Pith. sign in

REVIEW 3 major objections 5 minor 65 references

From Estimands to Robust Inference of Treatment Effects in Platform Trials

T0 review · 3 major / 5 minor · reviewed 2026-08-12 · deepseek-v4-flash

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

Pith's one-line read The paper establishes a framework for defining treatment effects on the entire concurrently eligible population, so estimands in platform trials no longer depend on randomization ratios or trial operation format.

desk verdict A careful formal treatment of the ECE estimand for platform trials with standard IPW/post-stratification machinery, conditional on a real but standard Assumption 1; worth refereeing with revisions. read the letter →

arxiv 2411.12944 v4 pith:XOLA7SO6 submitted 2024-11-20 stat.ME

Yuhan Qian , Yifan Yi , Jun Shao , Yanyao Yi , Gregory Levin , Nicole Mayer-Hamblett , Patrick J. Heagerty , Ting Ye This is my paper · ORCID
classification stat.ME MSC 62F1262P1062D05
keywords platformtrialsmasterprotocolsestimandentireconcurrentlyeligiblepopulationinverseprobabilityweightingpost-stratificationcovariateadjustmentrelativeefficiency
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

Platform trials randomize patients under constraints: some arms are unavailable to some patients, and assignment probabilities change with enrollment windows and patient characteristics. The paper argues that this flexibility makes the usual "who is the target population?" question ill-posed, because estimates based on patients actually assigned to a treatment or sub-study shift whenever the randomization ratio or trial format changes. Its central proposal is the entire concurrently eligible (ECE) population: all individuals who, at some point during the trial, have positive probability of being assigned to either of the two treatments being compared. Defining the estimand on this population makes the treatment effect invariant to randomization ratios and trial operation format, and the paper shows that inverse probability weighting, post-stratification, and model-assisted versions of both can estimate it consistently under the same minimal assumptions used in traditional randomized trials. Applied to the SIMPLIFY cystic fibrosis trial, the framework produces similar non-inferiority conclusions across the proposed estimators while avoiding the population drift seen in sub-study-only analyses.

What carries the argument

The mechanism that carries the argument is Assumption 1: there is an observed baseline variable $Z$ (enrollment window, site, disease subtype, and similar) such that treatment assignment $A$ is independent of potential outcomes and baseline covariates given $Z$, and the assignment probabilities $\pi_j(Z)$ are known, nonnegative, and sum to one. The ECE population is the support $\{\pi_j(Z)>0,\ \pi_k(Z)>0\}$ determined by these probabilities. Estimation then works by reweighting observed outcomes with $1/\pi_j(Z)$ (IPW and SIPW), by adding a fitted outcome-model residual (AIPW and SAIPW), or by splitting the ECE sample into post-strata on which $\pi_j$ and $\pi_k$ are constant and averaging within-stratum means (PS and APS). The asymptotic results hinge on the known probabilities and on Assumption 2, which requires the fitted working model to converge to a fixed limit so misspecified outcome models do not break consistency.

What would settle it

Simulate a platform trial in which randomization actually depends on an unobserved enrollment-time or site variable not included in $Z$, then apply the proposed IPW and PS estimators using the protocol probabilities; if their confidence intervals fail to cover the true ECE treatment effect at the nominal rate, or the estimates depart from the truth beyond sampling error, the central claim is falsified.

Watch

Extended reading notes

Core claim

The paper's central claim is that a treatment effect in a platform trial should be defined on the ECE population, the set of individuals with $\pi_j(Z)>0$ and $\pi_k(Z)>0$ for the two treatments $j$ and $k$, where $Z$ is the observed baseline variable governing the known randomization probabilities $\pi_j(Z)$. Conditional on this population, the estimand is $\vartheta_{jk}=(E[Y(j)\mid \text{ECE}], E[Y(k)\mid \text{ECE}])^T$, and the treatment effect is a contrast such as $\theta_{jk}-\theta_{kj}$. Under Assumption 1 (conditional randomization given $Z$ with known probabilities) and Assumption 2 (stability of the working outcome model, when used), all six estimators are consistent and asymptotically normal with explicit covariance matrices; the stabilized and covariate-adjusted versions are asymptotically at least as efficient, and AIPW and SAIPW attain the semiparametric efficiency bound when the working models are correctly specified. The paper also proves that post-stratification by strata in which $\pi_j$ and $\pi_k$ are constant is asymptotically equivalent to stabilized augmented weighting with the strata as covariates, and that adjusted post-stratification matches stabilized augmented weighting under condition (4).

Load-bearing premise

The load-bearing premise is that the observed baseline variable $Z$ fully captures the randomization mechanism: conditional on $Z$, treatment assignment is independent of potential outcomes and covariates, and the known probabilities $\pi_j(Z)$ are correct; if $Z$ omits anything the randomization actually used, such as site blocks, randomization lists, or unrecorded enrollment time, the ECE support, weights, and strata are misspecified and the asymptotic results do not apply.

Editorial extensions

If this is right

  • Changing randomization ratios over time, as in the 1:1 to 3:1 shift in the SIMPLIFY trial, no longer changes the population the estimated treatment effect refers to.
  • All six estimators are consistent and asymptotically normal with explicit covariance matrices and robust variance estimators, so the framework is directly usable for confirmatory analysis.
  • Model-assisted adjustment is safe under misspecification: AIPW and SAIPW remain asymptotically unbiased when the working outcome model is wrong, and under conditions (4)-(6) they are asymptotically at least as efficient as weighting or post-stratification alone.
  • Post-stratification should be built on strata in which the two assignment probabilities are constant, not on all joint levels of $Z$; redundant strata can cause small-stratum instability.
  • Sub-study-only analyses in umbrella and platform trials target a different, design-dependent population; in the SIMPLIFY application this produced a different point estimate for the DA comparison and wider confidence intervals than the ECE-based estimators.

Reading between the lines

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

  • One testable prediction of the invariance claim is that two trial formats with the same ECE support but different randomization ratios should produce estimates that agree up to sampling error; a simulation or reanalysis varying only the ratios could check this directly.
  • The reliance on known $\pi_j(Z)$ suggests a practical sensitivity check: compare estimates using the protocol probabilities with estimates using sample-proportion probabilities, and treat systematic divergence as evidence that the recorded randomization mechanism is incomplete.
  • The ECE population could serve as a natural benchmark for quantifying how much nonconcurrent-control borrowing changes the estimand, giving a bias-variance trade-off for methods that use nonconcurrent data.
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

3 major / 5 minor

Summary. This paper addresses two foundational questions in platform trials: how to define a treatment-effect estimand that is not an artifact of randomization ratios or trial format, and how to estimate and perform inference for that estimand robustly. The authors define the ECE population as the set of individuals with positive assignment probability to both treatments under the observed randomization mechanism, propose the corresponding estimand, and develop six estimators: IPW, SIPW, AIPW, SAIPW, PS, and APS. The main theoretical contribution is Theorem 1, which gives asymptotic normality for all six estimators under Assumptions 1 and 2, along with explicit asymptotic covariance matrices and efficiency comparisons. The methodology is illustrated on the SIMPLIFY cystic fibrosis trial. Under the stated assumptions, the derivations are careful and the central claims are largely correct.

Significance. If the assumptions hold, this is a valuable formalization: the ECE estimand gives a clinically interpretable target that is invariant to design choices such as the randomization ratio between sub-studies, and the proposed estimators provide robust inference while allowing efficiency gains through covariate adjustment and pooling across arms. The explicit variance formulas, efficiency ordering results, simulation evidence, and the accompanying R package are strengths, and the paper goes beyond prior work by allowing distinct eligibility criteria and non-uniform assignment probabilities. The main caveats are that the identification and inference results are conditional on a strong observed-randomization-mechanism assumption, and that some practical recommendations are not covered by the stated theory.

major comments (3)
  1. [3.1, Assumption 1; 3.2, ECE definition] Assumption 1 is the load-bearing condition for every result in the paper: it requires an observed baseline variable Z such that A is independent of potential outcomes given Z and such that the known π_j(Z) are the true conditional assignment probabilities. In many platform trials the actual randomization probability may depend on variables not contained in a coarse baseline Z, such as exact enrollment time within a window, site-level blocks, or, under response-adaptive randomization, the history of previous outcomes. If Z omits such a variable, then the identification formula (3) fails, the post-strata in Section 4.4 are mis-specified, and the ECE set {π_j(Z)>0, π_k(Z)>0} may not coincide with the population that could truly receive either treatment. The manuscript asserts that Z 'usually' includes these variables but offers no diagnostic, sensitivity analysis, or guidance for checking whether Assumption 1 is credible. Because this assumption defines both the estimand and the estimators, I would ask for an explicit discussion of its scope and at least a sensitivity analysis for omitted randomization variables, or a concrete balance-type diagnostic using the known π_j(Z).
  2. [3.1, superpopulation iid assumption] The asymptotic theory in Theorem 1 rests on the assumption that (W_i,Y_i(1),...,Y_i(J),A_i) is an iid sample from a superpopulation. Platform trials unfold over calendar time, with treatment arms entering and leaving and with enrollment rates that may be non-stationary; under a fixed-sequence interpretation, the iid assumption is not automatic and the estimand itself depends on the stochastic process generating enrollment windows. The theorem conditions on n_jk but not on the realized sequence of windows, and no martingale or conditional asymptotic argument is provided for the time-dependent case. Please either state clearly that the target is a random-effects superpopulation in which enrollment windows are exchangeable, or relax the iid assumption and show how the results extend to fixed time trends and sequentially enrolled cohorts.
  3. [4.3, remark on estimating π_j(Z)] The sentence 'Note that when Zi is discrete, πj(Zi) can be estimated using sample proportions and used in place of the true value πj(Z) in any of the above weighting estimators' is not covered by Theorem 1. When π_j(Z) is replaced by a sample proportion, the estimator changes its influence function; for example, the IPW estimator with estimated π_j(Z) becomes algebraically equivalent to a post-stratification estimator, whose asymptotic variance is different from the variance in Theorem 1(a). The variance estimators in Section S1.4 are derived for fixed, known π_j(Z), and plugging in estimated weights without accounting for their variability can produce invalid confidence intervals. Please either remove this remark, or provide the asymptotic theory for the estimated-weight versions and modify the variance estimators accordingly.
minor comments (5)
  1. [Abstract and Section 1.2] The phrase 'the same minimal assumptions used in traditional randomized trials' is overstated: Assumption 1 requires conditional independence given an observed Z and a known conditional assignment mechanism, which is stronger than the unconditional independence that suffices in a completely randomized trial. Please rephrase or clarify the relationship.
  2. [Section 4.4, PS estimator] The PS estimator is undefined if a post-stratum has no individuals assigned to treatment j, even though π_j(Z)>0 in that stratum. This finite-sample issue is acknowledged indirectly in the simulation discussion of PS(Z), but it should be stated explicitly in the main text along with a recommendation (e.g., pooling strata or using an IPW-type estimator).
  3. [Section 6, SIMPLIFY application] The application excludes 10 (1.7%) participants with missing outcomes and excludes data recorded after re-enrollment; these exclusions require additional assumptions (such as missingness independent of potential outcomes given Z and treatment, and no outcome-relevant effect of re-enrollment) for the reported estimates to be consistent for the ECE estimand. The paper should state these assumptions or explicitly label the empirical analysis as illustrative under these restrictions.
  4. [Section 5.2, Corollary 4] In the text preceding the display, 'the APS estimator ˆϑ apw jk' contains a typo: the superscript should be 'aps', not 'apw'.
  5. [Supplement, Table S1] In Table S1, 'Baseline Age, yeas' should read 'years'.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: the ECE estimand and all six estimators are derived from stated assumptions, not from fitted constants or self-citations.

full rationale

The paper's derivation chain is self-contained. The ECE population is formally defined as {pi_j(Z) > 0, pi_k(Z) > 0} (Section 3.2), and the estimand is the corresponding conditional mean of potential outcomes (Equation 1). The IPW identification formula (3) is proven in S3.2 directly from Assumption 1, and Theorem 1's asymptotic normality is proven in S3.4 using the central limit theorem and Slutsky's theorem; no fitted constant is embedded in the estimand, and the asymptotic variance formulas are derived rather than assumed. The efficiency comparisons in Corollaries 1-6 are also derived analytically. The only overlapping-author citations (Ye et al. 2023; Bannick et al. 2025) are used to illustrate conditions (4)-(6) for efficiency gains; the linear ANHECOVA case is actually proved in S3.11, and the joint calibration citation is not used to establish the main consistency or identification results. Assumption 1 is a substantive assumption, not a conclusion; if it fails the results are conditional, which is a sensitivity/correctness concern rather than circularity. The claim that the ECE population is invariant to randomization ratio and trial format follows directly from its definition in terms of positivity of the known assignment probabilities, not from fitting or circular reduction.

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

No free parameters are fitted to force the central claim; the covariate-adjustment working models are allowed to be misspecified and are not part of the estimand. The main technical premises are Assumptions 1 and 2, the iid sampling condition, and the explicit conditions (4)-(6) for efficiency comparisons. The ECE population is a definitional choice rather than an invented physical entity.

assumptions (4)
  • domain assumption Assumption 1: there exists observed baseline variable Z such that A is independent of (W,Y(1),...,Y(J)) given Z, P(A=j|Z)=pi_j(Z) known, 0<=pi_j(Z)<1, sum pi_j=1.
    Used to establish IPW identification (3) and all asymptotic results; requires Z to capture every variable involved in randomization and pi to be known exactly.
  • standard math Assumption 2: estimated working model mu_hat_jk converges to a limit mu_jk in L2, with Donsker condition if the model is not parametric.
    Standard regularity for covariate-adjusted estimators; needed for Theorem 1 parts (c), (d), (f) and for the efficiency comparisons.
  • domain assumption Independent and identically distributed sampling from (W,Y(1),...,Y(J),A) with finite second-order moments.
    Stated in Section 3.1; justifies CLT-based inference and the superpopulation interpretation of the ECE estimand. This is strong for platform settings with drifting enrollment over calendar time.
  • ad hoc to paper Conditions (4)-(6) in Corollaries 3 and 4: conditional mean residual zero within strata, conditional covariance zero, and cross-covariance zero for working models.
    Sufficient conditions for a guaranteed efficiency gain after covariate adjustment; not guaranteed by randomization and require special working models such as ANHECOVA or joint calibration to hold.

how reviews work

0 comments
Cite this review

Pith. "Pith review of From Estimands to Robust Inference of Treatment Effects in Platform Trials." pith.science (2026). https://pith.science/paper/XOLA7SO6

@misc{pith2026241112944,
  author       = {Pith},
  title        = {Pith review of: From Estimands to Robust Inference of Treatment Effects in Platform Trials},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/XOLA7SO6}},
  note         = {Machine review of arXiv:2411.12944}
}
read the original abstract

A platform trial is an innovative clinical trial design that uses a master protocol to evaluate multiple treatments, where patients are often assigned to different subsets of treatment arms based on individual characteristics, enrollment timing, and treatment availability. While offering increased flexibility, this constrained and non-uniform treatment assignment poses inferential challenges, with two fundamental ones being the precise definition of treatment effects and robust, efficient inference on these effects. Such challenges arise primarily because some commonly used analysis approaches may target estimands defined on populations inadvertently depending on randomization ratios or trial operation format, thereby undermining interpretability. This article, for the first time, presents a formal framework for constructing a clinically meaningful estimand with precise specification of the population of interest. Specifically, the proposed entire concurrently eligible (ECE) population not only preserves the integrity of randomized comparisons but also remains invariant to both the randomization ratio and trial operation format. Then, we develop weighting and post-stratification methods to estimate treatment effects under the same minimal assumptions used in traditional randomized trials. We also consider model-assisted covariate adjustment to fully unlock the efficiency potential of platform trials while maintaining robustness against model misspecification. For all proposed estimators, we derive asymptotic distributions and propose robust variance estimators and compare them in theory and through simulations. The SIMPLIFY trial, a master protocol assessing continuation versus discontinuation of two common therapies in cystic fibrosis, is utilized to further highlight the practical significance of this research. All analyses are conducted using the R package RobinCID.

Figures

Figures reproduced from arXiv: 2411.12944 by the authors.

Figure 1
Figure 1. SIMPLIFY design schema. Individuals on a single therapy enter into the corre [PITH_FULL_IMAGE:figures/full_fig_p008_1.png] view at source ↗
Figure 2
Figure 2. A stylistic master protocol trial in two operating formats: (a) sub-study format, [PITH_FULL_IMAGE:figures/full_fig_p010_2.png] view at source ↗
Figure 3
Figure 3. Comparison of traditional parallel-group and platform trial designs in a hypo [PITH_FULL_IMAGE:figures/full_fig_p013_3.png] view at source ↗
Figures from the paper (3 more)
Figure 4
Figure 4. Figure 4: A hypothetical umbrella trial (Case II) with a population with different disease [PITH_FULL_IMAGE:figures/full_fig_p014_4.png]
Figure 5
Figure 5. Figure 5: Efficiency comparisons among all robust estimators, with the corresponding [PITH_FULL_IMAGE:figures/full_fig_p027_5.png]
Figure 6
Figure 6. Figure 6: Estimates and 95% confidence intervals (in %) in the SIMPLIFY trial. Naive [PITH_FULL_IMAGE:figures/full_fig_p029_6.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

65 extracted references · 56 canonical work pages

  1. [1]

    S., Shao, J., Liu, J., Du, Y., Yi, Y., and Ye, T

    Bannick, M. S., Shao, J., Liu, J., Du, Y., Yi, Y., and Ye, T. (2025). A general form of covariate adjustment in clinical trials under covariate-adaptive randomization. Biometrika , page asaf029

    work page 2025

  2. [2]

    Barker, A., Sigman, C., Kelloff, G., Hylton, N., Berry, D., and Esserman, L. (2009). I-spy 2: an adaptive breast cancer trial design in the setting of neoadjuvant chemotherapy. Clinical Pharmacology & Therapeutics , 86(1):97--100

    work page 2009

  3. [3]

    J., Benzinger, T

    Bateman, R. J., Benzinger, T. L., Berry, S., Clifford, D. B., Duggan, C., Fagan, A. M., Fanning, K., Farlow, M. R., Hassenstab, J., McDade, E. M., et al. (2017). The dian-tu next generation alzheimer's prevention trial: adaptive design and disease progression model. Alzheimer's & Dementia , 13(1):8--19

    work page 2017

  4. [4]

    M., Connor, J

    Berry, S. M., Connor, J. T., and Lewis, R. J. (2015). The platform trial: an efficient strategy for evaluating multiple treatments. Journal of the American Medical Association , 313(16):1619--1620

    work page 2015

  5. [5]

    Bofill Roig, M., Burgwinkel, C., Garczarek, U., Koenig, F., Posch, M., Nguyen, Q., and Hees, K. (2023). On the use of non-concurrent controls in platform trials: a scoping review. Trials , 24(1):408

    work page 2023

  6. [6]

    Bofill Roig, M., Glimm, E., Mielke, T., and Posch, M. (2024). Optimal allocation strategies in platform trials with continuous endpoints. Statistical Methods in Medical Research , 33(5):858--874

    work page 2024

  7. [7]

    M., Hees, K., Jacko, P., Koenig, F., Magirr, D., Mesenbrink, P., et al

    Bofill Roig, M., Krotka, P., Burman, C.-F., Glimm, E., Gold, S. M., Hees, K., Jacko, P., Koenig, F., Magirr, D., Mesenbrink, P., et al. (2022). On model-based time trend adjustments in platform trials with non-concurrent controls. BMC Medical Research Methodology , 22(1):1--16

    work page 2022

  8. [8]

    Burki, T. (2023). Platform trials: the future of medical research? The Lancet Respiratory Medicine , 11(3):232--233

    work page 2023

Show all 65 references
  1. [9]

    Collignon, O., Gartner, C., Haidich, A.-B., James Hemmings, R., Hofner, B., P \'e tavy, F., Posch, M., Rantell, K., Roes, K., and Schiel, A. (2020). Current statistical considerations and regulatory perspectives on the planning of confirmatory basket, umbrella, and platform tr...

    2020

  2. [10]

    and Rose, S

    Degtiar, I. and Rose, S. (2023). A review of generalizability and transportability. Annual Review of Statistics and Its Application , 10(1):501--524

    2023

  3. [11]

    Ding, P. (2023). A first course in causal inference. arXiv preprint arXiv:2305.18793

    2023 arXiv

  4. [12]

    E., Freidlin, B., and Korn, E

    Dodd, L. E., Freidlin, B., and Korn, E. L. (2021). Platform trials—beware the noncomparable control group. New England Journal of Medicine , 384(16):1572--1573

    2021

  5. [13]

    J., Palesch, Y

    Elm, J. J., Palesch, Y. Y., Koch, G. G., Hinson, V., Ravina, B., and Zhao, W. (2012). Flexible analytical methods for adding a treatment arm mid-study to an ongoing clinical trial. Journal of Biopharmaceutical Statistics , 22(4):758--772

    2012

  6. [14]

    Ulcerative colitis: developing drugs for treatment

    FDA (2022). Ulcerative colitis: developing drugs for treatment. Guidance for Industry. Center for Drug Evaluation and Research and Center for Biologics Evaluation and Research, Food and Drug Administration (FDA), U.S. Department of Health and Human Services

    2022

  7. [15]

    Adjusting for covariates in randomized clinical trials for drugs and biological products

    FDA (2023a). Adjusting for covariates in randomized clinical trials for drugs and biological products. Guidance for Industry. Center for Drug Evaluation and Research and Center for Biologics Evaluation and Research, Food and Drug Administration (FDA), U.S. Department of Health...

    2023

  8. [16]

    Master protocols for drug and biological product development

    FDA (2023b). Master protocols for drug and biological product development. Draft Guidance for Industry. Center for Drug Evaluation and Research and Center for Biologics Evaluation and Research, Food and Drug Administration (FDA), U.S. Department of Health and Human Services. D...

    2023

  9. [17]

    Fuller, W. A. (2009). Sampling Statistics . Wiley

    2009

  10. [18]

    M., Bofill Roig, M., Miranda, J

    Gold, S. M., Bofill Roig, M., Miranda, J. J., Pariante, C., Posch, M., and Otte, C. (2022). Platform trials and the future of evaluating therapeutic behavioural interventions. Nature Reviews Psychology , 1(1):7--8

    2022

  11. [19]

    Guo, B., Wang, L., and Yuan, Y. (2024). Treatment comparisons in adaptive platform trials adjusting for temporal drift. Statistics in Biopharmaceutical Research , pages 1--10

    2024

  12. [20]

    an essay on the logical foundations of survey sampling, part one

    H \'a jek, J. (1971). Comment on “an essay on the logical foundations of survey sampling, part one”. The Foundations of Survey Sampling , 236

    1971

  13. [21]

    S., Gandara, D

    Herbst, R. S., Gandara, D. R., Hirsch, F. R., Redman, M. W., LeBlanc, M., Mack, P. C., Schwartz, L. H., Vokes, E., Ramalingam, S. S., Bradley, J. D., et al. (2015). Lung master protocol (lung-map)—a biomarker-driven protocol for accelerating development of therapies for squamo...

    2015

  14. [22]

    P., Pestana, R

    Hobbs, B. P., Pestana, R. C., Zabor, E. C., Kaizer, A. M., and Hong, D. S. (2022). Basket trials: review of current practice and innovations for future trials. Journal of Clinical Oncology , 40(30):3520--3528

    2022

  15. [23]

    E., Jairath, V., Danese, S., Vicaut, E., and Peyrin-Biroulet, L

    Honap, S., Sands, B. E., Jairath, V., Danese, S., Vicaut, E., and Peyrin-Biroulet, L. (2024). Basket, umbrella, and platform trials: The potential for master protocol--based trials in inflammatory bowel disease. Gastroenterology , 167(4):636--642

    2024

  16. [24]

    Horvitz, D. G. and Thompson, D. J. (1952). A generalization of sampling without replacement from a finite universe. Journal of the American Statistical Association , 47(260):663--685

    1952

  17. [25]

    Huang, T.-J., Luedtke, A., and GROUP, A. I. (2023). Improved efficiency for cross-arm comparisons via platform designs. Biostatistics , 24(4):1106--1124

    2023

  18. [26]

    Statistical principles for clinical trials E9

    ICH E9 (1998). Statistical principles for clinical trials E9 . International Council for Harmonisation (ICH)

    1998

  19. [27]

    Addendum on estimands and sensitivity analysis in clinical trials to the guideline on statistical principles for clinical trials E9(R1)

    ICH E9 (R1) (2019). Addendum on estimands and sensitivity analysis in clinical trials to the guideline on statistical principles for clinical trials E9(R1) . International Council for Harmonisation

    2019

  20. [28]

    Jiang, Z., Lu, C., Liu, J., Roychoudhury, S., Meyer, D., Huang, B., and Chu, H. (2023). Nonconcurrent controls in platform trials: Can we borrow their concurrent observation data? Statistics in Biopharmaceutical Research , pages 1--10

    2023

  21. [29]

    M., Hobbs, B

    Kaizer, A. M., Hobbs, B. P., and Koopmeiners, J. S. (2018). A multi-source adaptive platform design for testing sequential combinatorial therapeutic strategies. Biometrics , 74(3):1082--1094

    2018

  22. [30]

    S., Herbst, R

    Kim, E. S., Herbst, R. S., Wistuba, I. I., Lee, J. J., Blumenschein Jr, G. R., Tsao, A., Stewart, D. J., Hicks, M. E., Erasmus Jr, J., Gupta, S., et al. (2011). The battle trial: personalizing therapy for lung cancer. Cancer discovery , 1(1):44--53

    2011

  23. [31]

    M., Brown, L

    Lee, K. M., Brown, L. C., Jaki, T., Stallard, N., and Wason, J. (2021). Statistical consideration when adding new arms to ongoing clinical trials: the potentials and the caveats. Trials , 22(1):203

    2021

  24. [32]

    Lee, K. M. and Wason, J. (2020). Including non-concurrent control patients in the analysis of platform trials: is it worth it? BMC Medical Research Methodology , 20:1--12

    2020

  25. [33]

    Lunceford, J. K. and Davidian, M. (2004). Stratification and weighting via the propensity score in estimation of causal treatment effects: a comparative study. Statistics in Medicine , 23(19):2937--2960

    2004

  26. [34]

    Marschner, I. C. and Schou, I. M. (2022). Analysis of adaptive platform trials using a network approach. Clinical Trials , 19(5):479--489

    2022

  27. [35]

    H., Riekert, K

    Mayer-Hamblett, N., Ratjen, F., Russell, R., Donaldson, S. H., Riekert, K. A., Sawicki, G. S., Odem-Davis, K., Young, J. K., Rosenbluth, D., Taylor-Cousar, J. L., et al. (2023). Discontinuation versus continuation of hypertonic saline or dornase alfa in modulator treated peopl...

    2023

  28. [36]

    L., Mesenbrink, P., Mielke, T., Parke, T., Evans, D., and K \"o nig, F

    Meyer, E. L., Mesenbrink, P., Mielke, T., Parke, T., Evans, D., and K \"o nig, F. (2021). Systematic review of available software for multi-arm multi-stage and platform clinical trial design. Trials , 22(1):1--14

    2021

  29. [37]

    Neyman, J. (1923). On the application of probability theory to agricultural experiments. Statistical Science , 5(4):465--472. Translation by D.M. Dabrowska and T.P. Speed (1990)

    1923

  30. [38]

    Normand, S.-L. T. (2021). The recovery platform. New England Journal of Medicine , 384(16):757--758

    2021

  31. [39]

    O., Wason, J

    Ouma, L. O., Wason, J. M., Zheng, H., Wilson, N., and Grayling, M. (2022). Design and analysis of umbrella trials: Where do we stand? Frontiers in medicine , 9:1037439

    2022

  32. [40]

    J., Wistuba, I

    Papadimitrakopoulou, V., Lee, J. J., Wistuba, I. I., Tsao, A. S., Fossella, F. V., Kalhor, N., Gupta, S., Byers, L. A., Izzo, J. G., Gettinger, S. N., et al. (2016). The battle-2 study: a biomarker-integrated targeted therapy study in previously treated patients with advanced ...

    2016

  33. [41]

    J., Hsu, G., Siden, E

    Park, J. J., Hsu, G., Siden, E. G., Thorlund, K., and Mills, E. J. (2020). An overview of precision oncology basket and umbrella trials for clinicians. CA: a cancer journal for clinicians , 70(2):125--137

    2020

  34. [42]

    J., Siden, E., Zoratti, M

    Park, J. J., Siden, E., Zoratti, M. J., Dron, L., Harari, O., Singer, J., Lester, R. T., Thorlund, K., and Mills, E. J. (2019). Systematic review of basket trials, umbrella trials, and platform trials: a landscape analysis of master protocols. Trials , 20:1--10

    2019

  35. [43]

    W., Yarnell, C

    Pitre, T., Cheng, S., Cusano, E., Khan, N., Mikhail, D., Leung, G., Vernooij, R. W., Yarnell, C. J., Goligher, E., Murthy, S., et al. (2023). Methodology and design of platform trials: a meta-epidemiological study. Journal of Clinical Epidemiology , 157:1--12

    2023

  36. [44]

    R., Vestrucci, M., Detry, M

    Quintana, M., Saville, B. R., Vestrucci, M., Detry, M. A., Chibnik, L., Shefner, J., Berry, J. D., Chase, M., Andrews, J., Sherman, A. V., et al. (2023). Design and statistical innovations in a platform trial for amyotrophic lateral sclerosis. Annals of Neurology , 94(3):547--560

    2023

  37. [45]

    and Gerber, D

    Rashdan, S. and Gerber, D. E. (2016). Going into battle: umbrella and basket clinical trials to accelerate the study of biomarker-based therapies. Annals of translational medicine , 4(24):529

    2016

  38. [46]

    Redig, A. J. and J \"a nne, P. A. (2015). Basket trials and the evolution of clinical trial design in an era of genomic medicine. J Clin Oncol , 33(9):975--977

    2015

  39. [47]

    W., Papadimitrakopoulou, V

    Redman, M. W., Papadimitrakopoulou, V. A., Minichiello, K., Hirsch, F. R., Mack, P. C., Schwartz, L. H., Vokes, E., Ramalingam, S., Leighl, N., Bradley, J., et al. (2020). Biomarker-driven therapies for previously treated squamous non-small-cell lung cancer (lung-map swog s140...

    2020

  40. [48]

    and Sargent, D

    Renfro, L. and Sargent, D. (2017). Statistical controversies in clinical research: basket trials, umbrella trials, and other master protocols: a review and examples. Annals of Oncology , 28(1):34--43

    2017

  41. [49]

    M., Rotnitzky, A., and Zhao, L

    Robins, J. M., Rotnitzky, A., and Zhao, L. P. (1994). Estimation of regression coefficients when some regressors are not always observed. Journal of the American statistical Association , 89(427):846--866

    1994

  42. [50]

    Rosenbaum, P. R. and Rubin, D. B. (1983). The central role of the propensity score in observational studies for causal effects. Biometrika , 70(1):41--55

    1983

  43. [51]

    Rubin, D. B. (1974). Estimating causal effects of treatments in randomized and nonrandomized studies. Journal of Educational Psychology , 6(5):688--701

    1974

  44. [52]

    M., Zhang, X., and D \' az, I

    Santacatterina, M., Giron, F. M., Zhang, X., and D \' az, I. (2025). Identification and estimation of causal effects using non-concurrent controls in platform trials. Statistics in Medicine , 44(6):e70017

    2025

  45. [53]

    R., Berry, D

    Saville, B. R., Berry, D. A., Berry, N. S., Viele, K., and Berry, S. M. (2022). The bayesian time machine: Accounting for temporal drift in multi-arm platform trials. Clinical Trials , 19(5):490--501

    2022

  46. [54]

    Saville, B. R. and Berry, S. M. (2016). Efficiencies of platform clinical trials: a vision of the future. Clinical Trials , 13(3):358--366

    2016

  47. [55]

    R., Parmar, M

    Sydes, M. R., Parmar, M. K., Mason, M. D., Clarke, N. W., Amos, C., Anderson, J., de Bono, J., Dearnaley, D. P., Dwyer, J., Green, C., et al. (2012). Flexible trial design in practice-stopping arms for lack-of-benefit and adding research arms mid-trial in stampede: a multi-arm...

    2012

  48. [56]

    A stronger clinical trial infrastructure for better health outcomes

    The White House Office of Science and Technology (2023). A stronger clinical trial infrastructure for better health outcomes. https://www.whitehouse.gov/ostp/news-updates/2023/10/26/a-stronger-clinical-trial-infrastructure-for-better-health-outcomes/

    2023

  49. [57]

    A., Davidian, M., Zhang, M., and Lu, X

    Tsiatis, A. A., Davidian, M., Zhang, M., and Lu, X. (2008). Covariate adjustment for two-sample treatment comparisons in randomized clinical trials: A principled yet flexible approach. Statistics in Medicine , 27(23):4658--4677

    2008

  50. [58]

    Ventz, S., Cellamare, M., Parmigiani, G., and Trippa, L. (2018). Adding experimental arms to platform clinical trials: randomization procedures and interim analyses. Biostatistics , 19(2):199--215

    2018

  51. [59]

    L., and Soon, G

    Wang, C., Lin, M., Rosner, G. L., and Soon, G. (2023). A bayesian model with application for adaptive platform trials having temporal changes. Biometrics , 79(2):1446--1458

    2023

  52. [60]

    and LaVange, L

    Woodcock, J. and LaVange, L. M. (2017). Master protocols to study multiple therapies, multiple diseases, or both. New England Journal of Medicine , 377(1):62--70

    2017

  53. [61]

    Ye, T., Shao, J., Yi, Y., and Zhao, Q. (2023). Toward better practice of covariate adjustment in analyzing randomized clinical trials. Journal of the American Statistical Association , 118:2370--2382

    2023

  54. [62]

    Yuan, Y., Guo, B., Munsell, M., Lu, K., and Jazaeri, A. (2016). Midas: a practical bayesian design for platform trials with molecularly targeted agents. Statistics in Medicine , 35(22):3892--3906

    2016

  55. [63]

    Master protocols for drug and biological product development

    FDA (2023). Master protocols for drug and biological product development. Draft Guidance for Industry. Center for Drug Evaluation and Research and Center for Biologics Evaluation and Research, Food and Drug Administration (FDA), U.S. Department of Health and Human Services. De...

    2023

  56. [64]

    Pocock, S. J. (1976). The combination of randomized and historical controls in clinical trials. Journal of chronic diseases , 29(3):175--188

    1976

  57. [65]

    van der Vaart, A. W. (1998). Asymptotic Statistics . Cambridge Series in Statistical and Probabilistic Mathematics. Cambridge University Press

    1998

Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.