Pith. sign in

REVIEW 1 major objections 6 minor 31 references

Which Regularized Propensity-Score and Doubly Robust Methods Are Best Calibrated When Exposures or Outcomes Are Rare? A Plasmode Study of Proxy-Based Confounding Adjustment

T0 review · 1 major / 6 minor · reviewed 2026-07-09 · glm-5.2

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

Pith's one-line read Rare exposures break standard confounding adjustment; targeted selection fixes them

desk verdict Useful benchmark of regularized confounding-adjustment pipelines, but the coverage ranking is confounded by inference method read the letter →

arxiv 2607.07065 v1 pith:NQKPBO6U submitted 2026-07-08 stat.AP stat.COstat.ME

M. Ehsan Karim , Wanqing Hu This is my paper
classification stat.APstat.COstat.ME
keywords propensityscoredoublyrobustestimationTMLEvariableselectionLASSOconfoundingadjustmentplasmodesimulationrareexposure
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 sets up a head-to-head contest among ten statistical pipelines used to remove confounding bias in observational health studies where hundreds of proxy variables compete for a few outcome events. Using a plasmode simulation—real covariate data from a national health survey with a simulated null effect injected so that any nonzero estimate is pure residual bias—the authors show that when the exposure is rare, the most common approach (LASSO-selected propensity scores combined with inverse-probability weighting) produces the largest bias and unstable estimates. Switching the downstream estimator from weighting to a doubly robust targeted maximum likelihood step removes that bias and instability, at the cost of slightly under-covering confidence intervals. Methods that select variables based on their association with the outcome rather than the exposure—outcome-adaptive LASSO and group LASSO (GLiDeR)—maintain near-nominal 95% coverage across all rarity settings. The highly adaptive LASSO used as pure G-computation achieves near-zero bias but produces absurdly narrow intervals that cover the truth nearly 100% of the time, inflating relative error to 106–186%. The best-calibrated methods are also the slowest, ranging from under one second to over sixteen hours per analysis on a single core.

What carries the argument

The comparison hinges on two axes: (1) five regularized variable-selection families—traditional LASSO, collaborative-controlled LASSO, outcome-adaptive LASSO (OAL), group LASSO/GLiDeR, and highly adaptive LASSO (HAL)—that determine which proxies enter the adjustment set, and (2) two downstream estimators—IPTW (weighting by inverse treatment probability) and TMLE (doubly robust targeted updating of an outcome regression). The plasmode simulation design preserves real covariate correlations from NHANES data while imposing a known null risk difference, so any deviation from zero is measurable confounding bias. Performance is assessed via bias, coverage of 95% intervals, relative error of model–

What would settle it

If outcome-aware selection (OAL, GLiDeR) or HAL-TMLE failed to maintain near-nominal coverage under rare exposure or rare outcome in an independent plasmode with a different anchor dataset and a misspecified propensity model, the central recommendation would not hold.

Watch

Extended reading notes

Core claim

The decisive stressor is not the number of variables or the outcome rarity alone but the combination of rare exposure with weighting-based estimation. Under rare exposure (9.4% prevalence), LASSO-IPTW bias reaches −5.2×10⁻³ with inflated standard errors and conservative over-coverage near 98%, while replacing IPTW with TMLE for the same nuisance models cuts bias to near zero and reduces empirical SE, though coverage drops to 91–93%. Outcome-aware selection strategies (OAL, GLiDeR) and HAL-TMLE maintain 94–95% coverage across all three scenarios, making the choice between selection strategy and downstream estimator the central lever for calibration under rarity.

Load-bearing premise

The simulation generates exposure from a correctly specified main-terms logistic model, so the true propensity score lies within the parametric class that all propensity-based pipelines fit. This removes propensity-model misspecification as a bias source, meaning the strong calibration of outcome-aware methods is conditional on a correctly specified exposure model—a condition unlikely to hold in real healthcare database studies.

Editorial extensions

If this is right

  • Researchers using healthcare databases with rare exposures should avoid LASSO-IPTW and either adopt outcome-adaptive selection or pair their selection with a doubly robust TMLE step to avoid the bias and instability documented here.
  • The six-order-of-magnitude runtime spread (sub-second to 16+ hours) means that method choice in applied pharmacoepidemiology is effectively a compute-budget decision as much as a statistical one, with HAL-TMLE offering the best calibration-per-compute trade-off.
  • The finding that HAL G-computation produces near-unity coverage with 106–186% relative error suggests that bootstrap-based inference for highly flexible estimators can systematically misrepresent uncertainty even when point estimates are accurate.
  • The rare-exposure arm exposed the largest methodological gaps, suggesting that future proxy-adjustment benchmarks should default to testing under rarity rather than balanced conditions.

Reading between the lines

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

  • If the true propensity model were misspecified—as it likely is in real claims data where exposure drivers are poorly captured—the near-nominal calibration of OAL and GLiDeR might degrade, since the simulation's correctly specified PS gives all PS-based pipelines a common-mode advantage that would not hold in practice.
  • The mild undercoverage of TMLE pipelines under rarity (91–93%) may reflect a general tension: influence-curve standard errors condition on the selected nuisance model and thus ignore selection uncertainty, whereas bootstrap-based methods propagate it—at the cost of hours of computation.
  • The prescription-derived proxies in this anchor dataset are predominantly outcome predictors with weak treatment association, so the simulation may under-test scenarios where proxies are strong confounders of treatment rather than outcome.
  • Extending the comparison to non-null effects would test whether the calibration ranking at the null transfers to power and bias under realistic effect sizes, which the authors flag as a one-argument change to their released pipeline.
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

1 major / 6 minor

Summary. This manuscript compares ten regularized confounding-adjustment pipelines—spanning traditional LASSO, collaborative-controlled LASSO, outcome-adaptive LASSO (OAL), group LASSO/GLiDeR, and highly adaptive LASSO (HAL), each paired with IPTW and/or TMLE—under a plasmode simulation anchored on NHANES 2013–2018 data. Three scenarios (frequent, rare-exposure, rare-outcome) are evaluated under a known null (RD = 0), with bias, coverage, relative error, and runtime reported. The central finding is that outcome-aware selection (OAL, GLiDeR) and doubly robust estimation (HAL-TMLE) are best calibrated, while LASSO-IPTW shows large bias under rare exposure and HAL G-computation over-covers with large relative error. The design is well-structured (ADEMP framework, 1000 replicates, common-replicate comparison, null truth anchor), and the runtime accounting is a valuable practical contribution.

Significance. The paper addresses a genuine gap: no prior single-design study has assembled this breadth of regularized selection families crossed with IPTW versus doubly robust estimation while varying exposure prevalence and reporting compute cost. The null-anchored plasmode design is a strength—it isolates residual-confounding bias cleanly. The runtime table (Table 4) and practical guidance table (Table 5) are useful for practitioners. The reproducible code repository and bundled anchor data are commendable. The finding that replacing IPTW with TMLE removes rare-exposure bias and instability is practically important and well-demonstrated.

major comments (1)
  1. §4.3 and Table 5: The calibration ranking identifying OAL (IPTW) and GLiDeR as 'best calibrated' (coverage 94–95%) while LASSO-TMLE, C-TMLE, and Standard TMLE 'under-cover modestly' (91–93%) is confounded by the inference method. OAL and GLiDeR use 200-replicate bootstrap SEs that propagate selection uncertainty through the full pipeline, while every under-covering TMLE method uses efficient influence-curve SEs that condition on the cross-validated nuisance model. The authors acknowledge this in §4.3 ('the calibration and runtime comparisons are therefore partly confounded by which error sources each SE captures'), but Table 5's practical recommendation treats calibration as a property of the selection/estimation strategy rather than the inference method. The systematic pattern is striking: all bootstrap-based methods (OAL, GLiDeR, HAL G-Comp) achieve near-nominal or conservative, while
minor comments (6)
  1. §2.5, Table 2: The realized exposure prevalence in the rare-exposure scenario is 9.4%, which is moderate rather than truly rare by pharmacoepidemiology standards. The authors should clarify how this maps to its intended severity.
  2. §2.3, Table 1: The traditional LASSO pipelines enforce inclusion of all investigator-specified covariates, whereas the other methods do not. This difference is mentioned only in the limitations (§4.5) and should be noted in the methods.
  3. §3.1, Figure 1: The caption notes that interval widths are not strictly comparable across methods due to different inference types. This is important context that should be stated more prominently.
  4. §4.5: The statement that higher HAL degrees were 'computationally infeasible' could quantify the attempted max_degree values and approximate runtime.
  5. Table 3: The Monte Carlo error is stated as ~0.7 pp for coverage near 95%, but the bolding threshold is |Δ| ≤ 1.5 pp. Clarify why 1.5 rather than ~1.4 pp was chosen.
  6. §4.2: The comparison with prior work is thorough but could note that the Franklin et al. (2017) plasmode also used a null, making the design choice less novel than implied.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: the plasmode simulation's known null (RD=0) makes bias directly measurable, and all compared methods use independent published implementations.

full rationale

The paper's core evaluation logic is not circular. The plasmode simulation fixes the true risk difference at zero (RD=0) with engineered confounding, so any nonzero estimate is by construction measurable residual-confounding bias—this is a calibration design, not a self-fulfilling prediction. The ten compared pipelines (LASSO, C-TMLE, OAL, GLiDeR, HAL) each use independent published implementations from their respective origin studies (Shortreed 2017, Koch 2018, Benkeser 2016, Ju 2019, Wyss 2024), and the comparison results do not reduce to any self-cited theorem or fitted-then-predicted quantity. Self-citations exist (Karim 2018, 2025 for the LASSO baseline and the NHANES anchor dataset), but these are not load-bearing for the central comparative claims: the anchor dataset is a real public survey, and the LASSO baseline is one of ten pipelines evaluated on equal footing. The authors transparently acknowledge that the calibration comparison is partly confounded by inference method (bootstrap vs. influence-curve SEs, §4.3), and that the PS-based pipelines benefit from correct propensity specification (§4.5)—but these are validity caveats, not circularity. No step in the derivation chain reduces to its inputs by definition.

Assumptions & free parameters 5 free parameters · 5 assumptions · 0 invented entities

The paper introduces no new entities, particles, or postulated objects. It compares existing methods on existing data. The free parameters are design choices for the simulation (scaling, truncation, tuning, degree, bootstrap count) rather than fitted constants. The axioms are standard causal inference assumptions (exchangeability, positivity, consistency, SUTVA) plus the design-specific null-benchmark and correct-PS-specification premises.

free parameters (5)
  • Proxy-burden count coefficient scaling = 5-fold scaling
    The outcome-model coefficient on the proxy-burden count was scaled fivefold to engineer strong confounding (§2.5). This is a design choice, not fitted to data, but it determines the difficulty of the adjustment problem.
  • PS truncation threshold = 5/(sqrt(n) * log(n))
    Propensity scores in LASSO-based and TMLE pipelines are truncated at this level (§2.3, Table S1). This is a methodological choice from prior literature (Gruber et al. 2022) applied uniformly.
  • OAL tuning-parameter range = See Web Appendix B
    The OAL tuning-parameter range is stated as justified in Web Appendix B, not in the main text. This range affects which variables OAL retains.
  • HAL max_degree = 1
    HAL was fit with max_degree=1 (additive, no interactions) due to computational infeasibility at n=4500 with 167 predictors (§4.5). This restriction affects HAL G-computation's over-concentration.
  • Bootstrap resamples = 200
    Bootstrap intervals use 200 percentile resamples (§2.3). This is a fixed design choice affecting SE estimates for bootstrap-based methods.
assumptions (5)
  • domain assumption Conditional exchangeability given (L, Z)
    Identification of the RD relies on {Y(0), Y(1)} ⊥ A | (L, Z) (§2.1). In the simulation this holds by construction; in the real-data analysis it is untestable.
  • domain assumption Positivity: 0 < P(A=1|L,Z) < 1
    Stated in §2.1 as identification assumption (ii). The rare-exposure scenario stresses this; overlap diagnostics in Table S4 confirm positivity stress with largest weight ~56.
  • domain assumption Correctly specified main-terms logistic propensity model
    Exposure is generated from a fitted logistic propensity model on L (§2.5), so the true PS lies within the parametric class fitted by PS-based pipelines. The authors acknowledge this is a limitation (§4.5).
  • ad hoc to paper Null effect (RD=0) as a valid calibration benchmark
    The entire evaluation is anchored at RD=0 with engineered confounding (§2.5). The authors argue this isolates adjustment quality, but behavior at non-null effects is untested.
  • domain assumption Proxy variables capture unmeasured confounders
    The paper assumes prescription-derived proxies 'can capture otherwise unmeasured confounders' (§1.1, §2.4). In the simulation, the proxy-burden count is a strong confounder by design; in real data this is an assumption.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Which Regularized Propensity-Score and Doubly Robust Methods Are Best Calibrated When Exposures or Outcomes Are Rare? A Plasmode Study of Proxy-Based Confounding Adjustment." pith.science (2026). https://pith.science/paper/NQKPBO6U

@misc{pith2026260707065,
  author       = {Pith},
  title        = {Pith review of: Which Regularized Propensity-Score and Doubly Robust Methods Are Best Calibrated When Exposures or Outcomes Are Rare? A Plasmode Study of Proxy-Based Confounding Adjustment},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/NQKPBO6U}},
  note         = {Machine review of arXiv:2607.07065}
}
read the original abstract

Purpose. Confounding adjustment in health-care database studies screens large proxy libraries where events per variable are low, straining standard propensity score (PS) methods, and many regularized variable-selection strategies exist (outcome-adaptive LASSO [OAL], group LASSO/GLiDeR, highly adaptive LASSO [HAL]). Yet few comparisons have varied exposure prevalence within such a selection menu, and none pairs it with doubly robust estimation, compute accounting, and a null-RD truth anchor. Methods. We conducted a plasmode simulation anchored on National Health and Nutrition Examination Survey data (2013-2018; 25 investigator-specified covariates, 142 prescription-derived proxies), comparing ten pipelines combining these strategies with inverse probability of treatment weighting (IPTW) and targeted maximum likelihood estimation (TMLE). Three scenarios were evaluated under a known null (true risk difference, RD = 0): frequent, rare-exposure, and rare-outcome. We report bias, standard error (SE), relative error, 95% coverage, and runtime. Results. HAL (G-Computation) had near-zero bias but highly concentrated estimates, giving near-unity coverage and large relative error (106-186%). OAL (IPTW), GLiDeR, and HAL (TMLE) were best calibrated, whereas the regularized-LASSO TMLE pipelines under-covered modestly (91-93%) in the rare scenarios. Under rare exposure, LASSO-IPTW had the largest bias and inflated SE and over-covered (conservatively), problems that TMLE removed. On real data, methods agreed (RD approximately 0.07-0.085). Runtimes spanned <1 s to >16 h. Conclusions. Under a null benchmark, pairing outcome-aware selection (OAL, GLiDeR) or doubly robust estimation (TMLE) with regularized models best balanced bias, calibration, and robustness to rarity. The rare-exposure arm exposed the largest gaps; method choice should weigh the prioritized metric against compute.

Figures

Figures reproduced from arXiv: 2607.07065 by the authors.

Figure 1
Figure 1. Estimated risk difference for the association between obesity and diabetes in the NHANES data, by method. Pipeline labels combine the selection strategy with its downstream estimator and, for the traditional LASSO baseline, the cross-validation loss used to select proxies: ‘IPTW’ vs. ‘TMLE’ names the estimator and ‘dev’ vs. ‘mse’ names deviance vs. mean-squared-error loss—so, e.g., LASSO (IPTW, dev) is LASSO proxy s… view at source ↗
Figure 2
Figure 2. 95% confidence-interval coverage by method under the frequent, rare-exposure, and rare-outcome scenarios; the dashed line marks the nominal 95% level. Bias, empirical standard error, and relative error appear in Supporting Information (Figures S1–S3). 3.2.1 Frequent exposure and outcome Point estimates were close to the truth for all methods ( [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗

Discussion (0). Sign in to comment.

Reference graph

Works this paper leans on

31 extracted references · 31 canonical work pages

  1. [1]

    How effective are machine learning and doubly robust estimators in incorporating high-dimensional proxies to reduce residual confounding? Pharmacoepidemiology and Drug Safety

    Karim ME, Lei Y. How effective are machine learning and doubly robust estimators in incorporating high-dimensional proxies to reduce residual confounding? Pharmacoepidemiology and Drug Safety . 2025;34(5):e70155

    work page 2025

  2. [2]

    Can we train machine learning methods to outperform the high- dimensional propensity score algorithm? Epidemiology

    Karim ME, Pang M, Platt R W. Can we train machine learning methods to outperform the high- dimensional propensity score algorithm? Epidemiology. 2018;29(2):191-198

    work page 2018

  3. [3]

    High-dimensional propensity score and its machine learning extensions in residual con- founding control

    Karim ME. High-dimensional propensity score and its machine learning extensions in residual con- founding control. The American Statistician . 2025;79(1):72-90

    work page 2025

  4. [4]

    National Health and Nutrition Examination Survey Data, 2013–2018

    Centers for Disease Control and Prevention, National Center for Health Statistics. National Health and Nutrition Examination Survey Data, 2013–2018. Published online 2018. Accessed July 7, 2026. https://wwwn.cdc.gov/nchs/nhanes/

    work page 2013

  5. [5]

    Machine learning for improving high-dimensional proxy con- founder adjustment in healthcare database studies: An overview of the current literature

    Wyss R, Yanover C, El-Hay T, et al. Machine learning for improving high-dimensional proxy con- founder adjustment in healthcare database studies: An overview of the current literature. Pharma- coepidemiology and Drug Safety . 2022;31(9):932-943

    work page 2022

  6. [6]

    Collaborative-controlled LASSO for constructing propensity score-based estimators in high-dimensional data

    Ju C, Wyss R, Franklin JM, Schneeweiss S, Häggström J, Laan MJ van der. Collaborative-controlled LASSO for constructing propensity score-based estimators in high-dimensional data. Statistical meth- ods in medical research . 2019;28(4):1044-1063

    work page 2019

  7. [7]

    Targeted learning with an undersmoothed LASSO propen- sity score model for large-scale covariate adjustment in health-care database studies

    Wyss R, Laan M van der, Gruber S, et al. Targeted learning with an undersmoothed LASSO propen- sity score model for large-scale covariate adjustment in health-care database studies. American Jour- nal of Epidemiology . 2024;193(11):1632-1640

    work page 2024

  8. [8]

    Outcome-adaptive lasso: Variable selection for causal inference

    Shortreed SM, Ertefaie A. Outcome-adaptive lasso: Variable selection for causal inference. Biometrics. 2017;73(4):1111-1122

    work page 2017

Show all 31 references
  1. [9]

    Covariate selection with group lasso and doubly robust estimation of causal effects

    Koch B, Vock DM, Wolfson J. Covariate selection with group lasso and doubly robust estimation of causal effects. Biometrics. 2018;74(1):8-17

    2018

  2. [10]

    The highly adaptive lasso estimator

    Benkeser D, Van Der Laan M. The highly adaptive lasso estimator. In: 2016 IEEE International Conference on Data Science and Advanced Analytics (DSAA) . IEEE; 2016:689-696. 12

    2016

  3. [11]

    Highly adaptive LASSO: Machine learning that provides valid nonparametric inference in realistic models

    Butzin-Dozier Z, Qiu S, Hubbard AE, Shi JS, Laan MJ van der. Highly adaptive LASSO: Machine learning that provides valid nonparametric inference in realistic models. medRxiv. Published online 2024

    2024

  4. [12]

    reader reaction to ‘outcome-adaptive lasso: Variable selection for causal inference’ by shortreed and ertefaie (2017)

    Jones J, Ertefaie A, Shortreed SM. Rejoinder to “reader reaction to ‘outcome-adaptive lasso: Variable selection for causal inference’ by shortreed and ertefaie (2017). ” Biometrics. 2023;79(1):521-525. doi:10.1111/biom.13681

    2017 doi

  5. [13]

    Flexible collaborative estimation of the average causal effect of a treatment using the outcome-highly-adaptive lasso

    Ju C, Benkeser D, Laan M van der. Flexible collaborative estimation of the average causal effect of a treatment using the outcome-highly-adaptive lasso. arXiv preprint arXiv:180606784 . Published online 2018

    2018

  6. [14]

    Robust inference on the average treatment effect using the outcome highly adaptive lasso

    Ju C, Benkeser D, Der Laan MJ van. Robust inference on the average treatment effect using the outcome highly adaptive lasso. Biometrics. 2020;76(1):109-118

    2020

  7. [15]

    Constructing inverse probability weights for marginal structural models

    Cole SR, Hernán MA. Constructing inverse probability weights for marginal structural models. Amer- ican Journal of Epidemiology . 2008;168(6):656-664

    2008

  8. [16]

    Dealing with limited overlap in estimation of average treatment effects

    Crump RK, Hotz VJ, Imbens GW, Mitnik OA. Dealing with limited overlap in estimation of average treatment effects. Biometrika. 2009;96(1):187-199

    2009

  9. [17]

    Diagnosing and responding to violations in the positivity assumption

    Petersen ML, Porter KE, Gruber S, Wang Y, Laan MJ van der. Diagnosing and responding to violations in the positivity assumption. Statistical Methods in Medical Research . 2012;21(1):31-54

    2012

  10. [18]

    Doubly robust estimation in missing data and causal inference models

    Bang H, Robins JM. Doubly robust estimation in missing data and causal inference models. Biomet- rics. 2005;61(4):962-973

    2005

  11. [19]

    Targeted maximum likelihood learning

    Laan MJ van der, Rubin D. Targeted maximum likelihood learning. The International Journal of Biostatistics. 2006;2(1)

    2006

  12. [20]

    Targeted Learning: Causal Inference for Observational and Experimental Data

    Laan MJ van der, Rose S. Targeted Learning: Causal Inference for Observational and Experimental Data. Springer; 2011

    2011

  13. [21]

    Data-adaptive selection of the propensity score truncation level for inverse-probability-weighted and targeted maximum likelihood estimators of marginal point treatment effects

    Gruber S, Phillips R V, Lee H, Laan MJ van der. Data-adaptive selection of the propensity score truncation level for inverse-probability-weighted and targeted maximum likelihood estimators of marginal point treatment effects. American Journal of Epidemiology . 2022;191(9):1640...

    2022 doi

  14. [22]

    Why does obesity cause diabetes? Cell metabolism

    Klein S, Gastaldelli A, Yki-Järvinen H, Scherer PE. Why does obesity cause diabetes? Cell metabolism. 2022;34(1):11-20

    2022

  15. [23]

    Plasmode simulation for the evaluation of pharmacoepidemiologic methods in complex healthcare databases

    Franklin JM, Schneeweiss S, Polinski JM, Rassen JA. Plasmode simulation for the evaluation of pharmacoepidemiologic methods in complex healthcare databases. Computational Statistics & Data Analysis. 2014;72:219-226

    2014

  16. [24]

    Regularized regression versus the high- dimensional propensity score for confounding adjustment in secondary database analyses

    Franklin JM, Eddings W, Glynn RJ, Schneeweiss S. Regularized regression versus the high- dimensional propensity score for confounding adjustment in secondary database analyses. American Journal of Epidemiology . 2015;182(7):651-659. doi: 10.1093/aje/kwv108

    2015 doi

  17. [25]

    Using simulation studies to evaluate statistical methods

    Morris TP, White IR, Crowther MJ. Using simulation studies to evaluate statistical methods. Statis- tics in Medicine . 2019;38(11):2074-2102. 13

    2019

  18. [26]

    A cautionary note for plasmode simulation studies in the setting of causal inference

    Shaw PA, Gruber S, Williamson BD, et al. A cautionary note for plasmode simulation studies in the setting of causal inference. Published online 2025. https://arxiv.org/abs/2504.11740

    2025 arXiv

  19. [27]

    Rsimsum: Summarise results from monte carlo simulation studies

    Gasparini A. Rsimsum: Summarise results from monte carlo simulation studies. Journal of Open Source Software. 2018;3(26):739

    2018

  20. [28]

    High-dimensional propen- sity score adjustment in studies of treatment effects using health care claims data

    Schneeweiss S, Rassen JA, Glynn RJ, A vorn J, Mogun H, Brookhart MA. High-dimensional propen- sity score adjustment in studies of treatment effects using health care claims data. Epidemiology. 2009;20(4):512-522. doi: 10.1097/EDE.0b013e3181a663cc

    2009 doi

  21. [29]

    Covariate selection in high-dimensional propen- sity score analyses of treatment effects in small samples

    Rassen JA, Glynn RJ, Brookhart MA, Schneeweiss S. Covariate selection in high-dimensional propen- sity score analyses of treatment effects in small samples. American Journal of Epidemiology . 2011;173(12):1404-1413. doi: 10.1093/aje/kwr001

    2011 doi

  22. [30]

    Comparing the performance of propensity score methods in healthcare database studies with rare outcomes

    Franklin JM, Eddings W, Austin PC, Stuart EA, Schneeweiss S. Comparing the performance of propensity score methods in healthcare database studies with rare outcomes. Statistics in Medicine . 2017;36(12):1946-1963. doi: 10.1002/sim.7250

    2017 doi

  23. [31]

    outcome-adaptive lasso: Variable selection for causal inference

    Baldé I, Yang YA, Lefebvre G. Reader reaction to “outcome-adaptive lasso: Variable selection for causal inference” by shortreed and ertefaie (2017). Biometrics. 2023;79(1):514-520. 14

    2017

Pith tools

Reviewed July 9, 2026 · model on record in the stance chip above.