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REVIEW 3 major objections 5 minor 47 references

Estimating Misreporting in the Presence of Genuine Modification: A Causal Perspective

T0 review · 3 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read This paper proves the misreporting rate is identifiable from the gap between nominal and true causal effects of a feature on its downstream outcome, with no access to the true feature.

desk verdict Clean identification argument and a smart negative control, but Assumption 4 carries more weight than the paper acknowledges and the real-data evidence is indirect. read the letter →

arxiv 2505.23954 v1 pith:VW2HYOLY submitted 2025-05-29 cs.LG

Dylan Zapzalka , Trenton Chang , Lindsay Warrenburg , Sae-Hwan Park , Daniel K. Shenfeld , Ravi B. Parikh , Jenna Wiens , Maggie Makar This is my paper
classification cs.LG
keywords misreportingratecausaleffectidentificationstrategicclassificationMedicareAdvantageupcodingriskadjustment
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper claims that the average rate at which agents lie about a binary feature can be estimated exactly, even when agents also genuinely change that feature. The central formula equates the misreporting rate P_a(X* = 0 | X = 1) with the ratio (τ'_a − τ_a)/δ'_a, where τ_a is the apparent causal effect of the reported feature on a downstream outcome, τ'_a is the true causal effect of the underlying feature transported from a clean dataset, and δ'_a is the true effect among the group without the genuine feature. The identification works because genuine modification changes downstream outcomes while misreporting does not. If correct, the result turns 'upcoding' and similar gaming behaviors into quantities measurable from two datasets, without ever observing the true feature.

What carries the argument

The load-bearing object is the ratio identity MR_a = (τ'_a − τ_a)/δ'_a, operationalized as the Causal Misreporting Estimator (CMRE). The three ingredients are: τ_a, the nominal average causal effect of the reported feature X on the outcome Y among the reported group (computed from manipulated data); τ'_a, the true average causal effect of the unobserved feature X* on Y, learned from unmanipulated data and averaged over the same reported group's confounder distribution; and δ'_a, that same true effect averaged over the X* = 0 group that could be misreported. The mechanism is the descendant asymmetry: genuine modification alters Y through X*, while misreporting alters only X, leaving Y untouched — so the gap between nominal and true effects is exactly the misreporting rate times the effect on the misreported group.

What would settle it

Audit a random sample of agents to obtain the true feature X* and the actual misreporting rate, then compare the CMRE estimate; the method is refuted if the discrepancy grows in settings where the conditional treatment effect of X* on Y is deliberately made different between the manipulated and unmanipulated populations. A simpler check: compute the MR for the same agent using two different downstream outcomes with large δ'_a; if the two estimates disagree beyond sampling error, the identifying assumptions fail.

Watch

Extended reading notes

Core claim

Under Assumptions 1–4, the paper proves Theorem 1: for δ'_a ≠ 0, the misreporting rate P_a(X* = 0 | X = 1) is identifiable from two datasets and equals (τ'_a − τ_a)/δ'_a. The proof shows that the nominal effect τ_a of the reported X on the descendant Y decomposes into the true effect τ'_a minus the misreporting rate times the true effect δ'_a on the misreported group; this decomposition relies on the fact that misreported features have no causal effect on descendants, so any discrepancy between nominal and true effects is attributable solely to lying. Assumption 4, which posits that conditional treatment effects of X* on Y are identical across the manipulated and unmanipulated populations, allows replacing the unobservable τ*_a and δ*_a with τ'_a and δ'_a estimated from clean data. The paper further derives the asymptotic variance of the estimator (Theorem 2), showing that the variance grows without bound as δ'_a approaches zero.

Load-bearing premise

The load-bearing premise is that the conditional effect of the true feature on the outcome is identical in the potentially-misreporting population and the clean comparison population; if genuine modification by agents changes how the true feature affects the outcome, the estimate is biased.

Editorial extensions

If this is right

  • A decision maker can estimate each agent's average misreporting rate per feature using only the manipulated dataset plus an unmanipulated dataset (e.g., pre-deployment or government data), with no access to true features or audit labels.
  • Among available downstream variables, the one with the largest causal effect δ'_a on the outcome should be used; the variance analysis shows estimates become unstable as δ'_a approaches zero.
  • The identifiability of P_a(X* = 0 | X = 1) extends directly to other estimands: the false positive rate P_a(X = 1 | X* = 0) and the marginal difference P_a(X = 1) − P_a(X* = 1) are also identifiable.
  • Empirically, the method reproduces the expected pattern in Medicare Advantage: non-payment HCCs (no incentive to lie) have misreporting rates indistinguishable from zero, while payment HCCs show significantly positive rates, whereas baseline methods give implausible estimates.
  • The method applies without change to settings with selection bias, unobserved confounding between agent and outcome, or mediator-based genuine modification, per the DAGs in Appendix A.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • A natural next use is triage: run CMRE on all agents to produce a misreporting rate per feature, then target expensive manual audits only at agents whose estimated rate is high, using the estimate as a cheap prior for where to look.
  • The same ratio identity could be combined with sensitivity analysis for unobserved confounding; the authors flag no-unmeasured-confounding as a limitation, but existing bounds on treatment effects could turn the point estimate into an interval.
  • A falsifiable consistency check within a single application would compute the MR using two different downstream outcomes Y1 and Y2; if the causal assumptions hold and both effects are nonzero, the point estimates should agree, giving a data-driven diagnostic for Assumption 4.
  • The insight may generalize beyond binary features to multivalued or continuous reports by aggregating over thresholds, though the paper only treats binary X.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 5 minor

Summary. The paper proposes a causal estimator for the rate at which strategic agents misreport a binary feature X* (the misreporting rate, MR = P_a(X*=0|X=1)) when the true feature is unobserved, in settings where agents may also genuinely modify the feature. The key idea is that genuine modification changes the causal descendants of X*, whereas misreporting of X does not affect the downstream outcome Y. Under Assumptions 1-4, the paper proves in Theorem 1 that MR = (τ'_a - τ_a)/δ'_a, where τ_a is the nominal effect of reported X on Y in the manipulated data, τ'_a is the true effect of X* on Y transported from unmanipulated data, and δ'_a is the true effect for the X*=0 group. The paper also provides an asymptotic variance formula (Theorem 2) and validates the method on a semi-synthetic loan-fraud simulation and on Medicare claims data, where the estimator is used to compare misreporting of payment versus nonpayment HCCs.

Significance. If the identification result holds, the paper offers a useful new tool for auditing and strategic classification: it estimates an aggregate misreporting rate without observing true features and without per-agent audits, using only a manipulated dataset and an unmanipulated dataset. The causal framing is elegant, and the paper gives a formal identifiability proof, a variance characterization that guides feature choice, and extensive semi-synthetic experiments with several baselines. The proof of Theorem 1 is algebraically sound under the stated assumptions, and the paper is honest about the need for no unobserved confounding. However, the practical value depends critically on Assumption 4 (transportability of conditional average treatment effects from the unmanipulated to the manipulated population), which is not validated in the real-data demonstration; the Medicare analysis also lacks ground truth and uses post-hoc selection on the very quantities entering the estimator. These issues do not invalidate the theoretical core but do limit the strength of the empirical claims.

major comments (3)
  1. [Section 3 (Assumption 4); Section 4.1 (Theorem 1); Section 5.2] Assumption 4 is the only bridge that replaces the unidentifiable τ*_a and δ*_a with the identifiable τ'_a and δ'_a in the proof of Theorem 1 (Appendix B.2). In the Medicare application, D* is Traditional Medicare stayers and D is switchers to private insurers; these populations differ in care and health trajectories, and the genuine modification that the method is designed to accommodate can itself change the conditional effect of an HCC on mortality. The nonpayment-HCC negative control in §5.2/Figure 3 tests the full estimator on HCCs with no payment incentive; it does not validate Assumption 4 for the payment HCCs, which are precisely the ones for which modification incentives exist. Please add a sensitivity analysis (e.g., bounds on MR as a function of the degree of violation of Assumption 4) or direct evidence that the relevant CATEs transport from TM stayers to MA switchers, and state plainly that the Medicare point estimates are conditional on untestable transportability.
  2. [Section 4.1 (Lemma 1); Appendix B.1-B.2] The proofs use an unstated random-misreporting assumption: in Step 2 of Lemma 1 (Appendix B.1) and in the proof of Theorem 1 (Appendix B.2), P_a(C|X*=0,X=1) is replaced by P_a(C|X*=0), which requires C⊥X|X*,A. The text states this informally ('the misreported group will be a random sample of the group where X*=0') but it is not listed among Assumptions 1-4 and is not defended in the Medicare application, where upcoding decisions may depend on enrollee demographics and prior HCCs. If misreporting is targeted based on C, the equality fails and the estimator is biased; please state this assumption explicitly and discuss its plausibility, or relax it.
  3. [Section 5.2; Tables 1-2] The real-data demonstration has no ground truth, and the HCC selection rule is applied after estimating the same quantities that enter the estimator: only HCCs with at least 1% prevalence and an estimated causal effect δ' > 0.1 are reported (Section 5.2 and Tables 1-2). This post-hoc selection is not accounted for in the bootstrap confidence intervals, so the 'sanity check' for nonpayment HCCs is not a falsifiable validation of the method. Please report the full set of HCCs (or pre-specify the selection rule) and explicitly frame the Medicare results as assumption-dependent estimates rather than measured misreporting rates.
minor comments (5)
  1. [Appendix C, Corollary A2] The statement 'P_a(X=1|X*=0) = (τ'_a - τ_a)/δ'_a × P_a(X=1)' is algebraically inconsistent with the proof, which derives a ratio involving P_a(X=0) + P_a(X=1,X*=0); please correct the stated formula.
  2. [Throughout] There are several typos ('Defnition', 'rearanging', 'maximume', 'eduction'); please proofread the manuscript carefully.
  3. [Theorem 2] Theorem 2 assumes N=M=n, but the Medicare experiment uses very different sample sizes for D and D* (868,255 stayers versus 166,539 switchers); please clarify whether the variance formula is intended for unequal sample sizes or note that it is a simplification.
  4. [Section 5.1 and Appendix E.4] The description of the OC-SVM baseline is inconsistent: Section 5.1 says it is trained on D* where X*=1, while Appendix E.4 says it is trained on (Y,C) from D*_1; please make the descriptions consistent.
  5. [Figure 3 caption] The caption refers to a vertical dashed line separating nonpayment and payment HCCs, but the left panel only shows the four HCC labels; please make the figure and legend self-contained.

Circularity Check

0 steps flagged · score 2.0 of 10

No circular derivation: Theorem 1 follows from Lemma 1 plus the explicit Assumption 4 (CATE invariance), and no fitted parameter is relabeled as a prediction; the only self-citation (Chang et al.) is in Related Work and is not load-bearing.

full rationale

The paper's central identification result, Theorem 1, is not equivalent to its inputs by construction. Lemma 1 derives MR = (tau*_a - tau_a)/delta*_a from the definitions of TAFR, NAFR, and TAFM, the DAG conditional independences, and Assumptions 1-3, via algebraic decomposition of tau_a. Theorem 1 then replaces tau*_a and delta*_a by tau'_a and delta'_a using Assumption 4, which states conditional average treatment effects of X* on Y are equal in P_a and P*. This is an identification assumption, not a circular reduction: the estimand P_a(X*=0|X=1) does not appear in the definition of tau'_a, tau_a, or delta'_a, and those quantities are separately estimable from D and D*. The proof also uses the DAG implication P_a(C|X=0)=P_a(C|X*=0), which follows from Assumption 1 and conditional independence, not from the target result. No parameter is fit to a subset of the target and then renamed a prediction; the semi-synthetic experiments use simulated ground truth, and the Medicare nonpayment-HCC comparison is an external sanity check. The only overlap with prior work by the same authors is the citation of Chang et al. [5] in Related Work, which is descriptive and not used as evidence for any theorem or estimator. The untestability and plausible violation of Assumption 4 in the Medicare application is a validity and robustness concern, not a circularity; the paper itself lists no-unmeasured-confounding as a limitation, and the negative control for nonpayment HCCs does not isolate Assumption 4 by itself. Accordingly, the derivation chain is self-contained apart from a minor, non-load-bearing self-citation, giving score 2.

Assumptions & free parameters 3 free parameters · 6 assumptions · 0 invented entities

The central claim rests on four untestable domain assumptions, especially Assumption 4 (CATE invariance across populations). No new entities are introduced. The simulation and baseline hyperparameters are experimental knobs rather than parameters of the identifiability theorem.

free parameters (3)
  • Simulation misreporting probability mu = picked to target MR (default 0.2)
    In the semi-synthetic loan experiments, mu controls the true misreporting rate; it is a simulation knob, not a parameter of the estimator.
  • XGBoost hyperparameters = learning rate 0.3, max depth 6, L2 reg 1
    Default hyperparameters used for causal effect nuisance models in CMRE and NDEE; chosen by hand, not fitted to the estimand.
  • OC-SVM hyperparameters = nu=0.01, gamma=0.1
    Baseline hyperparameters chosen for the one-class SVM anomaly detector; not central to the identifiability result.
assumptions (6)
  • domain assumption Assumption 1 (Optimal Misreporting): agents report X=1 whenever X*=1, and misreporting only flips X*=0 to X=1.
    Used to conclude X=0 implies X*=0 and to decompose tau_a; central to the proof of Lemma 1 and Theorem 1.
  • domain assumption Assumption 2 (Useful Modifications): agents may only misreport or genuinely modify X*, not other features.
    Restricts the manipulation model so that the causal asymmetry between X and X* is well defined.
  • domain assumption Assumption 3 (No unmeasured confounding, overlap, consistency): Y(0), Y(1) are independent of X* given C, and positivity holds in both populations.
    Standard causal inference assumptions needed to identify conditional average treatment effects from D and D*.
  • domain assumption Assumption 4 (CATE invariance): E_Pa[Y(1)-Y(0)|C=c] = E_P*[Y(1)-Y(0)|C=c] for all c and a.
    This transports conditional causal effects from the unmanipulated population to the manipulated population; if violated, the estimator is biased.
  • domain assumption C is independent of X given X* and A (misreporting is independent of confounders once the true feature and agent are fixed).
    Implied by the DAGs in Figure 4; used in the proof to equate Pa(C|X=0) with Pa(C|X*=0) and to factor the misreporting rate.
  • domain assumption X* and X are binary.
    The proof and estimands are stated for binary features; continuous features would require a different decomposition.

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Pith. "Pith review of Estimating Misreporting in the Presence of Genuine Modification: A Causal Perspective." pith.science (2026). https://pith.science/paper/VW2HYOLY

@misc{pith2026250523954,
  author       = {Pith},
  title        = {Pith review of: Estimating Misreporting in the Presence of Genuine Modification: A Causal Perspective},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/VW2HYOLY}},
  note         = {Machine review of arXiv:2505.23954}
}
read the original abstract

In settings where ML models are used to inform the allocation of resources, agents affected by the allocation decisions might have an incentive to strategically change their features to secure better outcomes. While prior work has studied strategic responses broadly, disentangling misreporting from genuine modification remains a fundamental challenge. In this paper, we propose a causally-motivated approach to identify and quantify how much an agent misreports on average by distinguishing deceptive changes in their features from genuine modification. Our key insight is that, unlike genuine modification, misreported features do not causally affect downstream variables (i.e., causal descendants). We exploit this asymmetry by comparing the causal effect of misreported features on their causal descendants as derived from manipulated datasets against those from unmanipulated datasets. We formally prove identifiability of the misreporting rate and characterize the variance of our estimator. We empirically validate our theoretical results using a semi-synthetic and real Medicare dataset with misreported data, demonstrating that our approach can be employed to identify misreporting in real-world scenarios.

Figures

Figures reproduced from arXiv: 2505.23954 by the authors.

Figure 1
Figure 1. Causal DAGs that describe the setting of this paper. White nodes are unobserved whereas [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Results from the loan fraud dataset. The [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. For each plot, the y-axis represents the estimated MR for an HCC code and the error bars represent a 95% confidence interval. (Left) The x-axis has two nonpayment HCCs (HCC117 and HCC50) and two payment HCCs (HCC21 and HCC8). Our approach (CMRE) has a MR estimate close to zero for nonpayment HCCs and significantly above zero for the payment HCCs, which aligns with what is expected in current literature. Baselines th… view at source ↗
Figures from the paper (7 more)
Figure 4
Figure 4. Figure 4: Causal DAGs that describe the setting of this paper. White nodes are unobserved, whereas [PITH_FULL_IMAGE:figures/full_fig_p013_4.png]
Figure 5
Figure 5. Figure 5: presents our Medicare experiments including the results from the OC-SVM estimator. The estimated misreporting rate for the OC-SVM is consistent across all HCC codes and agents, reflecting the results from our semi-synthetic loan dataset experiments. This suggests that …
Figure 6
Figure 6. Figure 6: The x-axis is the causal effect of A on X∗ (left), causal effect of X∗ on Y (middle), and the misreporting rate (right). The y-axis is the estimated misreporting rate. Dashed lines represent the true misreporting rate and the error bars represent the standard deviation…
Figure 7
Figure 7. Figure 7: The x-axis is the direct causal effect of A on X∗ (left), causal effect of X∗ on Y (middle), and the misreporting rate (right). The y-axis is the estimated misreporting rate. Dashed lines represent the true misreporting rate and the error bars represent the standard de…
Figure 8
Figure 8. Figure 8: The x-axis is the direct causal effect of A on X∗ (left), causal effect of X∗ on Y (middle), and the misreporting rate (right). The y-axis is the estimated misreporting rate. Dashed lines represent the true misreporting rate and the error bars represent the standard de…
Figure 9
Figure 9. Figure 9: The x-axis is the direct causal effect of A on X∗ (left), causal effect of X∗ on Y (middle), and the misreporting rate (right). The y-axis is the estimated misreporting rate. Dashed lines represent the true misreporting rate and the error bars represent the standard de…
Figure 10
Figure 10. Figure 10: The x-axis is the direct causal effect of A on X∗ (left), causal effect of X∗ on Y (middle), and the misreporting rate (right). The y-axis is the estimated misreporting rate. Dashed lines represent the true misreporting rate and the error bars represent the standard d…

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Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.