the supplementary derivation ends with −E_P[h(A)]E_P[θ_A^P(t)]. These two quantities are not generally equal. Moreover, the supplementary expression is not mean-zero; its expectation is 2Cov_P(h(A), θ_A^P(t)) − E_P[h(A)]E_P[θ_A^P(t)] in general, which is impossible for an influence function. Since the one-step estimator in Eq. (5), the covariance estimator in §5.3, and the proof of Theorem 3 are all stated in terms of D_P, the proof of Theorem 3 is internally inconsistent until this discrepancy is resolved.","section":"Theorem 2 and Supplementary Materials, Proof of Theorem 2"},{"comment":"Theorem 3 rests on conditions (B1)-(B3), which require the estimated efficient influence functions to fall in a P-Donsker class and the nuisance estimators to satisfy L2 convergence and a product-rate condition. Section 5.1 recommends survival random forests, survival super learner, and kernel density estimation via the highly adaptive lasso. For these data-adaptive estimators, the paper does not verify or cite results establishing (B1)-(B3); indeed, for such methods the Donsker condition is known to be fragile and may fail. As a consequence, the theoretical guarantee of uniform asymptotic linearity and the resulting Gaussian-process null distribution is not established for the implementations used in the simulations and application. The authors should either prove or cite conditions under which these specific nuisance estimators satisfy (B1)-(B3), or present the theoretical results as conditional on unverified assumptions.","section":"Conditions (B1)-(B3) in §4.1 and nuisance estimators in §5.1"},{"comment":"The abstract and introduction claim the method tests whether the counterfactual survival probability is constant across the full continuous exposure range (H0 in Eq. (1)). However, the test is formally for the relaxed null H̄0 in Eq. (3): sup_{h∈H} |ψ_P,t(h)| = 0 for a chosen class H. As the paper notes, H̄0 may hold while H0 is false. The contribution as stated should be carefully qualified: the proposed test controls type-1 error for the relaxed null and has power only against alternatives detectable by H. The abstract and introduction should be amended to avoid overclaiming the scope of the null hypothesis being tested.","section":"Abstract, Introduction, and Eq. (3) in §3"}],"minor_comments":[{"comment":"The label \"knots Max\" in Figure 1 is unclear; it should be explained that \"Max\" corresponds to κ = n for the class in Eq. (9).","section":"§6, Figure 1"},{"comment":"D_n is called a plug-in estimator for the efficient influence function, but the displayed expression only contains the censoring-adjustment term. The relationship between D_n and the full D_P of Theorem 2 should be clarified, in particular how the remaining terms of D_P are handled by the plug-in component ψ_n,t(h).","section":"§4.1, Eq. (5)"},{"comment":"In the rate calculation for rII_n, the term (n^{-1}Σ_i h(A_i) − E[h(A)])^2 is OP(n^{-1}), not OP(n^{-1/2}); the stated conclusion that the product is oP(n^{-1/2}) still follows, but the displayed rate should be corrected.","section":"Supplementary Materials, proof of Theorem 3, rII_n"},{"comment":"The paper states that the supporting code is available on GitHub, but no repository URL is provided; the authors should include the link.","section":"Data availability"},{"comment":"The claim that for a function θ̄_a^P(t) that changes sign K times, the sign function lies in a class with variation norm bounded by 2K should be justified or accompanied by a reference, as it is used to motivate the choice of H.","section":"§4.2, Eq. (8)"}],"recommendation":"major_revision","confidential_remarks":"The EIF discrepancy between Theorem 2 and the supplementary proof is the most serious issue: if the supplementary version were the true influence function, the one-step estimator would not be asymptotically linear and the Monte Carlo null distribution would be unjustified. The error is likely fixable, but it requires a careful re-derivation of the influence function and of the remainder terms in Theorem 3. The paper is otherwise well-motivated and the simulation study is informative. I would encourage the editor to allow a major revision rather than a rejection, given the potential value of the framework."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague, here's my read on arXiv:2412.09786. The central idea is sound and useful: they take the linear-contrast testing approach from Westling (2022) and Hudson et al. (2023) and adapt it to right-censored survival outcomes with a continuous exposure. That fills a real gap, and the paper is well-written and transparent about the relaxed null over a function class H. The simulation study is thorough, and the AMP application is a nice real-data demonstration. So there is genuine value here.\n\nBut there is a load-bearing problem. The EIF stated in Theorem 2 and the EIF derived in the supplementary proof are different expressions. Theorem 2 has a term -2 E[h(A)θbar_A(t)], while the supplementary ends with -E[h(A)]E[θ_A(t)]. These aren't equivalent. Worse, the supplementary version does not have mean zero in general, so it cannot be an influence function. The one-step estimator in Eq. (5) and the Monte Carlo null distribution are built from this object, so until this is resolved, Theorem 3 and the proposed p-values are not justified. This isn't a nitpick; it's a contradiction between the main text and the appendix.\n\nOther issues are secondary: the abstract claims a test of the full null, but the method only controls the relaxed null over H; that's disclosed later, but the framing should be fixed. The Donsker and rate conditions (B1)-(B3) are not verified for the survival random forest / super learner / HAL density estimators they recommend, which is common in this literature but should be acknowledged. And the AMP analysis uses case-control sampling with known weights, but the paper doesn't say how the test incorporates those weights.\n\nFor peer review: this deserves a serious referee. The idea is important and the execution is mostly careful, but the EIF inconsistency must be fixed before publication. I'd send it out, with a request that the authors reconcile the two derivations and re-check the one-step estimator.","headline":"Useful extension of the linear-contrast testing framework to right-censored survival, but the efficient influence function in the main text and the supplementary proof are inconsistent, so the theoretical core needs repair before this is citable.","tokens_in":21382,"tokens_out":7017,"would_cite":false,"duration_ms":67009,"reading_group":"yes","serious_thinker":"no","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["62G05","62G10","62G20","62N01"],"pacs":[],"model":"deepseek-v4-flash","headline":"This paper develops a class of nonparametric tests for whether the counterfactual survival probability through a fixed time is constant across all levels of a continuous exposure, under right censoring and with machine-learning nuisance…","keywords":["causal inference","continuous exposure","hypothesis testing","nonparametric inference","survival analysis","right censoring","efficient influence function","one-step estimator"],"falsifier":"Run the proposed test in a null simulation where the conditional survival and censoring functions are rough and are estimated by survival random forests with limited data; if the empirical distribution of $\\sup_{h\\in H} n^{1/2}\\psi^\\dagger_{n,t}(h)$ across many datasets does not match the Monte Carlo Gaussian supremum distribution, or if type-1 error stays above the nominal level as the sample size grows, then conditions (B1)-(B3) are failing and the test's validity claim is refuted.","tokens_in":20258,"feed_emoji":"📊","tokens_out":11104,"duration_ms":98030,"temperature":0.7,"pith_summary":"The paper tackles a gap in causal survival analysis: how to test whether the counterfactual probability of surviving past a fixed time is constant across all levels of a continuous exposure, when the outcome is right-censored. The authors show that although the survival curve $\\theta_P^a(t)$ is not pathwise differentiable in a nonparametric model, certain linear contrasts $\\psi_{P,t}(h)$ of it are. They reformulate the null hypothesis as 'all such contrasts are zero' and construct a one-step bias-corrected estimator that is uniformly asymptotically linear over a class of contrast functions. Under regularity conditions, the supremum of the estimated contrasts converges to the supremum of a mean-zero Gaussian process, yielding a nonparametric test with machine-learning nuisance adjustment. A sympathetic reader would care because the test avoids binning continuous exposures and avoids parametric assumptions about exposure or survival models, making it applicable to biomarker-outcome questions like the HIV antibody trials analyzed in the paper.","feed_headline":"Continuous exposure effects on survival get a nonparametric test","feed_subtitle":"A one-step estimator and Gaussian supremum test check whether counterfactual survival is flat across exposure levels.","key_machinery":"The load-bearing object is the linear contrast functional $\\psi_{P,t}(h)$ and its efficient influence function $D_P(O; h)$, which combines the conditional survival curve, the conditional censoring function, and the conditional exposure density. The one-step bias correction adds the empirical mean of the estimated influence function to the plug-in estimator, removing first-order nuisance bias. Uniform convergence over $h\\in H$ is secured by condition (B1), which requires the influence functions to fall in a P-Donsker class (a function class whose empirical process is stochastically bounded) with probability tending to one, together with rate conditions (B2) and (B3) on the nuisance estimators, permitting flexible machine-learning nuisance estimation at slower than $n^{1/2}$ rates. The test statistic is the supremum of the one-step estimator over $H$; under the null it converges to the supremum of a mean-zero Gaussian process whose covariance is the inner product of the influence functions, approximated by Monte Carlo.","core_discovery":"The central claim is that the causal null $\\theta_P^a(t) = E_P[\\theta_P^A(t)]$ for all $a$ can be tested nonparametrically by targeting the function-valued contrast $\\psi_{P,t}(h) = E_P[(\\theta_P^A(t) - E_P[\\theta_P^A(t)])h(A)]$ over a suitably constrained class $H$ of functions $h$. Theorem 2 gives the efficient influence function $D_P(O; h)$ and shows $\\psi_{P,t}(h)$ is pathwise differentiable even though $\\theta_P^a(t)$ is not. The one-step estimator adds the empirical mean of the estimated influence function to a plug-in estimator, and Theorem 3 states that, under Donsker and rate conditions, the estimator is uniformly asymptotically linear: $\\psi^\\dagger_{n,t}(h) - \\psi_{P,t}(h) = n^{-1}\\sum_i D_P(O_i; h) + r_n(h)$ with $\\sup_{h\\in H}|r_n(h)| = o_p(n^{-1/2})$; consequently the process $n^{1/2}(\\psi^\\dagger_{n,t} - \\psi_{P,t})$ over $H$ converges weakly to a mean-zero Gaussian process. The null is tested with $\\Psi^\\dagger_{n,t}(H) = \\sup_{h\\in H}|\\psi^\\dagger_{n,t}(h)|$ compared to Monte Carlo draws from the limiting Gaussian supremum. The paper argues this yields asymptotically valid type-1 error control, and power is determined by whether $\\Psi_{P,t}(H)$ is a norm of the centered curve, for example an $\\ell^1$ or variance norm under monotonicity or bounded-variation constraints.","pith_inferences":["The same linear-contrast construction could be extended to test equality of entire survival curves across exposure levels by taking the supremum over time $t$ as well as $h$, yielding a functional test of stochastic dominance; the paper only treats one fixed time point.","The Donsker condition is the practical bottleneck: an empirical robustness check would compare p-values from provably regular contrast classes (for example, bounded-variation sieves) against those from survival random forest nuisances in a null simulation, to see whether inference is sensitive to nuisance irregularity.","Because the causal assumptions (A2) are unverifiable in observational data, the test is also interpretable as a nonparametric test of the conditional exposure-survival association, which remains meaningful even if causal identification fails.","One could attempt to choose the contrast class $H$ adaptively, for example by maximizing estimated power subject to a Donsker constraint; the paper leaves tuning selection as future work."],"forward_implications":["Under the relaxed null $\\sup_{h\\in H}|\\psi_{P,t}(h)|=0$, the proposed supremum test controls type-1 error asymptotically at the nominal level, for any contrast class $H$ satisfying the Donsker and rate conditions.","For monotone dose-response alternatives, choosing sign-function contrasts makes the power target the probability-weighted $\\ell^1$ norm of the centered counterfactual survival curve; under a variance constraint, the target is its $\\ell^2$ norm.","The method accommodates right censoring and uses flexible machine-learning nuisance estimators for survival, censoring, and exposure density, so it can be applied to observational studies and randomized trials with continuous biomarkers.","Applied to the AMP HIV monoclonal antibody trials, the test yields non-significant p-values across tuning parameters, consistent with a nearly flat estimated counterfactual survival curve across Day-61 VRC01 concentration.","As a corollary of Theorem 3, uniform asymptotic linearity makes possible simultaneous inference on the whole contrast process, not only the supremum statistic."],"supporting_citations":[{"why":"Establishes the linear-contrast testing framework for causal nulls with nondiscrete exposures in uncensored settings, which this paper extends to right-censored survival.","marker":"Westling [2022]"},{"why":"Develops nonparametric inference on the causal dose-response function and the kernel-based conditional density estimator used as a nuisance estimator here.","marker":"Hudson et al. [2023]"},{"why":"Provides the identification result (Theorem 1) and efficient estimation of counterfactual survival curves for discrete exposures, including the survival super learner the paper uses.","marker":"Westling et al. [2024]"},{"why":"Introduces restricted-score-test inference on function-valued parameters, the conceptual basis for testing via linear contrasts rather than pointwise estimates.","marker":"Hudson et al. [2021]"},{"why":"Supplies the one-step bias-correction method that turns the plug-in estimator into a uniformly asymptotically linear estimator.","marker":"Pfanzagl [1982]"},{"why":"Provides the empirical-process and Donsker-class results used to verify uniform asymptotic linearity in Theorem 3.","marker":"van der Vaart [2000]"},{"why":"The highly adaptive lasso used in the kernel density estimator for the exposure nuisance.","marker":"Benkeser and van der Laan [2016]"},{"why":"Survival random forests, one of the candidate nuisance estimators for conditional survival and censoring functions.","marker":"Ishwaran et al. [2008]"}],"fun_headline_variants":["New nonparametric test for survival under continuous treatments","Testing causal null for survival across continuous exposure","Nonparametric method tests if survival is flat over exposure","One-step estimator enables nonparametric causal survival test","Gaussian supremum test for continuous treatment survival effects"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The whole inference rests on an unverified regularity premise: the flexible machine-learning estimators used for survival, censoring, and exposure density must be well-behaved enough (belonging to a suitably regular function class with adequate convergence rates) that the one-step estimator's remainder vanishes uniformly; if those estimators are too erratic, the Gaussian null distribution and Monte Carlo p-values are not justified.","fun_headline_variants_meta":{"raw":{"variants":["New nonparametric test for survival under continuous treatments","Testing causal null for survival across continuous exposure","Nonparametric method tests if survival is flat over exposure","One-step estimator enables nonparametric causal survival test","Gaussian supremum test for continuous treatment survival effects"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000348,"raw_usage":{"total_tokens":2035,"prompt_tokens":1205,"completion_tokens":830,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":821,"completion_tokens_details":{"reasoning_tokens":758}},"tokens_in":821,"tokens_out":830,"duration_ms":8483,"temperature":1.0,"reasoning_tokens":758,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-11T16:44:11.284860+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Run the proposed test in a null simulation where the conditional survival and censoring functions are rough and are estimated by survival random forests with limited data; if the empirical distribution of $\\sup_{h\\in H} n^{1/2}\\psi^\\dagger_{n,t}(h)$ across many datasets does not match the Monte Carlo Gaussian supremum distribution, or if type-1 error stays above the nominal level as the sample size grows, then conditions (B1)-(B3) are failing and the test's validity claim is refuted.","supporting_citations":[{"cited_title":"Nonparametric tests of the causal null with nondiscrete exposures","cited_arxiv_id":null,"evidence_quote":"Establishes the linear-contrast testing framework for causal nulls with nondiscrete exposures in uncensored settings, which this paper extends to right-censored survival."},{"cited_title":"An Approach to Nonparametric Inference on the Causal Dose Response Function","cited_arxiv_id":"2306.07736","evidence_quote":"Develops nonparametric inference on the causal dose-response function and the kernel-based conditional density estimator used as a nuisance estimator here."},{"cited_title":"Inference on function-valued parameters using a restricted score test","cited_arxiv_id":"2105.06646","evidence_quote":"Introduces restricted-score-test inference on function-valued parameters, the conceptual basis for testing via linear contrasts rather than pointwise estimates."},{"cited_title":"Contributions to a general asymptotic statistical theory","cited_arxiv_id":null,"evidence_quote":"Supplies the one-step bias-correction method that turns the plug-in estimator into a uniformly asymptotically linear estimator."},{"cited_title":"Asymptotic statistics, volume 3","cited_arxiv_id":null,"evidence_quote":"Provides the empirical-process and Donsker-class results used to verify uniform asymptotic linearity in Theorem 3."},{"cited_title":"The highly adaptive lasso estimator","cited_arxiv_id":null,"evidence_quote":"The highly adaptive lasso used in the kernel density estimator for the exposure nuisance."}],"review_version":1}