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Real-world data make a randomized trial more efficient only when bias is modest; the gain erodes with sample size and needs a block-jackknife interval.

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2026-07-12 07:02 UTC pith:AEMNAXC4

load-bearing objection Honest finite-sample audit of A-TMLE fusion: magnitude (not complexity) drives the gain, it erodes with n, and only a block jackknife calibrates the data-adaptive efficiency ratio. the 3 major comments →

arxiv 2607.02787 v1 pith:AEMNAXC4 submitted 2026-07-02 stat.ME

When Does Real-World Data Make a Randomized Trial More Efficient, and How Would You Know? A Report Card, an Efficiency Map, and Selection-Aware Inference for Adaptive-TMLE

M. Ehsan Karim This is my paper
classification stat.ME MSC 62G0562F1262P10
keywords adaptive TMLEreal-world evidencedata fusionefficiency gainselection-aware inferenceblock jackknifehighly adaptive lassoRCT+RWD
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

Augmenting a randomized trial with real-world data is often sold as an efficiency win, but how much efficiency a given fusion actually delivers, and how to put an honest interval on that gain, has been left vague. Using adaptive targeted maximum likelihood estimation as the running example, this paper supplies three practical tools: a report card that audits the data-adaptively learned bias model; a magnitude-by-complexity map of when fusion helps versus hurts relative to an efficient trial-only estimator; and a selection-aware standard error for the efficiency gain itself. The central empirical finding is that the finite-sample gain is driven mainly by the size of the real-world bias rather than how complicated that bias is: it crosses break-even near a moderate bias of about one residual standard deviation, and it shrinks toward parity as the trial grows. An exact population variance identity explains why magnitude dominates. Of ten candidate standard errors for the data-adaptive gain, only a block jackknife attains nominal (conservative) coverage; naive, cross-fit, and related intervals undercover. Three open fusions — HIV, public health, and job training — span the map and show what an honest interval changes for real-world evidence.

Core claim

Relative to a matched efficient trial-only estimator, the finite-sample efficiency gain of A-TMLE is governed primarily by the magnitude of real-world bias rather than its functional complexity. The gain falls from roughly 1.15 at zero bias to well below one at large bias, crosses parity near one residual standard deviation of bias, and erodes toward one as the trial sample size grows; the advantage is therefore finite-sample rather than a form of super-efficiency. Only a block jackknife among ten candidates supplies a calibrated interval for this data-adaptive gain.

What carries the argument

The exact population-oracle variance identity for the pooled-projection influence curve, var(D_A) = a + b m^{2}, under a forced intercept-only working model. It shows that bias magnitude m enters at first order through m^{2} with no linear-in-m or first-order shape term, which explains why magnitude, not complexity, drives the efficiency map.

Load-bearing premise

The main simulation designs assign trial membership completely at random, so the enrollment-positivity condition holds automatically and does no real work; the paper’s efficiency and report-card conclusions are therefore strictly for that constant-positivity regime.

What would settle it

Re-run the magnitude-by-complexity efficiency map under genuinely W-dependent trial enrollment with the same matched trial-only reference: if the gain ceases to fall monotonically with bias magnitude, or if the parity crossing moves far from one residual SD, the magnitude-dominance claim fails.

Watch this falsifier — get emailed when new claim-graph text bears on it.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 4 minor

Summary. The paper develops three tools for honest assessment of RCT+RWD fusion under adaptive-TMLE: (1) a report card that audits the data-adaptively learned bias model τ_S (recovery, influence-curve variance attribution, drift); (2) an efficiency map of the finite-sample gain R = var(D_rct)/var(D_atmle) as a function of bias magnitude, complexity, reference estimator, and n, showing magnitude dominance, a break-even near m ≈ 1 residual SD, and erosion toward parity as the trial grows; and (3) selection-aware inference for R as a data-adaptive estimand, where among ten candidate SEs only a block jackknife attains nominal (conservative) fixed-truth coverage. Proposition 1 supplies a population-oracle identity explaining magnitude dominance of var(D_A) under a forced intercept-only working model. Three open fusions (ACTG175, WASH Benefits, LaLonde NSW) illustrate the toolkit.

Significance. If the results hold, the paper converts a qualitative promise of fusion efficiency into an inspectable, quantitative, and honestly interval-estimated object. Strengths include a large Monte Carlo grid (B=1000, 15 cells, zero failures), a proved population identity (Proposition 1, Web Appendix G) under stated restrictions, a three-reference panel and n-ladder, four robustness slices, fixed-truth scoring of coverage, and a public reproducibility harness built on the atmle package. The report card and selection-aware SE for a data-adaptive efficiency estimand are useful beyond A-TMLE and address a genuine gap in adaptive/debiased ML reporting for real-world evidence.

major comments (3)
  1. [Section 2; Web Appendix E] Section 2 scope caveat and Web Appendix E: main DGPs assign trial membership deterministically so Π(W) is constant and enrollment positivity holds vacuously. Under W-dependent enrollment the paper itself reports A-TMLE ATE coverage degradation that worsens with n at the wiggly large-bias corner (0.82 o0.72). The efficiency-map and report-card conclusions are therefore strictly for the constant-positivity regime. A fuller selective-enrollment map (or a clear statement that the headline map is restricted to constant Π) is needed before the practical recommendation can be taken as general.
  2. [Section 5; Discussion] Section 5.1–5.2: two of the three real fusions (ACTG175, WASH Benefits) use constructed within-trial external arms rather than independently collected observational data; only LaLonde uses genuine non-experimental controls and lands at or below parity. The illustrations demonstrate the toolkit end-to-end but do not exercise the large, unmeasured-confounded RWD regime that motivates the method. Pairing the report card and jackknife interval with at least one genuine observational fusion (as the original A-TMLE paper did) would strengthen external validity of the real-data claims.
  3. [Section 4.5; Recommendation] Section 4.5 and Recommendation: the block-jackknife result is empirical calibration (coverage 0.98–1.00, ratio ≈1.6–2.2), not a consistency theorem; the paper correctly states this. The recommendation to report gain CIs with the jackknife is therefore defensible only as the best-calibrated method among the ten candidates on this grid. The manuscript should state more prominently that the SE is inconsistent for this non-smooth statistic and that an exact selection-aware SE remains open, so that practitioners do not treat the interval as asymptotically exact.
minor comments (4)
  1. [Table 3] Table 3: recovery cor* is undefined at m=0; the table marks this with —, but a one-line note that recovery is only meaningful when there is bias to recover would help readers scanning the table.
  2. [Figure 2] Figure 2 alt text and caption are clear; ensure the published figure includes the arm-specific W1-dependence callout in the main caption, not only the alt text.
  3. [Section 4.3.1] Section 4.3.1: the MSE-ratio vs IC-variance gain discrepancy (MSE parity reached earlier) is important; a short sentence in the main text flagging that MSE-based claims of gain can be slightly more pessimistic would help applied readers.
  4. [Reproducibility] Web Appendix F maps results to code; a one-paragraph pointer in the main Reproducibility section to the exact commit and the laptop-vs-SLURM split would make the public harness easier to navigate.

Circularity Check

0 steps flagged

No significant circularity: efficiency map and SE calibration are empirical against external RCT-only benchmarks and a locked fixed truth; Proposition 1 is a restricted population identity used only to explain magnitude dominance of var(D_A).

full rationale

The paper's load-bearing claims are (i) a finite-sample efficiency map of A-TMLE vs matched RCT-only estimators, (ii) magnitude-over-complexity dominance of that gain, and (iii) block-jackknife-only calibrated SEs for the data-adaptive gain R. None reduces to its inputs by construction. R is defined as var(D_rct)/var(D_atmle) and then measured on a simulation grid (B=1000) against three external RCT-only references (matched GLM, SuperLearner, relaxed-HAL) computed on the same fits; coverage of candidate SEs is scored against a locked B=1000 truth, not each method's own mean—explicitly anti-circular design. Proposition 1 is an exact population-oracle identity under a forced intercept-only working model and stated nuisance assumptions, used only to explain why var(D_A) scales with m^{2}; the full finite-sample map, n-erosion, and complexity second-order effects remain empirical. A-TMLE/atmle citations are the running method under audit, not a self-citation uniqueness chain by the present author. The jackknife recommendation is empirical calibration with explicit non-consistency caveats. No fitted parameter is relabeled as a prediction; no uniqueness theorem is imported from overlapping authors; no known result is merely renamed. Score 0 is the honest finding.

Axiom & Free-Parameter Ledger

4 free parameters · 5 axioms · 2 invented entities

The paper is empirical-methodological: load-bearing content is simulation design, identification assumptions inherited from A-TMLE, and the oracle restriction in Proposition 1. Free parameters are design knobs (bias magnitude grid, sample sizes, jackknife fold structure), not fitted constants that force the central claim. Invented entities are diagnostic constructs (report card, efficiency gain R), not physical postulates.

free parameters (4)
  • bias magnitude grid m ∈ {0, 0.5, 1, 2, 4}
    Hand-chosen design levels that define the efficiency map; break-even near m≈1 is an empirical finding on this grid, not a universal constant.
  • n_rct ∈ {250, 400, 800} and external multiples 1×–3×
    Sample-size ladder chosen to match the original A-TMLE paper's scale; erosion-with-n claim is relative to these sizes.
  • block-jackknife fold structure (S-stratified leave-fold-out)
    Resampling design choice that delivers the only calibrated SE; coverage 0.98–1.00 and ratio 1.6–2.2 are empirical for this design.
  • HAL penalty multiplicity / undersmoothing n_λ ∈ {1,3,5}
    Smoothing choice checked in a dedicated slice; does not drive the map but affects finite-sample bias at large m.
axioms (5)
  • domain assumption Trial-population ATE identified from within-trial conditionals under consistency, RCT randomization, and treatment positivity; fusion adds trial-enrollment positivity 0<Π(W)<1.
    Section 2; standard causal identification for RCT+RWD fusion as stated by van der Laan et al. 2026.
  • domain assumption A-TMLE is √n-consistent and asymptotically linear for ψ0 up to a second-order remainder when the working model approximates the oracle bias at rate n^{-1/4}.
    Inherited from the running-example theory (van der Laan et al. 2026); used to interpret R as a variance contrast when bias is controlled.
  • ad hoc to paper Proposition 1: under oracle nuisances and forced intercept-only working model Φ≡1, var(D_A)=a+b m^2 with no linear-in-m term.
    Section 4.4 / Web Appendix G; the forced intercept-only restriction is assumed for the identity and is stronger than homogeneous within-trial CATE alone.
  • ad hoc to paper Main DGPs: homogeneous CATE=1.5, Gaussian noise, deterministic trial membership (constant Π), bias only in external arm.
    Section 4.1 design; makes efficiency a pure variance contrast and makes positivity hold trivially in the main grid.
  • domain assumption Efficiency gain R = var(D_rct)/var(D_atmle) is the right finite-sample object, with matched cross-fitted GLM-AIPW/TMLE as the primary reference.
    Section 2–4; reference-dependence is stated explicitly and probed with SuperLearner and HAL references.
invented entities (2)
  • Bias-model report card (recovery cor*, variance attribution, drift) independent evidence
    purpose: Make the data-adaptively learned τ_S auditable rather than an inferential nuisance.
    Diagnostic construct; recovery validated only on known DGPs; on real data only size and attribution are available.
  • Efficiency gain R as a data-adaptive estimand with selection-aware SE independent evidence
    purpose: Quantify and interval-estimate how much fusion buys relative to an efficient trial-only estimator.
    Defined from influence-curve variances; not a new physical entity but a new inferential target for this literature.

pith-pipeline@v1.1.0-grok45 · 31380 in / 3921 out tokens · 34519 ms · 2026-07-12T07:02:16.618679+00:00 · methodology

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read the original abstract

Augmenting a randomized controlled trial with real-world data promises greater efficiency, but how much a given fusion actually delivers, and how to attach honest uncertainty to that gain, is rarely characterized. Using adaptive targeted maximum likelihood estimation (A-TMLE) as the running example, we develop three reproducible tools for honest evidence from combined trial and real-world data. First, a report card that makes the estimator's data-adaptively learned bias model auditable, measuring how well it recovers the true enrollment-effect surface and attributing the estimator's variance to its structural parts. Second, a map of when fusion helps versus hurts, benchmarked against an efficient trial-only estimator: the gain is driven primarily by the magnitude of the real-world bias rather than its functional complexity, a dominance an exact variance identity explains; it crosses break-even near a moderate bias and erodes as the trial grows, so the advantage is finite-sample rather than a form of super-efficiency. Third, selection-aware inference for the gain, treated as a data-adaptive estimand: the naive standard error undercovers, and among ten candidate standard errors only a block jackknife is calibrated, though conservatively so. Three openly available fusions, in a biomedical HIV trial, a public-health trial, and a job-training trial, span the map and show the difference an honest interval makes for real-world evidence.

Figures

Figures reproduced from arXiv: 2607.02787 by M. Ehsan Karim.

Figure 1
Figure 1. Figure 1: Schematic. A-TMLE decomposes the trial-population ATE into a pooled projection Ψe (via the working model τA) minus a bias projection Ψ# (via the learned τS); the efficient influence curve is D = DA − DS. Contribution (1) audits τS (the report card); contribution (2) maps the gain R; contribution (3) builds a calibrated interval for R via the block jackknife. Alt text: Flow diagram. Trial-plus-real-world da… view at source ↗
Figure 2
Figure 2. Figure 2: Recovery surface. The learned bias model τbS(W, A) (solid, from cross-validated relaxed￾HAL) against the truth τS,0(W, A) = −B(W, A) (dashed), sliced at W2 = W3 = 0, by treatment arm (A = 0/A = 1, columns) and scenario (rows). The report card reproduces the structure of the enrollment-effect surface, including the arm-specific W1-dependence. Alt text: Grid of line plots. In each panel the learned bias-mode… view at source ↗
Figure 3
Figure 3. Figure 3: The efficiency gain map. Influence-curve gain (6) versus bias magnitude m, by complexity. The gain falls monotonically with magnitude and crosses parity just above m ≈ 1; complexity separates the curves only at large magnitude. Alt text: Line plot of the efficiency gain (vertical axis) against bias magnitude m (horizontal axis) for three bias complexities. All three curves fall monotonically with m and cro… view at source ↗
Figure 4
Figure 4. Figure 4: Fixed-truth coverage of the ten selection-aware SEs. 95% CI coverage of the efficiency gain, scored against the locked B = 1000 truth, by bias magnitude m and shape (faceted); the dashed line marks the 0.95 target. The block jackknife (gold) is the only method to reach the target (0.98–1.00); the other nine fall entirely within the shaded min–max envelope (never above 0.87), undercovering across all three … view at source ↗

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Reference graph

Works this paper leans on

70 extracted references · 5 canonical work pages

  1. [1]

    and Qiu, Sky and Tarp, Jens Magelund and van der Laan, Lars , title =

    van der Laan, Mark J. and Qiu, Sky and Tarp, Jens Magelund and van der Laan, Lars , title =. Journal of Causal Inference , year =

  2. [4]

    and Rubin, Daniel , title =

    van der Laan, Mark J. and Rubin, Daniel , title =. The International Journal of Biostatistics , year =

  3. [5]

    and Rose, Sherri , title =

    van der Laan, Mark J. and Rose, Sherri , title =. 2011 , isbn =

    2011

  4. [6]

    and Rose, Sherri , title =

    van der Laan, Mark J. and Rose, Sherri , title =. 2018 , isbn =

    2018

  5. [7]

    , title =

    Zheng, Wenjing and van der Laan, Mark J. , title =. Targeted Learning: Causal Inference for Observational and Experimental Data , editor =. 2011 , doi =

    2011

  6. [8]

    , title =

    Benkeser, David and van der Laan, Mark J. , title =. 2016 IEEE International Conference on Data Science and Advanced Analytics (DSAA) , pages =. 2016 , doi =

    2016

  7. [9]

    , title =

    van der Laan, Mark J. , title =. The International Journal of Biostatistics , year =

  8. [10]

    and Coyle, Jeremy R

    Hejazi, Nima S. and Coyle, Jeremy R. and van der Laan, Mark J. , title =. Journal of Open Source Software , year =

  9. [11]

    and Polley, Eric C

    van der Laan, Mark J. and Polley, Eric C. and Hubbard, Alan E. , title =. Statistical Applications in Genetics and Molecular Biology , year =

  10. [12]

    and Hejazi, Nima S

    Coyle, Jeremy R. and Hejazi, Nima S. and Malenica, Ivana and Phillips, Rachael V. and Sofrygin, Oleg , title =. 2023 , note =

    2023

  11. [13]

    and Kherad-Pajouh, Sara and van der Laan, Mark J

    Hubbard, Alan E. and Kherad-Pajouh, Sara and van der Laan, Mark J. , title =. The International Journal of Biostatistics , year =

  12. [14]

    The Econometrics Journal , year =

    Chernozhukov, Victor and Chetverikov, Denis and Demirer, Mert and Duflo, Esther and Hansen, Christian and Newey, Whitney and Robins, James , title =. The Econometrics Journal , year =

  13. [15]

    and Balakrishnan, Sivaraman and Wasserman, Larry , title =

    Kuchibhotla, Arun K. and Balakrishnan, Sivaraman and Wasserman, Larry , title =. Journal of the Royal Statistical Society: Series B (Statistical Methodology) , year =

  14. [16]

    The Annals of Statistics , year =

    Efron, Bradley and Stein, Charles , title =. The Annals of Statistics , year =

  15. [17]

    , title =

    Quenouille, Maurice H. , title =. Biometrika , year =

  16. [18]

    and Klaassen, Chris A

    Bickel, Peter J. and Klaassen, Chris A. J. and Ritov, Ya'acov and Wellner, Jon A. , title =. 1993 , isbn =

    1993

  17. [19]

    The American Statistician , year =

    Hines, Oliver and Dukes, Oliver and Diaz-Ordaz, Karla and Vansteelandt, Stijn , title =. The American Statistician , year =

  18. [20]

    Causal Inference Methods for Combining Randomized Trials and Observational Studies: A Review , journal =

    Colnet, B. Causal Inference Methods for Combining Randomized Trials and Observational Studies: A Review , journal =. 2024 , volume =

    2024

  19. [21]

    Journal of the Royal Statistical Society: Series B (Statistical Methodology) , year =

    Yang, Shu and Gao, Chenyin and Zeng, Donglin and Wang, Xiaofei , title =. Journal of the Royal Statistical Society: Series B (Statistical Methodology) , year =

  20. [22]

    Journal of the American Statistical Association , year =

    Yang, Shu and Ding, Peng , title =. Journal of the American Statistical Association , year =

  21. [23]

    Rosenman, Evan T. R. and Basse, Guillaume and Owen, Art B. and Baiocchi, Mike , title =. Biometrics , year =

  22. [24]

    2018 , month =

    Framework for. 2018 , month =

    2018

  23. [25]

    34) , year =

    21st Century Cures Act (Public Law 114-255, H.R. 34) , year =

  24. [26]

    and Rahman, Mahbubur and Arnold, Benjamin F

    Luby, Stephen P. and Rahman, Mahbubur and Arnold, Benjamin F. and Unicomb, Leanne and others , title =. The Lancet Global Health , year =

  25. [27]

    and Petersen, Maya and van der Laan, Mark , title =

    Dang, Lauren Eyler and Tarp, Jens Magelund and Abrahamsen, Trine Julie and Kvist, Kajsa and Buse, John B. and Petersen, Maya and van der Laan, Mark , title =. Journal of Causal Inference , year =

  26. [28]

    and Katzenstein, David A

    Hammer, Scott M. and Katzenstein, David A. and Hughes, Michael D. and Gundacker, Holly and Schooley, Robert T. and Haubrich, Richard H. and Henry, W. Keith and Lederman, Michael M. and Phair, John P. and Niu, Manette and Hirsch, Martin S. and Merigan, Thomas C. , title =. New England Journal of Medicine , year =

  27. [29]

    and Lu, Xiaomin and Zhang, Min and Davidian, Marie and Tsiatis, Anastasios A

    Juraska, Michal and Gilbert, Peter B. and Lu, Xiaomin and Zhang, Min and Davidian, Marie and Tsiatis, Anastasios A. , title =. 2022 , note =

    2022

  28. [30]

    and Robertson, Sarah E

    Dahabreh, Issa J. and Robertson, Sarah E. and Steingrimsson, Jon A. and Stuart, Elizabeth A. and Hern. Extending inferences from a randomized trial to a new target population , journal =. 2020 , volume =

    2020

  29. [31]

    and Cole, Stephen R

    Stuart, Elizabeth A. and Cole, Stephen R. and Bradshaw, Catherine P. and Leaf, Philip J. , title =. Journal of the Royal Statistical Society: Series A (Statistics in Society) , year =

  30. [32]

    and Lesko, Catherine R

    Westreich, Daniel and Edwards, Jessie K. and Lesko, Catherine R. and Stuart, Elizabeth and Cole, Stephen R. , title =. American Journal of Epidemiology , year =

  31. [33]

    Journal of the American Statistical Association , year =

    Efron, Bradley , title =. Journal of the American Statistical Association , year =

  32. [34]

    The Annals of Statistics , year =

    Berk, Richard and Brown, Lawrence and Buja, Andreas and Zhang, Kai and Zhao, Linda , title =. The Annals of Statistics , year =

  33. [35]

    and Sun, Dennis L

    Lee, Jason D. and Sun, Dennis L. and Sun, Yuekai and Taylor, Jonathan E. , title =. The Annals of Statistics , year =

  34. [36]

    2014 , journal =

    Optimal Inference After Model Selection , author =. 2014 , journal =. 1410.2597 , archivePrefix =

    Pith/arXiv arXiv 2014

  35. [37]

    Shao, Jun and Wu, C. F. J. , title =. The Annals of Statistics , year =

  36. [38]

    and Chen, Ming-Hui , title =

    Ibrahim, Joseph G. and Chen, Ming-Hui , title =. Statistical Science , year =

  37. [39]

    Biometrics , year =

    Schmidli, Heinz and Gsteiger, Sandro and Roychoudhury, Satrajit and O'Hagan, Anthony and Spiegelhalter, David and Neuenschwander, Beat , title =. Biometrics , year =

  38. [40]

    and Kinnersley, Nelson and Lindborg, Stacy and Micallef, Sandrine and Roychoudhury, Satrajit and Thompson, Laura , title =

    Viele, Kert and Berry, Scott and Neuenschwander, Beat and Amzal, Billy and Chen, Fang and Enas, Nathan and Hobbs, Brian and Ibrahim, Joseph G. and Kinnersley, Nelson and Lindborg, Stacy and Micallef, Sandrine and Roychoudhury, Satrajit and Thompson, Laura , title =. Pharmaceutical Statistics , year =

  39. [41]

    , title =

    Newey, Whitney K. , title =. Journal of Applied Econometrics , volume =. 1990 , doi =

    1990

  40. [42]

    , title =

    Pocock, Stuart J. , title =. Journal of Chronic Diseases , year =

  41. [43]

    21st century cures act (public law 114-255, h.r

    114th United States Congress . 21st century cures act (public law 114-255, h.r. 34), 2016. URL https://www.congress.gov/114/plaws/publ255/PLAW-114publ255.pdf. Enacted December 13, 2016

    2016

  42. [44]

    R. Berk, L. Brown, A. Buja, K. Zhang, and L. Zhao. Valid post-selection inference. The Annals of Statistics, 41 0 (2): 0 802--837, 2013. doi:10.1214/12-AOS1077

    doi:10.1214/12-aos1077 2013

  43. [45]

    Chernozhukov, D

    V. Chernozhukov, D. Chetverikov, M. Demirer, E. Duflo, C. Hansen, W. Newey, and J. Robins. Double/debiased machine learning for treatment and structural parameters. The Econometrics Journal, 21 0 (1): 0 C1--C68, 2018. doi:10.1111/ectj.12097

    doi:10.1111/ectj.12097 2018

  44. [46]

    Colnet, I

    B. Colnet, I. Mayer, G. Chen, A. Dieng, R. Li, G. Varoquaux, J.-P. Vert, J. Josse, and S. Yang. Causal inference methods for combining randomized trials and observational studies: A review. Statistical Science, 39 0 (1): 0 165--191, 2024. doi:10.1214/23-STS889. arXiv:2011.08047

    Pith/arXiv arXiv doi:10.1214/23-sts889 2024

  45. [47]

    I. J. Dahabreh, S. E. Robertson, J. A. Steingrimsson, E. A. Stuart, and M. A. Hern \'a n. Extending inferences from a randomized trial to a new target population. Statistics in Medicine, 39 0 (14): 0 1999--2014, 2020. doi:10.1002/sim.8426

    doi:10.1002/sim.8426 1999

  46. [48]

    L. E. Dang, J. M. Tarp, T. J. Abrahamsen, K. Kvist, J. B. Buse, M. Petersen, and M. van der Laan. Experiment-selector cross-validated targeted maximum likelihood estimator for hybrid RCT -external data studies. Journal of Causal Inference, 13 0 (1): 0 20240041, 2025. doi:10.1515/jci-2024-0041. arXiv:2210.05802

    work page doi:10.1515/jci-2024-0041 2025

  47. [49]

    Efron and C

    B. Efron and C. Stein. The jackknife estimate of variance. The Annals of Statistics, 9 0 (3): 0 586--596, 1981. doi:10.1214/aos/1176345462

    doi:10.1214/aos/1176345462 1981

  48. [50]

    Fithian, D

    W. Fithian, D. L. Sun, and J. Taylor. Optimal inference after model selection. arXiv preprint arXiv:1410.2597, 2014. doi:10.48550/arXiv.1410.2597

    Pith/arXiv arXiv doi:10.48550/arxiv.1410.2597 2014

  49. [51]

    S. M. Hammer, D. A. Katzenstein, M. D. Hughes, H. Gundacker, R. T. Schooley, R. H. Haubrich, W. K. Henry, M. M. Lederman, J. P. Phair, M. Niu, M. S. Hirsch, and T. C. Merigan. A trial comparing nucleoside monotherapy with combination therapy in HIV -infected adults with CD4 cell counts from 200 to 500 per cubic millimeter. New England Journal of Medicine,...

    doi:10.1056/nejm199610103351501 1996

  50. [52]

    A. E. Hubbard, S. Kherad-Pajouh, and M. J. van der Laan. Statistical inference for data adaptive target parameters. The International Journal of Biostatistics, 12 0 (1): 0 3--19, 2016. doi:10.1515/ijb-2015-0013

    work page doi:10.1515/ijb-2015-0013 2016

  51. [53]

    J. G. Ibrahim and M.-H. Chen. Power prior distributions for regression models. Statistical Science, 15 0 (1): 0 46--60, 2000. doi:10.1214/ss/1009212673

    doi:10.1214/ss/1009212673 2000

  52. [54]

    Juraska, P

    M. Juraska, P. B. Gilbert, X. Lu, M. Zhang, M. Davidian, and A. A. Tsiatis. speff2trial : Semiparametric Efficient Estimation for a Two-Sample Treatment Effect , 2022. URL https://CRAN.R-project.org/package=speff2trial. R package version 1.0.5; includes the ACTG175 dataset

    2022

  53. [55]

    A. K. Kuchibhotla, S. Balakrishnan, and L. Wasserman. The HulC : Confidence regions from convex hulls. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 86 0 (3): 0 586--622, 2024. doi:10.1093/jrsssb/qkad134. arXiv:2105.14577

    Pith/arXiv arXiv doi:10.1093/jrsssb/qkad134 2024

  54. [56]

    J. D. Lee, D. L. Sun, Y. Sun, and J. E. Taylor. Exact post-selection inference, with application to the lasso. The Annals of Statistics, 44 0 (3): 0 907--927, 2016. doi:10.1214/15-AOS1371

    doi:10.1214/15-aos1371 2016

  55. [57]

    Y. Li, S. Qiu, Z. Wang, and M. van der Laan. Regularized targeted maximum likelihood estimation in highly adaptive lasso implied working models. arXiv preprint arXiv:2506.17214, 2025. URL https://arxiv.org/abs/2506.17214. stat.ME

    Pith/arXiv arXiv 2025

  56. [58]

    S. P. Luby, M. Rahman, B. F. Arnold, L. Unicomb, et al. Effects of water quality, sanitation, handwashing, and nutritional interventions on diarrhoea and child growth in rural Bangladesh : A cluster randomised controlled trial. The Lancet Global Health, 6 0 (3): 0 e302--e315, 2018. doi:10.1016/S2214-109X(17)30490-4

    work page doi:10.1016/s2214-109x(17)30490-4 2018

  57. [59]

    S. J. Pocock. The combination of randomized and historical controls in clinical trials. Journal of Chronic Diseases, 29 0 (3): 0 175--188, 1976. doi:10.1016/0021-9681(76)90044-8

    work page doi:10.1016/0021-9681(76)90044-8 1976

  58. [60]

    M. H. Quenouille. Notes on bias in estimation. Biometrika, 43 0 (3--4): 0 353--360, 1956. doi:10.1093/biomet/43.3-4.353

    work page doi:10.1093/biomet/43.3-4.353 1956

  59. [61]

    E. T. R. Rosenman, G. Basse, A. B. Owen, and M. Baiocchi. Combining observational and experimental datasets using shrinkage estimators. Biometrics, 79 0 (4): 0 2961--2973, 2023. doi:10.1111/biom.13827. arXiv:2002.06708

    Pith/arXiv arXiv doi:10.1111/biom.13827 2023

  60. [62]

    Schmidli, S

    H. Schmidli, S. Gsteiger, S. Roychoudhury, A. O'Hagan, D. Spiegelhalter, and B. Neuenschwander. Robust meta-analytic-predictive priors in clinical trials with historical control information. Biometrics, 70 0 (4): 0 1023--1032, 2014. doi:10.1111/biom.12242

    doi:10.1111/biom.12242 2014

  61. [63]

    E. A. Stuart, S. R. Cole, C. P. Bradshaw, and P. J. Leaf. The use of propensity scores to assess the generalizability of results from randomized trials. Journal of the Royal Statistical Society: Series A (Statistics in Society), 174 0 (2): 0 369--386, 2011. doi:10.1111/j.1467-985X.2010.00673.x

    Pith/arXiv arXiv doi:10.1111/j.1467-985x.2010.00673.x 2011

  62. [64]

    Food and Drug Administration

    U.S. Food and Drug Administration . Framework for FDA's real-world evidence program. Technical report, U.S. Food and Drug Administration, 12 2018. URL https://www.fda.gov/media/120060/download

    2018

  63. [65]

    van der Laan, M

    L. van der Laan, M. Carone, A. Luedtke, and M. van der Laan. Adaptive debiased machine learning using data-driven model selection techniques. arXiv preprint arXiv:2307.12544, 2023. URL https://arxiv.org/abs/2307.12544. stat.ME

    arXiv 2023

  64. [66]

    M. J. van der Laan and D. Rubin. Targeted maximum likelihood learning. The International Journal of Biostatistics, 2 0 (1): 0 Article 11, 2006. doi:10.2202/1557-4679.1043

    doi:10.2202/1557-4679.1043 2006

  65. [67]

    M. J. van der Laan, S. Qiu, J. M. Tarp, and L. van der Laan. Adaptive- TMLE for the average treatment effect based on randomized controlled trial augmented with real-world data. Journal of Causal Inference, 14 0 (1): 0 20240025, 2026. doi:10.1515/jci-2024-0025. arXiv:2405.07186

    Pith/arXiv arXiv doi:10.1515/jci-2024-0025 2026

  66. [68]

    Viele, S

    K. Viele, S. Berry, B. Neuenschwander, B. Amzal, F. Chen, N. Enas, B. Hobbs, J. G. Ibrahim, N. Kinnersley, S. Lindborg, S. Micallef, S. Roychoudhury, and L. Thompson. Use of historical control data for assessing treatment effects in clinical trials. Pharmaceutical Statistics, 13 0 (1): 0 41--54, 2014. doi:10.1002/pst.1589

    doi:10.1002/pst.1589 2014

  67. [69]

    Westreich, J

    D. Westreich, J. K. Edwards, C. R. Lesko, E. Stuart, and S. R. Cole. Transportability of trial results using inverse odds of sampling weights. American Journal of Epidemiology, 186 0 (8): 0 1010--1014, 2017. doi:10.1093/aje/kwx164

    doi:10.1093/aje/kwx164 2017

  68. [70]

    Yang and P

    S. Yang and P. Ding. Combining multiple observational data sources to estimate causal effects. Journal of the American Statistical Association, 115 0 (531): 0 1540--1554, 2020. doi:10.1080/01621459.2019.1609973

    doi:10.1080/01621459.2019.1609973 2020

  69. [71]

    S. Yang, C. Gao, D. Zeng, and X. Wang. Elastic integrative analysis of randomised trial and real-world data for treatment heterogeneity estimation. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 85 0 (3): 0 575--596, 2023. doi:10.1093/jrsssb/qkad017. arXiv:2005.10579

    Pith/arXiv arXiv doi:10.1093/jrsssb/qkad017 2023

  70. [72]

    Zheng and M

    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 Learning: Causal Inference for Observational and Experimental Data, chapter 27, pages 459--474. Springer, New York, 2011. doi:10.1007/978-1-4419-9782-1_27

    doi:10.1007/978-1-4419-9782-1_27 2011