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REVIEW 3 major objections 4 minor 42 references

Assumption-Lean Differential Variance Inference for Heterogeneous Treatment Effect Detection

T0 review · 3 major / 4 minor · reviewed 2026-08-03 · deepseek-v4-flash

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Pith's one-line read This paper shows that a nonzero difference in the variances of potential outcomes under treatment and control is a symptom of heterogeneous treatment effects, and that this difference can be estimated and tested statistically even when the

desk verdict Solid new variance-contrast estimators; but the null result can't 'gauge' homogeneity—the blind spot is not pathological. read the letter →

arxiv 2512.03254 v4 pith:FFQUFVUX submitted 2025-12-02 stat.ME

Philippe A. Boileau , Hani Zaki , Gabriele Lileikyte , Niklas Nielsen , Patrick R. Lawler , Mireille E. Schnitzer This is my paper
classification stat.ME MSC 62G0562G2062P10
keywords treatmenteffectheterogeneitydifferentialvarianceefficientinfluencefunctiondoublyrobustestimationtargetedmaximumlikelihoodconditionalexchangeabilitymeasurementerrorcausalinference
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 homogeneous treatment effect assumption—each patient benefits identically—can be checked without measuring the variables that actually modify the effect. The key idea is to compare the variances of the potential outcomes under treatment and control: if the standard deviations differ, the treatment effect cannot be constant. The authors derive one-step and targeted maximum likelihood estimators of this variance contrast based on its efficient influence function, and prove they are doubly robust and asymptotically linear. This yields Wald-type hypothesis tests that keep their nominal level under mild conditions. This matters because standard conditional-average-treatment-effect methods need the effect modifiers to be observed, while the new tests continue to work when those modifiers are missing or mismeasured, as demonstrated in simulations and in a re-analysis of the TTM2 cardiac-arrest trial.

What carries the argument

The efficient influence function (EIF) is the central object: a functional derivative that gives the optimal first-order correction term for plug-in estimation. Proposition 1 derives the EIF of each potential-outcome variance in terms of the propensity score and the conditional outcome moments Q̄ and Q̄². The one-step estimator adds the empirical mean of the EIF to the plug-in estimate; the TMLE tilts the outcome-regression nuisance parameters so that the EIF has empirical mean zero; cross-fitted versions avoid Donsker conditions. These components deliver the doubly robust, asymptotically linear behavior that makes valid hypothesis testing possible.

What would settle it

Simulate an observational study with a strong unmeasured confounder W that influences treatment assignment and outcome, while keeping the individual treatment effect truly constant, so the potential outcome variances are equal but the observed variances differ by assignment. If the proposed Wald test rejects the null in more than the nominal fraction of simulations, the causal interpretation of the variance contrast fails.

Watch

Extended reading notes

Core claim

Under conditional exchangeability, consistency, and positivity, the difference of the potential outcomes' standard deviations and the ratio of their variances are identified causal contrasts. Theorem 1 proves that if this absolute contrast is nonzero, the individual treatment effect cannot be constant: Y(0) cannot equal Y(1) minus a fixed constant. The paper obtains explicit efficient influence functions for each potential-outcome variance, constructs one-step estimators and targeted maximum likelihood estimators with K-fold cross-fitting, and establishes double robustness and asymptotic linearity under product-rate conditions on the nuisance estimators. Consequently, formal tests of the hom

Load-bearing premise

The causal interpretation of the variance contrast requires full conditional exchangeability—no unmeasured confounders of treatment and outcome—so in an observational study any hidden common cause can make the test reject for non-causal reasons.

Editorial extensions

If this is right

  • In a randomized trial, the homogeneous-effect assumption can be tested without adjusting for any baseline covariates and without knowing the true effect modifiers.
  • In observational studies, the same test is valid if no unmeasured confounding is present; the estimators are consistent when either the propensity score or the outcome regressions are estimated consistently.
  • Simulations show the variance-based tests retain power when a true effect modifier is completely mismeasured, a setting where conditional-average-treatment-effect procedures lose nearly all power.
  • Applying the procedure to the TTM2 trial rejects the homogeneous treatment effect assumption, although the estimated difference in standard deviations is small and the authors caution it may not be clinically meaningful.

Reading between the lines

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

  • Editorial extension: because the test targets marginal variances, heterogeneity that changes only conditional means while leaving variances unchanged is invisible to it; combining this test with a conditional-mean-based procedure would cover both failure modes.
  • Editorial extension: the same EIF-based strategy could plausibly be generalized to censored survival outcomes, multiple treatment arms, or multivariate outcomes by deriving the corresponding variance functionals, an extension the paper notes but does not develop.
  • Editorial extension: a statistically significant differential variance result should be read alongside effect size and clinical context; the TTM2 example shows a small estimated difference that is unlikely to change practice.
  • Editorial extension: this method could serve as an inexpensive first-pass screen for heterogeneity before investing in expensive measurement of candidate effect modifiers, reserving CATE analyses for settings where the variance test signals a violation of homogeneity.
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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 / 4 minor

Summary. This paper proposes to detect violations of the homogeneous individual treatment effect (ITE) assumption by making inference on contrasts of the variances of the two potential outcomes, rather than on conditional average treatment effects that require observed effect modifiers. The absolute contrast Ψ is the difference of standard deviations; the relative contrast Λ is the variance ratio. Theorem 1 shows Ψ≠0 implies the ITE is heterogeneous; Theorem 2 gives identification under conditional exchangeability, consistency, and positivity. The main methodological work derives efficient influence functions for the potential-outcome variances, constructs one-step and TMLE estimators with cross-fitted versions, and states double-robustness and asymptotic-linearity theorems. Finite-sample behavior is studied in three simulation experiments, and the method is applied to re-analyze the TTM and TTM2 targeted-temperature-management trials, finding a statistically significant variance contrast in TTM2 but not TTM.

Significance. The paper contributes a useful, assumption-lean supplement to CATE-based heterogeneity detection: it can detect heterogeneity even when effect modifiers are unmeasured, provided the causal identification conditions hold. The EIF derivations and estimator construction are technically sound, and the authors provide open-source software and reproducible simulation code, which strengthens the credibility of the paper. The principal limitation is that the procedure is fundamentally one-directional: Ψ=0 does not imply homogeneity, and the paper's dismissal of such cases as 'pathological' is incorrect (see major comment). This does not invalidate the detection result, but it means the procedure cannot 'gauge' homogeneity as claimed. With reframing and boundary fixes, the paper would be a solid methodological contribution.

major comments (3)
  1. [Section 2.2 and Theorem 1] The contrapositive ΨF≠0 ⇒ heterogeneity is correct, but the paper's framing overstates its inferential reach. The text states that equal variances with heterogeneous effects are expected 'only ... in pathological DGPs.' This is false. Let W∼N(0,1), let ε be independent of W with Var(ε)=1, Y(0)=W+ε, and Y(1)=−W+ε. Then Var(Y(0))=Var(Y(1))=2, so ΨF=0, but the ITE is Y(1)−Y(0)=−2W, a strongly heterogeneous linear effect-modifier model. This is a standard additive linear model. Consequently any Wald test of H0:Ψ=0 has asymptotic rejection rate equal to its size for this DGP at every n; a non-rejection carries no evidence for homogeneity. The abstract's claim that the homogeneous-ITE hypothesis 'can be gauged' is therefore too strong. Please reframe the procedure as a one-directional detector of variance-induced heterogeneity and explicitly state that Ψ=0 is uninformative about homogeneity.
  2. [Section 3.5.1, Eq. (3) and DΨ] The absolute contrast is defined as sqrt(σ2_OS(1))−sqrt(σ2_OS(0)), and its EIF divides by sqrt(σ2(P0;a)). But Section 3.3 states one-step variance estimators 'may produce negative estimates,' and Simulation 2 reports near-zero variance estimates causing problems. For σ2_OS≤0 the square root is undefined; the paper gives no modification (e.g., lower-bound truncation) or corresponding asymptotic theory. This is a concrete gap in the headline estimator. Please provide a well-defined boundary treatment and assess its impact on coverage and power.
  3. [Section 3.4, Theorem 4, condition 2] The theorem assumes ∥Dσ2(Pn;O)−Dσ2(P0;O)∥2 = oP(n−1/2). The following text says this condition is 'satisfied if ... the nuisance parameter estimators are consistent.' Consistency alone does not imply n−1/2 L2 convergence; this is a rate condition. Moreover, condition 2 is essentially a first-order expansion assumption, so without primitive sufficient conditions the theorem is close to assuming the desired asymptotic linearity. Please provide verifiable rate conditions (e.g., products of nuisance errors) or clearly label condition 2 as high-level and correct the explanatory statement.
minor comments (4)
  1. [Abstract and Section 2.2] The word 'gauged' suggests two-sided inference. Recommend replacing with 'detect certain violations of' or 'screen for' and adding a sentence that non-rejection is not evidence of homogeneity.
  2. [Proof of Proposition 1] The line 'Dσ2(a)(P;O)=Dμ2(a)(P;O)+2μ(P;a)Dμ(a)(P;O)' has the wrong sign; the second term should be −2μDμ. The final formula in the proposition is correct, so the proof text should be corrected.
  3. [Section 3.3, Eq. (8)] In the cross-fitted TMLE, the second term uses EPn instead of EPn,k; check whether this is intentional. If not, replace with EPn,k for consistency with the first term.
  4. [Table 1] Report the units of the estimates explicitly (days of survival time) so that the clinical interpretation of the TTM2 contrast (<1 day) is transparent.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the variance-contrast result follows by direct algebra from the definition of homogeneous ITE, and the estimators are derived from first-principles semiparametric theory.

full rationale

The paper's central claim (Theorem 1) is self-contained: it proves that if the potential outcomes differ by a constant γ, then the two potential-outcome standard deviations are equal, so a nonzero differential variance implies the treatment effect cannot be homogeneous. This is a direct algebraic consequence, not an assumption smuggled in. The estimator construction proceeds from the efficient influence function of σ²(P0; a), derived explicitly in Proposition 1 from the functional delta method and standard semiparametric theory, and the double-robustness and asymptotic-linearity results are proven from nuisance-rate conditions, not assumed as conclusions. Self-citations (e.g., Boileau et al. 2025a, 2025b) are used only as supporting empirical context in the introduction and do not carry the load-bearing derivation. The acknowledged one-directionality of Ψ = 0 — that zero differential variance does not imply homogeneity — is explicitly stated in Section 2.2 and is a substantive inferential limitation (also reflected in the skeptical reading), but it is not a circular step: the paper does not claim the converse as a theorem, and the testing procedure is presented as a one-sided refutation tool. No fitted parameter is renamed as a prediction, no uniqueness theorem is imported from the authors' prior work, and no ansatz is justified solely by self-citation. Therefore no significant circularity is present.

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

No free parameters are fit to the data to obtain the central result; the method's only inputs are data-driven nuisance estimates. The axioms are standard causal identifiability conditions and asymptotic rate assumptions.

assumptions (6)
  • domain assumption Conditional exchangeability A ⊥⊥ (Y(0), Y(1)) | W
    Invoked in Theorem 2 to identify potential-outcome variances; requires full independence, stronger than mean independence.
  • domain assumption Consistency Y = A Y(1) + (1−A) Y(0)
    Standard causal assumption, listed in Theorem 2.
  • domain assumption Positivity 0 < P(A=1|W) < 1 a.s.
    Required for the EIF to have bounded variance and for the TMLE fluctuation steps.
  • standard math Outcomes bounded in [0,1] without loss of generality
    Used to define the logistic loss for the TMLE; authors explain scaling and re-scaling.
  • domain assumption Additive potential outcome decomposition Y(a) = f(a)(W) + ε(a) with f(a)(W) ⊥ ε(a)
    Used in Theorem 1 to characterize the homogeneous ITE assumption; frames the causal null.
  • domain assumption Rate conditions for asymptotic linearity (Donsker class, product rate oP(n^{-1/2}), µ rate oP(n^{-1/4}))
    Theorem 4 conditions; the authors note cross-fitting avoids the Donsker condition but other rate conditions remain.

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Cite this review

Pith. "Pith review of Assumption-Lean Differential Variance Inference for Heterogeneous Treatment Effect Detection." pith.science (2026). https://pith.science/paper/FFQUFVUX

@misc{pith2026251203254,
  author       = {Pith},
  title        = {Pith review of: Assumption-Lean Differential Variance Inference for Heterogeneous Treatment Effect Detection},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/FFQUFVUX}},
  note         = {Machine review of arXiv:2512.03254}
}
read the original abstract

The conditional average treatment effect (CATE) is frequently estimated in clinical studies to refute a homogeneous treatment effect hypothesis. Under this regime, all patients making up the population experience identical benefit from a given treatment relative to a comparator. Uncovering heterogeneous treatment effects through inference about the CATE, however, requires that covariates truly modifying the treatment effect be reliably collected at baseline. CATE-based techniques will necessarily fail to detect violations when effect modifiers are omitted from the data due to, for example, resource constraints. Severe measurement error has a similar impact. Clinical decision makers can be misled as a result. To address these limitations, we prove that a practical homogeneous treatment effect hypothesis can be gauged through inference about contrasts of the potential outcomes' variances even when effect modifiers are missing from the data. We derive causal machine learning estimators of these contrasts and study their asymptotic properties. We establish that these estimators are doubly robust and asymptotically linear under mild conditions, permitting formal hypothesis testing about the treatment effect heterogeneity. Numerical experiments demonstrate that these estimators' asymptotic guarantees are approximately achieved in finite-sample randomized and observational study data alike. These inference procedures are then used to detect heterogeneous treatment effects in the re-analysis of randomized controlled trials investigating targeted temperature management in cardiac arrest patients.

Figures

Figures reproduced from arXiv: 2512.03254 by the authors.

Figure 1
Figure 1. Double robustness: The absolute empirical bias of the relative differential variance one-step estimator and TMLE, as well as their cross-fitted counterparts, across various sample sizes and nuisance parameter estimator scenarios. Outlying values are truncated and represented by stars to facilitate the interpretation of results. The dashed horizontal lines correspond to the idealized absolute empirical bias. Variable… view at source ↗
Figure 2
Figure 2. Asymptotic linearity: The absolute empirical bias, empirical variance, scaled absolute empirical bias, and empirical coverage of the one-step estimator, TMLE, cross-fitted one-step estimator, and cross-fitted TMLE for the absolute differential variance. Outlying values are truncated and represented by stars to facilitate the interpretation of results. The dashed horizontal lines correspond to the idealized values fo… view at source ↗
Figure 3
Figure 3. Homogeneous Individual Treatment Effect Hypothesis Testing: The empirical power of hypothesis tests about the homogeneous ITE assumption based on the absolute differential variance estimators and Causal Forests in several treatment effect modifier mismeasurement scenarios. The dashed horizontal lines correspond to the idealized empirical power. implemented in the grf R package for the causal forest CATE estimator [T… view at source ↗

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Works this paper leans on

42 extracted references · 15 canonical work pages

  1. [5]

    doi:10.1016/S1470-2045(13)70510-2

    ISSN 1470-2045. doi:10.1016/S1470-2045(13)70510-2. Center for Drug Evaluation and Research and Center for Biologics Evaluation and Research. Adjusting for Covariates in Randomized Clinical Trials for Drugs and Biological Products. https://www.fda.gov/regulatory-information/search- fda-guidance-documents/adjusting-covariates-randomized-clinical-trials-drug...

    work page doi:10.1016/s1470-2045(13)70510-2

  2. [8]

    doi:10.1257/aer.p20171038

    ISSN 0002-8282. doi:10.1257/aer.p20171038. V . Chernozhukov, M. Demirer, E. Duflo, and I. Fernández-Val. Generic Machine Learning Inference on Heterogeneous Treatment Effects in Randomized Experiments, with an Application to Immunization in India. Technical Report w24678, National Bureau of Economic Research, Cambridge, MA, June

    doi:10.1257/aer.p20171038

  3. [13]

    doi:10.1080/00031305.2021.2021984

    ISSN 0003-1305. doi:10.1080/00031305.2021.2021984. O. Hines, K. Diaz-Ordaz, and S. Vansteelandt. Variable importance measures for heterogeneous causal effects, 2025+. K. G. Hirsch, E. Amorim, P. J. Coppler, I. R. Drennan, A. Elliott, A. J. Gordon, J. C. Jentzer, N. J. Johnson, A. Moskowitz, B. E. Mumma, A. M. Presciutti, A. J. Rodriguez, A. F. Yen, and J....

    arXiv 2021

  4. [16]

    doi:10.1214/23-EJS2157

    ISSN 1935-7524, 1935-7524. doi:10.1214/23-EJS2157. E. H. Kennedy. Semiparametric doubly robust targeted double machine learning: A review. InHandbook of Statistical Methods for Precision Medicine. Chapman and Hall/CRC,

    doi:10.1214/23-ejs2157 1935

  5. [17]

    ISBN 978-1-003-21622-3. E. H. Kennedy, S. Balakrishnan, and M. G’Sell. Sharp instruments for classifying compliers and generalizing causal effects.The Annals of Statistics, 48(4):2008–2030, Aug

    2008

  6. [20]

    doi:10.1515/jci-2019-0003

    ISSN 2193-3685. doi:10.1515/jci-2019-0003. A. R. Luedtke and M. J. van der Laan. Super-Learning of an optimal dynamic treatment rule.The International Journal of Biostatistics, 12(1):305–332, May

    work page doi:10.1515/jci-2019-0003 2019

  7. [22]

    doi:10.1016/j.jacadv.2025.102042

    ISSN 2772-963X. doi:10.1016/j.jacadv.2025.102042. 19 Assumption-Lean Differential Variance Inference for Heterogeneous Treatment Effect Detection J. Neyman, D. M. Dabrowska, and T. P. Speed. On the application of probability theory to agricultural experiments. essay on principles. Section 9.Statistical Science, 5(4):465–472,

    arXiv 2025

  8. [25]

    doi:10.1093/ije/dyad023

    ISSN 0300-5771. doi:10.1093/ije/dyad023. R Core Team.R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria,

    work page doi:10.1093/ije/dyad023

Show all 42 references
  1. [27]

    doi:10.1214/aos/1176350055

    ISSN 0090-5364, 2168-8966. doi:10.1214/aos/1176350055. O. M. Stitelman, V . D. Gruttola, and M. J. van der Laan. A General Implementation of TMLE for Longitudinal Data Applied to Causal Inference in Survival Analysis.The International Journal of Biostatistics, 8(1),

  2. [30]

    doi:10.1515/ijb-2015-0097

    ISSN 1557-4679. doi:10.1515/ijb-2015-0097. M. J. van der Laan and J. M. Robins.Unified Methods for Censored Longitudinal Data and Causality. Springer Series in Statistics. Springer, New York, NY ,

    2015 doi

  3. [34]

    doi:10.2202/1557-4679.1043

    ISSN 1557-4679. doi:10.2202/1557-4679.1043. M. J. van der Laan, E. C. Polley, and A. E. Hubbard. Super Learner.Statistical Applications in Genetics and Molecular Biology, 6(1), Sept

  4. [37]

    doi:10.1080/01621459.2017.1319839

    ISSN 0162-1459. doi:10.1080/01621459.2017.1319839. B. D. Williamson, P. B. Gilbert, M. Carone, and N. Simon. Nonparametric variable importance assessment using machine learning techniques.Biometrics, 77(1):9–22,

    2017

  5. [38]

    doi:10.1111/biom.13392

    ISSN 1541-0420. doi:10.1111/biom.13392. B. D. Williamson, P. B. Gilbert, N. R. Simon, and M. Carone. A general framework for inference on algorithm-agnostic variable importance.Journal of the American Statistical Association, 118(543):1645–1658,

    doi

  6. [39]

    doi:10.1080/01621459.2021.2003200

    ISSN 0162-1459. doi:10.1080/01621459.2021.2003200. Q. Zhao, D. S. Small, and A. Ertefaie. Selective inference for effect modification via the lasso.Journal of the Royal Statistical Society Series B: Statistical Methodology, 84(2):382–413,

    2021

  7. [40]

    doi:10.1111/rssb.12483

    ISSN 1369-7412. doi:10.1111/rssb.12483. 20 Assumption-Lean Differential Variance Inference for Heterogeneous Treatment Effect Detection W. Zheng and M. J. van der Laan. Cross-validated targeted minimum-loss-based estimation. In M. J. van der Laan and S. Rose, editors,Targeted ...

    doi

  8. [41]

    doi:10.1007/978-1-4419-9782-1_27

    ISBN 978-1-4419-9782-1. doi:10.1007/978-1-4419-9782-1_27. A. X. Zhu, J. O. Park, B.-Y . Ryoo, C.-J. Yen, R. Poon, D. Pastorelli, J.-F. Blanc, H. C. Chung, A. D. Baron, T. E. F. Pfiffer, T. Okusaka, K. Kubackova, J. Trojan, J. Sastre, I. Chau, S.-C. Chang, P. B. Abada, L. Yang,...

    doi

  9. [43]

    doi:10.1111/sjos.70001

    ISSN 1467-9469. doi:10.1111/sjos.70001. 21

    doi

  10. [1947]

    doi:10.1214/aoms/1177730385

    ISSN 0003-4851, 2168-8990. doi:10.1214/aoms/1177730385. S. Wager and S. Athey. Estimation and inference of heterogeneous treatment effects using Random Forests.Journal of the American Statistical Association, 113(523):1228–1242, July

  11. [1974]

    doi:10.1037/h0037350

    ISSN 1939-2176. doi:10.1037/h0037350. A. Schick. On asymptotically efficient estimation in semiparametric models.The Annals of Statistics, 14(3):1139–1151, Sept

    1939 doi

  12. [1985]

    doi:10.1524/strm.1985.3.34.379

    ISSN 2196-7040. doi:10.1524/strm.1985.3.34.379. R. V . Phillips, M. J. van der Laan, H. Lee, and S. Gruber. Practical considerations for specifying a super learner. International Journal of Epidemiology, 52(4):1276–1285, Aug

    1985 doi

  13. [1986]

    doi:10.1080/01621459.1986.10478354

    ISSN 0162-1459. doi:10.1080/01621459.1986.10478354. E. H. Kennedy. Towards optimal doubly robust estimation of heterogeneous causal effects.Electronic Journal of Statistics, 17(2):3008–3049, Jan

    1986

  14. [1987]

    doi:10.1016/0021-9681(87)90171-8

    ISSN 0021-9681. doi:10.1016/0021-9681(87)90171-8. S. Chen, L. Tian, T. Cai, and M. Yu. A general statistical framework for subgroup identification and comparative treatment scoring.Biometrics, 73(4):1199–1209, Dec

    doi

  15. [1991]

    doi:10.1214/aos/1176347963

    ISSN 0090-5364, 2168-8966. doi:10.1214/aos/1176347963. R. D. Gill, M. J. van der Laan, and J. A. Wellner. Inefficient estimators of the bivariate survival function for three models.Annales de l’I.H.P . Probabilités et statistiques, 31(3):545–597,

  16. [2001]

    doi:10.1023/A:1010933404324

    ISSN 1573-0565. doi:10.1023/A:1010933404324. C. Butts, M. A. Socinski, P. L. Mitchell, N. Thatcher, L. Havel, M. Krzakowski, S. Nawrocki, T.-E. Ciuleanu, L. Bosquée, J. M. Trigo, A. Spira, L. Tremblay, J. Nyman, R. Ramlau, G. Wickart-Johansson, P. Ellis, O. Gladkov, J. R. Pere...

    doi

  17. [2003]

    doi:10.1007/978-0-387- 21700-0

    ISBN 978-1-4419-3055-2 978-0-387-21700-0. doi:10.1007/978-0-387- 21700-0. M. J. van der Laan and S. Rose.Targeted Learning: Causal Inference for Observational and Experimental Data. Springer Series in Statistics. Springer, New York, NY ,

    doi

  18. [2006]

    doi:10.1007/0-387-37345-4

    ISBN 978-0-387-32448-7. doi:10.1007/0-387-37345-4. M. van der Laan. A generally efficient targeted minimum loss based estimator based on the Highly Adaptive Lasso. The International Journal of Biostatistics, 13(2), Nov

    doi

  19. [2007]

    doi:10.2202/1544-6115.1309

    ISSN 1544-6115. doi:10.2202/1544-6115.1309. R. von Mises. On the asymptotic distribution of differentiable statistical functions.The Annals of Mathematical Statistics, 18(3):309–348, Sept

  20. [2010]

    doi:10.2202/1557- 4679.1260

    ISSN 1557-4679. doi:10.2202/1557- 4679.1260. O. Hines, O. Dukes, K. Diaz-Ordaz, and S. Vansteelandt. Demystifying statistical learning based on ef- ficient influence functions.The American Statistician, 76(3):292–304, July

  21. [2011]

    doi:10.1007/978-1-4419-9782-1

    ISBN 978-1-4419-9781-4 978-1-4419-9782-1. doi:10.1007/978-1-4419-9782-1. M. J. van der Laan and S. Rose.Targeted Learning in Data Science: Causal Inference for Complex Longitudinal Studies. Springer Series in Statistics. Springer International Publishing, Cham,

    doi

  22. [2012]

    doi:10.1515/1557-4679.1334

    ISSN 1557-4679. doi:10.1515/1557-4679.1334. J. Tibshirani, S. Athey, E. Sverdrup, and S. Wager.grf: Generalized Random Forests,

  23. [2013]

    doi:10.1056/NEJMoa1310519

    ISSN 0028-4793. doi:10.1056/NEJMoa1310519. J. Pfanzagl and W. Wefelmeyer. Contributions to a general asymptotic statistical theory.Statistics & Risk Modeling, 3 (3-4):379–388, Apr

    doi

  24. [2014]

    doi:10.1200/JCO.2013.53.5633

    ISSN 0732-183X. doi:10.1200/JCO.2013.53.5633. A. Bahamyirou, M. E. Schnitzer, E. H. Kennedy, L. Blais, and Y . Yang. Doubly robust adaptive LASSO for effect modi- fier discovery.The International Journal of Biostatistics, 18(2):307–327,

    2013 doi

  25. [2015]

    ISSN 1470-2045. S. C. Ziersen and T. Martinussen. Variable importance measures for heterogeneous treatment effects with survival outcome.Scandinavian Journal of Statistics, n/a(n/a):1–51,

  26. [2016]

    doi:10.1515/ijb-2015-0052

    ISSN 1557-4679. doi:10.1515/ijb-2015-0052. J. D. Mark, J. L. Lopez, W. Wahood, R. A. Colombo, M. Danckers, A. A. Damluji, J. N. Katz, and C. L. Alviar. Personalizing Temperature Targets After Cardiac Arrest.JACC: Advances, 4(10):102042, Aug

    2015 doi

  27. [2017]

    doi:10.1111/biom.12676

    ISSN 0006-341X. doi:10.1111/biom.12676. 18 Assumption-Lean Differential Variance Inference for Heterogeneous Treatment Effect Detection V . Chernozhukov, D. Chetverikov, M. Demirer, E. Duflo, C. Hansen, and W. Newey. Double/debiased/Neyman machine learning of treatment effects...

    doi

  28. [2018]

    doi:10.1007/978-3-319-65304-4

    ISBN 978-3-319-65303-7 978-3-319-65304-4. doi:10.1007/978-3-319-65304-4. M. J. van der Laan and D. Rubin. Targeted maximum likelihood learning.The International Journal of Biostatistics, 2 (1), Dec

    doi

  29. [2020]

    doi:10.1214/19- AOS1874

    ISSN 0090-5364, 2168-8966. doi:10.1214/19- AOS1874. C. A. J. Klaassen. Consistent estimation of the influence function of locally asymptotically linear estimators.The Annals of Statistics, 15(4):1548–1562, Dec

    doi

  30. [2021]

    doi:10.1056/NEJMoa2100591

    ISSN 0028-4793. doi:10.1056/NEJMoa2100591. I. Díaz and M. Rosenblum. Targeted Maximum Likelihood Estimation using Exponential Families, June

    doi

  31. [2022]

    doi:10.1515/ijb- 2020-0073

    ISSN 1557-4679. doi:10.1515/ijb- 2020-0073. A. F. Bibaut and M. J. van der Laan. Fast rates for empirical risk minimization over càdlàg functions with bounded sectional variation norm, Aug

    2020 doi

  32. [2023]

    doi:10.1093/biostatistics/kxac029

    ISSN 1465-4644. doi:10.1093/biostatistics/kxac029. P. Boileau, N. Leng, and S. Dudoit. Guidance on individualized treatment rule estimation in high dimensions.The International Journal of Biostatistics, May 2025a. ISSN 1557-4679. doi:10.1515/ijb-2024-0005. P. Boileau, N. Leng,...

    2024 doi

  33. [2024]

    URL https://doi.org/10.21105/joss

    doi:10.21105/joss.06156. URL https://doi.org/10.21105/joss. 06156. J. H. Friedman. Multivariate Adaptive Regression Splines.The Annals of Statistics, 19(1):1–67, Mar

    doi

  34. [2025]

    doi:10.1161/CIR.0000000000001375. P. W. Holland. Statistics and Causal Inference.Journal of the American Statistical Association, 81(396):945–960, Dec

    doi

Pith tools

Reviewed August 3, 2026 · model on record in the stance chip above.