Pith. sign in

REVIEW 4 major objections 4 minor 62 references

A Unified Causal Inference Framework for the Desirability of Outcome Ranking Paradigm in Benefit-Risk Evaluation

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

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read This paper derives the nonparametric efficient influence function for the DOOR probability and uses it to build doubly robust estimators, cross-fitting, and EIF-based confidence intervals for covariate-adjusted benefit-risk comparisons.

desk verdict Solid EIF derivation and thorough simulations for the DOOR probability, but EIF-based inference demonstrably undercovers in the hardest overlap/allocation settings and the paper's preferred estimator is endorsed beyond what its own Table 1 supports. read the letter →

arxiv 2608.05244 v1 pith:OCOAXMA4 submitted 2026-08-05 stat.ML cs.LGstat.ME

Yuan Feng , Shiyu Shu , Yixin Fang , Ionut Bebu , Toshimitsu Hamasaki , Scott Evans , Guoqing Diao This is my paper · ORCID
classification stat.MLcs.LGstat.ME MSC 62G0562G2062F1262P10
keywords desirabilityofoutcomerankingDOORprobabilitybenefit-riskevaluationefficientinfluencefunctiondoublyrobustestimationtargetedmaximumlikelihoodcross-fittingordinaloutcomes
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

This paper builds a single causal inference framework for the desirability of outcome ranking (DOOR) probability, a pairwise benefit-risk measure that compares ordinal outcomes under two treatments on a patient-centered desirability scale. It represents the DOOR probability as a bilinear function of the two marginal treatment-specific category distributions, $\psi = (p^1)^\top M p^0$, and derives the nonparametric efficient influence function for $\psi$ directly. If that derivation is correct, the same machinery yields doubly robust point estimators (AIPW and TMLE) and EIF-based standard errors and confidence intervals for both randomized trials and observational studies, without imposing a proportional-odds assumption. In the simulation studies, targeted maximum likelihood estimation with Super Learner nuisance estimates, especially after cross-fitting, showed the strongest overall point-estimation and inference performance among the methods examined.

What carries the argument

The framework rests on the finite-category bilinear representation of the DOOR probability as $\Phi(p^1,p^0)=(p^1)^\top M p^0$, combined with sequential risk-set hazards $h_{a,j}(X)=P(Y=j\mid Y\ge j, A=a, X)$ to model the conditional ordinal distributions without proportional-odds assumptions. This factorization separates the estimand from nuisance learning: any estimator of the treatment-specific marginal cumulative probabilities can be mapped through the same DOOR map. The efficient influence function of $\psi$ is then assembled by applying the functional delta method to the EIFs of the marginal category probabilities, yielding the bilinear combination in Eq. (2.13) that carries the inference.

What would settle it

Run the same estimators in a setting with severe treatment-overlap violation and compare the influence-function standard error with the Monte Carlo empirical standard error; the paper's Table 1 already provides such a case, with TMLE-SL showing IF SE 0.010 versus empirical SE 0.016 and 79.3 percent coverage, which would contradict the claim that the EIF yields valid inference in that setting.

Watch

Extended reading notes

Core claim

Under the four standard identifying assumptions, the causal DOOR probability $\psi=P(Y^1>Y^0)+\tfrac12 P(Y^1=Y^0)$ is identified by the bilinear map $\psi=(p^1)^\top M p^0$, where $p^a$ are the marginal category probabilities under each treatment and $M_{k\ell}=1(k>\ell)+\tfrac12 1(k=\ell)$ is the comparison matrix. The central derived object is the efficient influence function of $\psi$, given in Eq. (2.13) as $D_{\psi,EIF}(O) = D_p^{1,EIF}(O)^\top M p^0 + (p^1)^\top M D_p^{0,EIF}(O)$, obtained by the functional delta method from the EIFs of the marginal category probabilities. The paper then shows that AIPW and TMLE, with either GLM or Super Learner nuisance estimation and with or without cross-fitting, inherit this representation for point estimation and for influence-function-based standard errors. In the studied settings, TMLE-SL had the most consistent point-estimation performance, and CVTMLE-SL the strongest overall inference, with cross-fitting improving confidence-interval coverage in small-overlap and imbalanced designs.

Load-bearing premise

The EIF-based standard errors and confidence intervals are valid only when the estimated treatment-probability model and ordinal-outcome model converge fast enough and when every treatment is possible at every covariate value; the paper's own small-overlap imbalanced simulations show coverage below 95 percent in that setting.

Editorial extensions

If this is right

  • Covariate-adjusted DOOR analysis can be implemented with one modular pipeline: estimate sequential risk-set hazards, convert them to marginal category probabilities, apply the bilinear DOOR map, and construct EIF-based confidence intervals.
  • In the studied simulation scenarios, TMLE-SL gave the strongest and most consistent point estimates, with AIPW-SL second, and cross-fitted CVTMLE-SL gave the strongest overall inference, especially under small overlap and imbalanced treatment allocation.
  • A method can perform well on the scalar DOOR probability while recovering the underlying ordinal outcome distributions poorly, so applied DOOR analyses should report distribution-recovery diagnostics alongside the scalar estimate.
  • In the MDRO application, covariate adjustment moved the estimated DOOR probability from 0.422 to about 0.469-0.471, substantially weakening the crude evidence favoring monotherapy, with confidence intervals reaching or closely approaching 0.5.

Reading between the lines

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

  • Because the EIF formula is derived for a general finite number of ordinal categories, a natural extension would give EIF-based inference for other pairwise benefit-risk summaries that are bilinear in marginal outcome distributions, such as generalized Mann-Whitney contrasts or net-benefit measures.
  • The paper's Table 1 shows that even cross-fitted intervals remain below nominal coverage in small-overlap imbalanced designs, suggesting that applied users should report overlap and effective-sample-size diagnostics alongside EIF-based intervals, an implication the paper notes as a limitation rather than a tested feature.
  • The simulation pattern in which scalar DOOR bias masked larger errors in the underlying ordinal distributions suggests that the framework's estimate of $p^1$ and $p^0$ should be reported even when the DOOR probability is the primary output, since related DOOR-type summaries depend on those distributions.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 4 minor

Summary. The paper develops a framework for covariate-adjusted causal inference on the desirability of outcome ranking (DOOR) probability, defined as a Mann–Whitney-type pairwise comparison of the marginal potential-outcome distributions. The estimand is written as a bilinear functional p1^T M p0 of treatment-specific marginal category probabilities, identified under consistency, no interference, conditional exchangeability, and positivity. Conditional ordinal distributions are modeled through sequential risk-set hazards, and the nonparametric efficient influence function of the DOOR probability is derived in Eq. (2.13). The paper then compares G-computation, normalized IPW, AIPW, and TMLE using GLM and Super Learner nuisance estimation, and evaluates EIF-based inference for AIPW-SL, TMLE-SL, CV AIPW-SL, and CVTMLE-SL across scenarios varying overlap, treatment-effect heterogeneity, and treatment allocation. The headline empirical claims are that TMLE-SL has the best point-estimation performance and CVTMLE-SL is the preferred implementation overall. The method is applied to an observational MDRO network dataset comparing monotherapy versus combination therapy.

Significance. The EIF derivation in Section 2.6 is a useful and apparently correct contribution: it reduces inference for the DOOR probability to the EIFs of marginal category probabilities composed through the functional delta method, and it extends sequential-hazard estimation to a covariate-dependent treatment mechanism with doubly robust and cross-fitted implementations. The simulation design is thorough, with Monte Carlo truth, 1000 replications, eight inferential scenarios, effective-sample-size diagnostics, and distributional recovery summaries (theta_max and p_max) that go beyond scalar DOOR bias. The paper is also honest about its limitations, explicitly acknowledging residual undercoverage in the hardest settings and the absence of overlap diagnostics in the application. If the method were paired with practical diagnostics for the conditions under which EIF-based standard errors are reliable, it would be directly useful for benefit-risk analyses in both randomized and observational studies.

major comments (4)
  1. [See Section 2.10, Eq. (2.21), and Table 1.] The validity of the EIF-based standard errors and the transformed Wald intervals requires the second-order remainder of the one-step/TMLE expansion to vanish, which in turn requires the propensity-score and ordinal-hazard estimators to converge faster than n^{-1/4} in the relevant norms; this condition is not stated explicitly in Section 2.10. Table 1 shows exactly where the condition fails: in the imbalanced small-overlap homogeneous scenario, TMLE-SL has IF SE 0.010 versus empirical SE 0.016 with 79.3% coverage, and CVTMLE-SL has IF SE 0.013 versus empirical SE 0.015 with 89.7% coverage; the heterogeneous version shows similar gaps with 82.7% and 92.8% coverage. Because the central inferential claim is that EIF-based standard errors provide valid inference, the manuscript should state the requisite rate conditions and either verify them in the simulations or provide practical diagnostics, such as overlap, effective sample size, and influence-function stability, that practitioners can use to decide when the reported standard errors are trustworthy.
  2. [See Section 4, Table 3, and the Discussion.] The MDRO application uses a treatment ratio of 390 combination-therapy patients to 1145 monotherapy patients, close to the 1:3 imbalanced simulation arm, and the Discussion concedes that no formal propensity-overlap, extreme-weight, effective-sample-size, or model-sensitivity diagnostics were available for this application. Given that Table 1 shows 89.7–92.8% coverage for CVTMLE-SL in analogous imbalanced small-overlap scenarios, the confidence intervals reported for the MDRO analysis are not verified for this data setting. Reporting the propensity-score distribution, effective sample sizes, and a summary of the estimated influence-function contributions would be necessary to support the real-data conclusions.
  3. [See Section 3.6, Table 1, and the final paragraph of Section 5.] The claim that CVTMLE-SL is the preferred implementation is a holistic judgment that is not formally operationalized. In the two hardest imbalanced small-overlap scenarios, CV AIPW-SL achieves higher coverage than CVTMLE-SL (91.1% versus 89.7% and 93.1% versus 92.8%), while CVTMLE-SL generally has lower RMSE and better ordinal-distribution recovery; because no prespecified ranking metric, equivalence test, or formal comparison is given, the headline ordering is not uniquely determined by the table. Please specify the decision rule used to combine coverage, RMSE, and distributional recovery, or present the comparison as scenario-specific without a global preference claim.
  4. [See Section 2.8.] The TMLE implementation stops when the empirical mean squared change in hazard predictions is at most 10^{-4}/n or after 100 iterations, but the EIF variance estimator in Eq. (2.21) presumes that the fluctuation score equations are solved sufficiently accurately. The manuscript does not report convergence diagnostics, such as the achieved norm of the score equations or the number of iterations used, so it is unclear whether approximate convergence contributes to the undercoverage observed in Table 1. Please report these diagnostics in the simulations and in the application.
minor comments (4)
  1. [See Supplementary Materials.] The main text refers to Supplementary Tables S1–S4, but those tables are not included in the reviewed submission; please ensure the supplementary file is uploaded with the revision.
  2. [See Section 2.9.] The description of CVTMLE as applying a single hazard-scale targeting update to stacked out-of-fold predictions is ambiguous: clarify whether this means a single fluctuation step or iteration to the same convergence criterion used for full-sample TMLE.
  3. [See Section 3.3.] For the imbalanced design, the shifted propensity mechanism e_rho(W) is calibrated to E{e_rho(W)}=0.25, but the text does not report the resulting overlap characteristics, such as the 5th–95th percentile range or the proportion of propensity scores near the boundaries; adding these summaries would help readers map the simulation to the MDRO application.
  4. [See the Data Availability Statement.] The paper provides a data availability statement for the MDRO data but does not state whether the simulation code and the DOOR estimation code will be released; since the simulations are the main evidence for the method's operating characteristics, a code availability statement would improve reproducibility.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: the EIF for the DOOR probability is derived by the functional delta method from standard cumulative-probability EIFs, and all estimator rankings are evaluated against independent Monte Carlo truth.

full rationale

The central derivation is self-contained: Eq. (2.13) is obtained by applying the functional delta method to the bilinear map in Eq. (2.3), with the component EIFs in Eqs. (2.10)-(2.11) given explicitly rather than fitted. The AIPW and TMLE constructions are standard one-step/targeted plug-ins from the stated EIF, and the CV variants use out-of-fold nuisance estimates; the cross-fitted standard error in Eq. (2.21) is the empirical variance of the estimated EIF contributions, not a refit of the estimand. Simulation evaluations use a separate Monte Carlo population of size 10^6 to fix cutpoints and compute the true DOOR probability, so estimator rankings are benchmarked against external truth rather than against the estimators' own fitted values. The self-citations (e.g., Shu et al. 2026) are contextual foundations for the DOOR estimand and parametric G-computation, not load-bearing evidence for the nonparametric EIF derivation. The only caveat is the standard regularity/rate condition on nuisance estimators underlying EIF-based standard errors, which the paper's Table 1 shows can fail in small-overlap imbalanced settings; this is a validity limitation acknowledged in Sections 3 and 5, not a circular reduction.

Assumptions & free parameters 4 free parameters · 6 assumptions · 0 invented entities

The central theoretical claim rests on standard causal identification assumptions and textbook semiparametric efficiency theory; it does not introduce fitted constants. The implementation hyperparameters listed under free parameters are chosen by hand and may affect the simulation-based ranking, but they are not part of the estimand or the EIF. No new physical or model entities are postulated.

free parameters (4)
  • Probability truncation bound = [0.001, 0.999]
    Applied to all fitted propensity scores and ordinal hazards, with bounds reapplied after TMLE updates (Sections 2.3 and 2.8). Chosen by hand; affects finite-sample bias and variance, especially under small overlap.
  • TMLE convergence threshold = 10^-4 / n
    Stopping rule for iterative hazard targeting (Section 2.8). Chosen by hand; the final TMLE only approximately solves the influence-function score equations.
  • Cross-fitting fold count V = 10
    Used for CV AIPW and CVTMLE (Section 2.9). Chosen by hand; coverage and variance estimates may depend on the number of folds.
  • Super Learner candidate library = main GLM, stepwise GLM, interaction GLM, elastic net, GAM, random forest
    Specified in Section 3.2. The simulation-based ranking of estimators is conditional on this library and on the truncation and tuning choices.
assumptions (6)
  • domain assumption Causal assumptions A1-A4: consistency, no interference, conditional exchangeability, positivity.
    Stated in Section 2.2; they identify p^a_k = E[Q_a(k|X)] and are required for the DOOR estimand to equal the causal contrast.
  • standard math The functional delta method applies to the bilinear map Phi(p1,p0) = p1^T M p0.
    Section 2.6 applies the derivative in (2.12) to the component efficient influence functions; this requires pathwise differentiability and regular estimators.
  • standard math The efficient influence functions have finite second moments and the plug-in nuisance estimators converge fast enough for the remainder terms to vanish.
    Section 2.10 uses the sample variance of estimated influence functions as the standard error; the paper's simulations show this assumption is strained under small overlap and imbalanced allocation.
  • standard math The sequential risk-set hazard factorization P(Y<=k|A=a,X) = 1 - product over j<=k of (1 - h_{a,j}) is used without error.
    Equation (2.5) is an identity for any ordinal distribution, so this is a safe model for the conditional outcome distribution.
  • domain assumption Super Learner and cross-fitting provide nuisance estimators with adequate convergence rates.
    Invoked in Sections 2.9 and 3.4 to justify inference with flexible learners; the empirical coverage results suggest this holds in many but not all settings.
  • domain assumption In the MDRO application, the measured covariates are sufficient for conditional exchangeability and positivity.
    Section 4.2 and the Discussion state that causal interpretation relies on these assumptions; residual confounding and lack of overlap diagnostics are acknowledged.

how reviews work

0 comments
Cite this review

Pith. "Pith review of A Unified Causal Inference Framework for the Desirability of Outcome Ranking Paradigm in Benefit-Risk Evaluation." pith.science (2026). https://pith.science/paper/OCOAXMA4

@misc{pith2026260805244,
  author       = {Pith},
  title        = {Pith review of: A Unified Causal Inference Framework for the Desirability of Outcome Ranking Paradigm in Benefit-Risk Evaluation},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/OCOAXMA4}},
  note         = {Machine review of arXiv:2608.05244}
}
read the original abstract

We developed a unified covariate-adjusted causal inference framework for estimating the desirability of outcome ranking (DOOR) probability for benefit-risk evaluation in randomized trials and observational studies. The framework expresses the DOOR probability as a bilinear functional of the marginal ordinal outcome distributions under the two treatment strategies, estimates conditional ordinal distributions through sequential risk-set hazards, and derives the efficient influence function (EIF) of the DOOR probability. The point-estimation simulations compared G-computation, normalized inverse probability weighting (IPW), augmented IPW (AIPW), and targeted maximum likelihood estimation (TMLE), with nuisance functions estimated using generalized linear models or Super Learner (SL). TMLE-SL showed the strongest and most consistent point-estimation performance, with AIPW-SL ranking second. EIF-based inference was then evaluated for AIPW-SL and TMLE-SL, with and without cross-fitting, across settings varying in overlap, treatment-effect heterogeneity, and treatment allocation. CVTMLE-SL showed the strongest overall performance across DOOR-scale bias, recovery of the underlying ordinal distributions, standard-error accuracy, and confidence-interval coverage. We illustrate the methodology using data from the multidrug-resistant organism network of the Antibacterial Resistance Leadership Group.

Figures

Figures reproduced from arXiv: 2608.05244 by the authors.

Figure 1
Figure 1. Workflow for covariate-adjusted estimation of the DOOR probability. G [PITH_FULL_IMAGE:figures/full_fig_p013_1.png] view at source ↗
Figure 2
Figure 2. True propensity-score distributions and treatment-assignment summaries under [PITH_FULL_IMAGE:figures/full_fig_p022_2.png] view at source ↗
Figure 3
Figure 3. Point-estimation operating characteristics in the X-working-model simulations. [PITH_FULL_IMAGE:figures/full_fig_p027_3.png] view at source ↗
Figures from the paper (2 more)
Figure 4
Figure 4. Figure 4: Maximum biases in the estimated ordinal outcome distributions in the X-working [PITH_FULL_IMAGE:figures/full_fig_p028_4.png]
Figure 5
Figure 5. Figure 5: Crude and covariate-adjusted DOOR probability estimates in the MDRO applica [PITH_FULL_IMAGE:figures/full_fig_p036_5.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

62 extracted references · 61 canonical work pages

  1. [1]

    Journal of Biopharmaceutical Statistics , year =

    Double machine learning methods for estimating average treatment effects: a comparative study , author =. Journal of Biopharmaceutical Statistics , year =

    work page

  2. [2]

    American Journal of Epidemiology , year =

    Variable selection for propensity score models , author =. American Journal of Epidemiology , year =

    work page

  3. [3]

    Biometrics , year =

    Enhanced precision in the analysis of randomized trials with ordinal outcomes , author =. Biometrics , year =

    work page

  4. [4]

    American Journal of Epidemiology , year =

    Constructing targeted minimum loss/maximum likelihood estimators: a simple illustration to build intuition , author =. American Journal of Epidemiology , year =

    work page

  5. [5]

    The International Journal of Biostatistics , year =

    Targeted maximum likelihood estimation of natural direct effects , author =. The International Journal of Biostatistics , year =

    work page

  6. [6]

    American Journal of Epidemiology , year =

    Pulling back the curtain: the road from statistical estimand to machine-learning-based estimator for epidemiologists (no wizard required) , author =. American Journal of Epidemiology , year =

    work page

  7. [7]

    and Doernberg, Sarah B

    Hamasaki, Toshimitsu and He, Yijie and Wu, Qihang and Howard-Anderson, Jessica and Boucher, Helen W. and Doernberg, Sarah B. and Holland, Thomas L. and Powers, III, John H. and Wang, Jing and Diao, Guoqing and van Duin, David and Fowler, Jr., Vance G. and Chambers, Henry F. and Evans, Scott R. , journal =. A patient-centric paradigm and tool for clinical ...

    work page 2026

  8. [8]

    Statistics in Medicine , volume=

    Generalized pairwise comparisons of prioritized outcomes in the two-sample problem , author=. Statistics in Medicine , volume=. 2010 , publisher=

    work page 2010

Show all 62 references
  1. [9]

    European Heart Journal , volume=

    The win ratio: a new approach to the analysis of composite endpoints in clinical trials based on clinical priorities , author=. European Heart Journal , volume=. 2012 , publisher=

    2012

  2. [10]

    and Rubin, Daniel and Follmann, Dean and Pennello, Gene and Huskins, W

    Evans, Scott R. and Rubin, Daniel and Follmann, Dean and Pennello, Gene and Huskins, W. Charles and Powers, John H. and Schoenfeld, David and Chuang-Stein, Christy and Cosgrove, Sara E. and Fowler, Jr., Vance G. and Lautenbach, Ebbing and Chambers, Henry F. , journal =. Desira...

    2015

  3. [11]

    Statistics in Biopharmaceutical Research , volume=

    Using outcomes to analyze patients rather than patients to analyze outcomes: a step toward pragmatism in benefit:risk evaluation , author=. Statistics in Biopharmaceutical Research , volume=. 2016 , publisher=

    2016

  4. [12]

    Trials , year =

    Statistical analyses of ordinal outcomes in randomised controlled trials: a scoping review , author =. Trials , year =

  5. [13]

    Clinical Trials , year =

    Evaluating whether the proportional odds models to analyse ordinal outcomes in COVID-19 clinical trials is providing clinically interpretable treatment effects: A systematic review , author =. Clinical Trials , year =

  6. [14]

    International Statistical Review , year =

    Estimating Mann--Whitney-type Causal Effects , author =. International Statistical Review , year =

  7. [15]

    Trials , year =

    The risks and rewards of covariate adjustment in randomized trials: an assessment of 12 outcomes from 8 studies , author =. Trials , year =

  8. [16]

    Improving precision and power in randomized trials for

    Benkeser, David and D. Improving precision and power in randomized trials for. Biometrics , year =

  9. [17]

    Biometrika , year =

    The Central Role of the Propensity Score in Observational Studies for Causal Effects , author =. Biometrika , year =

  10. [18]

    Mathematical Modelling , year =

    A New Approach to Causal Inference in Mortality Studies with a Sustained Exposure Period---Application to Control of the Healthy Worker Survivor Effect , author =. Mathematical Modelling , year =

  11. [19]

    Epidemiology , year =

    Marginal Structural Models and Causal Inference in Epidemiology , author =. Epidemiology , year =

  12. [20]

    Biometrics , year =

    Doubly Robust Estimation in Missing Data and Causal Inference Models , author =. Biometrics , year =

  13. [21]

    The International Journal of Biostatistics , year =

    Double Robust Efficient Estimators of Longitudinal Treatment Effects: Comparative Performance in Simulations and a Case Study , author =. The International Journal of Biostatistics , year =

  14. [22]

    American Journal of Epidemiology , year =

    A Double Robust Approach to Causal Effects in Case-Control Studies , author =. American Journal of Epidemiology , year =

  15. [23]

    The International Journal of Biostatistics , year =

    Targeted Maximum Likelihood Learning , author =. The International Journal of Biostatistics , year =

  16. [24]

    and Polley, Eric C

    van der Laan, Mark J. and Polley, Eric C. and Hubbard, Alan E. , journal =. 2007 , volume =

    2007

  17. [25]

    2011 , doi =

    Targeted Learning: Causal Inference for Observational and Experimental Data , author =. 2011 , doi =

    2011

  18. [26]

    Big Data , year =

    Targeted Learning in Healthcare Research , author =. Big Data , year =

  19. [27]

    American Journal of Epidemiology , year =

    Targeted Maximum Likelihood Estimation for Causal Inference in Observational Studies , author =. American Journal of Epidemiology , year =

  20. [28]

    Statistics in Medicine , year =

    Targeted Maximum Likelihood Estimation for a Binary Treatment: A Tutorial , author =. Statistics in Medicine , year =

  21. [29]

    Statistical Science , year =

    Demystifying Double Robustness: A Comparison of Alternative Strategies for Estimating a Population Mean from Incomplete Data , author =. Statistical Science , year =

  22. [30]

    The International Journal of Biostatistics , year =

    The Relative Performance of Targeted Maximum Likelihood Estimators , author =. The International Journal of Biostatistics , year =

  23. [31]

    2024 , doi =

    Causal Inference in Pharmaceutical Statistics , author =. 2024 , doi =

    2024

  24. [32]

    Doubly Robust Estimation of Desirability of Outcome Ranking (

    Shu, Shiyu and Hamasaki, Toshimitsu and Evans, Scott and Komarow, Lauren and van Duin, David and Diao, Guoqing , journal =. Doubly Robust Estimation of Desirability of Outcome Ranking (. 2026 , pages =

    2026

  25. [33]

    American Journal of Epidemiology , year =

    Constructing Inverse Probability Weights for Marginal Structural Models , author =. American Journal of Epidemiology , year =

  26. [34]

    Biometrika , year =

    Dealing with Limited Overlap in Estimation of Average Treatment Effects , author =. Biometrika , year =

  27. [35]

    Journal of the American Statistical Association , year =

    Balancing Covariates via Propensity Score Weighting , author =. Journal of the American Statistical Association , year =

  28. [36]

    American Journal of Epidemiology , year =

    Treatment Effects in the Presence of Unmeasured Confounding: Dealing with Observations in the Tails of the Propensity Score Distribution---A Simulation Study , author =. American Journal of Epidemiology , year =

  29. [37]

    Econometrica , year =

    On the Role of the Propensity Score in Efficient Semiparametric Estimation of Average Treatment Effects , author =. Econometrica , year =

  30. [38]

    1998 , doi =

    Asymptotic Statistics , author =. 1998 , doi =

    1998

  31. [39]

    Statistics in Medicine , year =

    Stratification and weighting via the propensity score in estimation of causal treatment effects: A comparative study , author =. Statistics in Medicine , year =

  32. [40]

    Biometrical Journal , year =

    Cannas, Massimo and Arpino, Bruno , title =. Biometrical Journal , year =

  33. [41]

    and van der Laan, Mark J

    Phillips, Rachael V. and van der Laan, Mark J. and Lee, Hana and Gruber, Susan , title =. International Journal of Epidemiology , year =

  34. [42]

    2010 , month = nov, note =

    Asymptotic Theory for Cross-validated Targeted Maximum Likelihood Estimation , author =. 2010 , month = nov, note =

    2010

  35. [43]

    Statistics in Medicine , year =

    Performance of Cross-Validated Targeted Maximum Likelihood Estimation , author =. Statistics in Medicine , year =

  36. [44]

    and Figueroa, Jairo and Herc, Erica and Cordova, Ezequiel and Weston, Gregory and Ananth Tambyah, Paul and Garcia-Diaz, Julia and Kaye, Keith S

    Wang, Minggui and Ge, Lizhao and Chen, Liang and Komarow, Lauren and Hanson, Blake and Reyes, Jinnethe and Cober, Eric and Alenazi, Thamer and Zong, Zhiyong and Xie, Qing and Liu, Zhengyin and Li, Lanjuan and Yu, Yunsong and Gao, Hainv and Kanj, Souha S. and Figueroa, Jairo an...

  37. [45]

    and Cober, Eric and Herc, Erica and Alenazi, Thamer and Kaye, Keith S

    Reyes, Jinnethe and Komarow, Lauren and Chen, Liang and Ge, Lizhao and Hanson, Blake M. and Cober, Eric and Herc, Erica and Alenazi, Thamer and Kaye, Keith S. and Garcia-Diaz, Julia and Li, Lanjuan and Kanj, Souha S. and Liu, Zhengyin and O. Global Epidemiology and Clinical Ou...

  38. [46]

    and Komarow, Lauren and Chen, Liang and Hanson, Blake M

    van Duin, David and Arias, Cesar A. and Komarow, Lauren and Chen, Liang and Hanson, Blake M. and Weston, Gregory and Cober, Eric and Garner, Omai B. and Jacob, Jesse T. and Satlin, Michael J. and Fries, Bettina C. and Garcia-Diaz, Julia and Doi, Yohei and Dhar, Sorabh and Kaye...

  39. [47]

    and Wu, Qihang and Hamasaki, Toshimitsu , journal =

    Evans, Scott R. and Wu, Qihang and Hamasaki, Toshimitsu , journal =. Patient-Centric Pragmatic Clinical Trials: Opening the. 2026 , volume =

    2026

  40. [48]

    , booktitle =

    Hamasaki, Toshimitsu and Evans, Scott R. , booktitle =. The Desirability of Outcome Ranking (. 2025 , doi =

    2025

  41. [49]

    , journal =

    Yin, Anqi and Yuan, Ao and Tan, Ming T. , journal =. Highly Robust Causal Semiparametric. 2024 , volume =

    2024

  42. [50]

    Statistics in Biosciences , year =

    Enhanced Doubly Robust Procedure for Causal Inference , author =. Statistics in Biosciences , year =

  43. [51]

    and Hochberg, Yosef and Reiser, Benjamin , journal =

    Simonoff, Jeffrey S. and Hochberg, Yosef and Reiser, Benjamin , journal =. Response to Estimating. 1988 , volume =

    1988

  44. [52]

    Edwardes, Michael D

    deB. Edwardes, Michael D. , journal =. A Confidence Interval for. 1995 , volume =

    1995

  45. [53]

    Statistics in Medicine , year =

    Analysis of Ordered Composite Endpoints , author =. Statistics in Medicine , year =

  46. [54]

    and Seymour, John F

    Falchi, Lorenzo and Nijland, Marcel and Huang, Huiqiang and Linton, Kim M. and Seymour, John F. and Tao, Rong and Kwiatek, Michal and Costa, Abel and Vassilakopoulos, Theodoros P. and Greil, Richard and Jim. Epcoritamab, Lenalidomide, and Rituximab versus Lenalidomide and Ritu...

  47. [55]

    Optimising Precision and Power by Machine Learning in Randomised Trials with Ordinal and Time-to-Event Outcomes with an Application to

    Williams, Nicholas and Rosenblum, Michael and D. Optimising Precision and Power by Machine Learning in Randomised Trials with Ordinal and Time-to-Event Outcomes with an Application to. Journal of the Royal Statistical Society: Series A (Statistics in Society) , year =

  48. [56]

    Clinical Trials , year =

    Causal Interpretation of the Hazard Ratio in Randomized Clinical Trials , author =. Clinical Trials , year =

  49. [57]

    arXiv preprint arXiv:2203.06469 , year =

    Semiparametric Doubly Robust Targeted Double Machine Learning: A Review , author =. arXiv preprint arXiv:2203.06469 , year =

    arXiv

  50. [58]

    1965 , publisher =

    Survey Sampling , author =. 1965 , publisher =

    1965

  51. [59]

    and Stuart, Elizabeth A

    Austin, Peter C. and Stuart, Elizabeth A. , journal =. Moving Towards Best Practice When Using Inverse Probability of Treatment Weighting (. 2015 , volume =

    2015

  52. [60]

    The Econometrics Journal , year =

    Double/Debiased Machine Learning for Treatment and Structural Parameters , author =. The Econometrics Journal , year =

  53. [61]

    American Journal of Epidemiology , year =

    Challenges in Obtaining Valid Causal Effect Estimates With Machine Learning Algorithms , author =. American Journal of Epidemiology , year =

  54. [62]

    On causal estimation using

    Mao, Lu , journal =. On causal estimation using. 2018 , volume =

    2018

Pith tools

Reviewed August 8, 2026 · model on record in the stance chip above.