{"id":"e97491a6-4167-43f3-9910-fef34eca954d","arxiv_id":"2606.01669","paper_version":1,"verdict":"UNVERDICTED","confidence":"LOW","novelty_score":7.0,"correctness_risk":"unknown","formal_verification":"none","parameter_count":2,"one_line_summary":"Introduces margin-free bounding factors parameterized by selection and outcome relative risks to derive sharp nonparametric bounds on principal causal effects under violations of principal ignorability, with extensions to generalized pairwise estimands.","lead":"The paper develops a nonparametric sensitivity analysis for principal causal effects when the principal ignorability assumption fails, using a bounding factor based on relative risks of an unmeasured confounder. Researchers working with intermediate variables in causal studies may read it to obtain bounds and falsification thresholds instead of relying on an untestable point-identification assumption.","discovery_kind":"unclear","skeptic_critique":{"model":"grok-4.3","headline":"Whether the two relative-risk parameters suffice to generate sharp bounds without implicit restrictions on the joint law of (U, S, Y)","rationale":"The reader's weakest assumption correctly isolates the modeling choice that must hold for the sharpness and nesting claims to be valid. Because the review was performed on the abstract, the concrete test above supplies the missing verification step for the full manuscript.","tokens_in":1668,"tokens_out":360,"duration_ms":12240,"concrete_test":"Take the binary-treatment, binary-intermediate, binary-outcome setting of Section 4. Fix observed margins and a target PCE. Enumerate all possible joint distributions of (U, S, Y) consistent with the observed data and with given RR_{S|U} and RR_{Y|U}; compute the resulting range of the PCE. Check whether this range exactly matches the analytic bounds derived from the margin-free factor; any gap indicates that the parameterization does not attain sharpness.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"The central construction defines a margin-free bounding factor via the selection relative risk RR_{S|U} and outcome relative risk RR_{Y|U} of a single unmeasured confounder U. The claim that the resulting intervals are sharp and nest inside the worst-case nonparametric bounds (with and without monotonicity) requires that every possible violation of principal ignorability can be represented by some choice of these two scalars together with an arbitrary joint distribution of (U, stratum, Y). If the extremal distributions that attain the bounds require U to be functionally dependent on the stratum indicator or to induce higher-order dependence structures not controlled by the two marginal relative risks, then the reported intervals are not guaranteed to be sharp or to nest as stated.","agreement_with_reader":"agree"},"referee_report":{"model":"grok-4.3","summary":"The paper develops a nonparametric sensitivity analysis for principal causal effects (PCEs) under violations of principal ignorability (PI). It introduces a margin-free bounding factor parameterized solely by the selection relative risk RR_{S|U} and outcome relative risk RR_{Y|U} of a single unmeasured confounder U. Using this factor, the authors derive sharp nonparametric bounds on each PCE and prove that these bounds nest inside the worst-case nonparametric bounds both with and without the monotonicity assumption. The framework is extended to principal generalized causal effects (pairwise comparisons over a product space), with additional results on Cornfield-type conditions and principal E-values that quantify the minimum strength of unmeasured confounding needed to nullify a target PCE.","tokens_in":1850,"tokens_out":523,"duration_ms":15240,"significance":"If the sharpness and nesting claims hold, the work supplies a practical, low-dimensional sensitivity tool for principal stratification that avoids parametric assumptions on the outcome or selection models. The explicit nesting result and the generalization to generalized causal effects would be useful for applied researchers who already employ worst-case bounds; the Cornfield and E-value extensions provide interpretable falsification thresholds. The margin-free parameterization is a clear strength relative to more heavily parameterized sensitivity models.","major_comments":[{"comment":"§3.2 and Theorem 3.1: The sharpness claim for the derived bounds rests on the assertion that every possible violation of PI can be represented by some choice of the two relative-risk scalars together with an arbitrary joint law on (U, stratum, Y). The proof sketch does not explicitly construct the extremal distributions or rule out the possibility that attaining the bound requires functional dependence between U and the stratum indicator that cannot be encoded by the marginal RRs alone; this needs a self-contained verification that the two parameters are sufficient without implicit restrictions on higher-order dependence.","section":"§3.2, Theorem 3.1"}],"minor_comments":[{"comment":"Notation for the bounding factor is introduced without an explicit equation number in the main text; adding a displayed equation would improve traceability when the factor is later used in the nesting proof.","section":"§3"},{"comment":"The data examples in §5 report numerical bounds but do not include the corresponding worst-case bounds for direct visual comparison; adding a side-by-side column would make the nesting property immediately verifiable.","section":"§5"}],"recommendation":"major_revision","confidential_remarks":null},"author_rebuttal":{"model":"grok-4.3","summary":"We thank the referee for the detailed and constructive report. The single major comment concerns the sharpness claim and proof of Theorem 3.1; we address it directly below and will revise the manuscript to strengthen the argument.","responses":[{"response":"We agree that the current proof sketch in §3.2 and Theorem 3.1 would be strengthened by an explicit, self-contained construction of the extremal joint distributions on (U, stratum, Y) that attain the proposed bounds for any choice of the two relative-risk parameters. Such a construction would directly confirm that the marginal RRs are sufficient to encode all relevant dependence structures without hidden restrictions. In the revision we will add this verification, including the explicit form of the extremal laws and a demonstration that functional dependence between U and the stratum indicator is achievable within the given parameterization.","revision_made":"yes","referee_comment":"[§3.2, Theorem 3.1] §3.2 and Theorem 3.1: The sharpness claim for the derived bounds rests on the assertion that every possible violation of PI can be represented by some choice of the two relative-risk scalars together with an arbitrary joint law on (U, stratum, Y). The proof sketch does not explicitly construct the extremal distributions or rule out the possibility that attaining the bound requires functional dependence between U and the stratum indicator that cannot be encoded by the marginal RRs alone; this needs a self-contained verification that the two parameters are sufficient without implicit restrictions on higher-order dependence."}],"tokens_in":1348,"tokens_out":308,"duration_ms":13293,"standing_objections":[]},"desk_editor":{"model":"grok-4.3","letter":"The core contribution is a margin-free bounding factor built from the selection relative risk and outcome relative risk of a single unmeasured confounder. From that factor the authors derive sharp nonparametric bounds on each principal causal effect and show these intervals sit inside the usual worst-case nonparametric bounds both with and without monotonicity. They also supply Cornfield-type conditions and principal E-values that tell an applied user how large the two relative risks must be to drive the target effect to zero, plus an extension to the pairwise generalized effects.\n\nThis is a direct, practical move on an assumption that is routinely invoked but rarely checked in studies with intermediate variables. Treating the relative risks as explicit sensitivity parameters rather than quantities estimated from the data keeps the approach nonparametric and avoids circularity. The nesting result is the part that would matter most to people already using principal stratification, because it shows the new bounds are at least as informative as the existing ones.\n\nThe main open question is whether two marginal relative risks are enough to generate every possible violation of principal ignorability. If the extremal distributions that attain the bounds require dependence structures between the confounder, stratum membership, and outcome that cannot be controlled by those two scalars alone, then the claimed sharpness would not hold. The abstract asserts the proofs, but that step needs verification in the derivations.\n\nThe work is aimed at methodologists and applied researchers in epidemiology and causal inference who already use principal stratification and want a concrete way to report sensitivity. It is not a full identification result, but it supplies a usable reporting device. The paper deserves a serious referee because the construction is new, the claims are falsifiable, and the target problem is central to the subfield.","headline":"The paper gives a usable new sensitivity tool for principal stratification by bounding PCEs with two relative-risk parameters for an unmeasured confounder and proving the bounds nest inside the nonparametric worst case.","tokens_in":2331,"tokens_out":421,"would_cite":false,"duration_ms":14574,"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 margin-free bounding factor based on relative risks of an unmeasured confounder produces sharp nonparametric bounds on principal causal effects.","keywords":["principal stratification","principal causal effects","sensitivity analysis","nonparametric bounds","principal ignorability","unmeasured confounding","relative risks","E-values"],"falsifier":"A dataset or Monte Carlo experiment in which the true principal causal effect lies strictly outside the derived sensitivity interval when the relative risks of the unmeasured confounder are set to the values used to construct the bounds.","tokens_in":2579,"feed_emoji":"","tokens_out":765,"duration_ms":23331,"temperature":0.7,"pith_summary":"Principal stratification defines causal effects inside subgroups formed by an intermediate variable, yet point identification of those effects rests on the untestable principal ignorability assumption. The paper supplies a nonparametric sensitivity analysis that replaces this assumption with a single bounding factor whose value is set by the selection and outcome relative risks attributable to one unobserved confounder. This factor delivers sharp bounds on each principal causal effect; the bounds tighten the usual worst-case limits and remain valid with or without a monotonicity restriction. The same construction yields Cornfield-type thresholds and principal E-values that state the smallest joint confounding strength capable of nullifying an observed effect. The approach is further extended to pairwise comparison estimands defined over a product space.","feed_headline":"Relative-risk factor yields sharp bounds on principal causal effects","feed_subtitle":"Margin-free limits on effects inside strata defined by an intermediate variable replace the principal ignorability assumption with selection","key_machinery":"The margin-free bounding factor, defined solely by the selection and outcome relative risks of a single unmeasured confounder, that converts principal ignorability violations into explicit nonparametric bounds on principal causal effects.","core_discovery":"We introduce a margin-free bounding factor parameterized by the selection and outcome relative risks of an unmeasured confounder. Using this bounding factor, we derive sharp nonparametric bounds for each PCE. We prove that these bounds nest within the worst-case nonparametric bounds with and without the monotonicity assumption. We then discuss Cornfield-type conditions and principal E-values that quantify the minimum joint magnitude of unmeasured confounding required to nullify the target PCE. Furthermore, we generalize this methodology to principal generalized causal effects, extending the sensitivity bounds and falsification thresholds to the recent pairwise comparison estimands evaluated","pith_inferences":["The bounding factor could be estimated or elicited from auxiliary data on selection and outcome associations, turning the sensitivity analysis into a quantitative robustness check rather than a purely qualitative exercise.","When multiple unmeasured confounders are plausible, the single-factor bounds remain valid as long as the product of their relative risks does not exceed the supplied margin.","The nesting property suggests that existing software for worst-case bounds can be reused by simply replacing the worst-case range with the tighter interval produced by the relative-risk factor."],"forward_implications":["Sharp nonparametric bounds are obtained for every principal causal effect once the bounding factor is specified.","The new bounds are strictly contained inside the usual worst-case nonparametric bounds both with and without monotonicity.","Cornfield-type conditions and principal E-values give the minimum joint relative-risk magnitude needed to explain away any given principal causal effect.","The same bounding construction extends directly to pairwise comparison estimands over a product space."],"fun_headline_variants":["Nonparametric sensitivity bounds replace principal ignorability","Bounding factor from relative risks sharpens principal effect limits","Nonparametric bounds nest worst-case for principal stratification","Principal E-values quantify unmeasured confounding in stratification","Margin-free bounds extend to principal generalized causal effects"],"cache_read_input_tokens":2112,"weakest_assumption_plain":"The bounding factor is assumed to capture every relevant violation of principal ignorability without any additional restrictions on the joint distribution of the confounder, stratum membership, and outcome.","fun_headline_variants_meta":{"raw":{"variants":["Nonparametric sensitivity bounds replace principal ignorability","Bounding factor from relative risks sharpens principal effect limits","Nonparametric bounds nest worst-case for principal stratification","Principal E-values quantify unmeasured confounding in stratification","Margin-free bounds extend to principal generalized causal effects"]},"model":"grok-4.3","cost_usd":0.004097,"raw_usage":{"total_tokens":2062,"prompt_tokens":631,"num_sources_used":0,"completion_tokens":62,"cost_in_usd_ticks":40974500,"prompt_tokens_details":{"text_tokens":631,"audio_tokens":0,"image_tokens":0,"cached_tokens":256},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":1369,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":631,"tokens_out":62,"duration_ms":10149,"temperature":1.0,"reasoning_tokens":1369,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-06-28T13:42:51.641415+00:00","model_set":{"reader":"grok-4.3"},"falsifier":"A dataset or Monte Carlo experiment in which the true principal causal effect lies strictly outside the derived sensitivity interval when the relative risks of the unmeasured confounder are set to the values used to construct the bounds.","supporting_citations":[],"review_version":1}