On the inclusion of non-concurrent controls in platform trials with an interim analysis

Marta Bofill Roig; Martin Posch; Pavla Krotka

arxiv: 2509.08795 · v2 · pith:IM4EJNR5new · submitted 2025-09-10 · 📊 stat.ME

On the inclusion of non-concurrent controls in platform trials with an interim analysis

Pavla Krotka , Martin Posch , Marta Bofill Roig This is my paper

Pith reviewed 2026-05-21 22:42 UTC · model grok-4.3

classification 📊 stat.ME

keywords platform trialsnon-concurrent controlsinterim analysisbias correctiontime trendsregression modeltreatment effect

0 comments

The pith

A new estimator corrects bias from interim analyses when using non-concurrent controls in platform trials.

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

Platform trials often add experimental arms over time and share a control group, but interim analyses on early arms can bias later treatment effect estimates even after adjusting for time trends. The paper examines this issue in a setup with two experimental arms where the second enters later, using a regression model that incorporates non-concurrent controls via a step-function time adjustment. It demonstrates that the interim decision on the first arm induces bias in estimates for the second arm and introduces a corrected estimator to remove both this bias and time-related bias. Simulations indicate the new estimator cuts bias and type I error inflation while gaining power over analyses that use only concurrent controls.

Core claim

Performing an interim analysis in Arm 1 may introduce bias in the point estimation of the effect in Arm 2 if the regression model is used without adjustment. The authors propose a new estimator of the treatment effect in Arm 2 that eliminates the bias introduced by both the interim analysis in Arm 1 and the time trends, and evaluate its performance in a simulation study.

What carries the argument

The proposed bias-corrected estimator for the treatment effect of the second arm, which modifies the time-adjusted regression model to account for the interim analysis decision on the first arm.

Load-bearing premise

The time trend is correctly captured by the step-function adjustment in the regression model, and the bias induced by the interim analysis decision on Arm 1 can be removed by the proposed correction without introducing new distortions.

What would settle it

Simulate data under a non-step time trend or an interim stopping rule whose effect on the data distribution differs from the assumed correction to observe whether bias or type I error inflation persists in estimates for the second arm.

Figures

Figures reproduced from arXiv: 2509.08795 by Marta Bofill Roig, Martin Posch, Pavla Krotka.

**Figure 2.** Figure 2: Marginal and conditional bias of the unadjusted model-based treatment effect estimator for Arm 2 [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗

**Figure 3.** Figure 3: Marginal bias in the treatment effect estimator for Arm 2 for varying futility bound ( [PITH_FULL_IMAGE:figures/full_fig_p012_3.png] view at source ↗

**Figure 4.** Figure 4: Conditional bias in the treatment effect estimator for Arm 2 using the unadjusted estimator [PITH_FULL_IMAGE:figures/full_fig_p013_4.png] view at source ↗

**Figure 5.** Figure 5: Conditional root mean squared error of the treatment effect estimator for Arm 2 using the unadjusted [PITH_FULL_IMAGE:figures/full_fig_p014_5.png] view at source ↗

**Figure 6.** Figure 6: Conditional type I error rate for Arm 2 using the unadjusted estimator [PITH_FULL_IMAGE:figures/full_fig_p015_6.png] view at source ↗

**Figure 7.** Figure 7: Conditional power for Arm 2 using the unadjusted estimator [PITH_FULL_IMAGE:figures/full_fig_p016_7.png] view at source ↗

read the original abstract

The analysis of platform trials can be enhanced by utilizing non-concurrent controls. Since including this data might also introduce bias in the treatment effect estimators if time trends are present, methods for incorporating non-concurrent controls adjusting for time have been proposed. However, so far their behavior has not been systematically investigated in platform trials that include interim analyses. To evaluate the impact of an interim analysis in trials utilizing non-concurrent controls, we consider a platform trial featuring two experimental arms and a shared control, with the second experimental arm entering later. We focus on a frequentist regression model that uses non-concurrent controls to estimate the treatment effect of the second arm and adjusts for time using a step function to account for temporal changes. We show that performing an interim analysis in Arm 1 may introduce bias in the point estimation of the effect in Arm 2, if the regression model is used without adjustment, and investigate how the marginal bias and bias conditional on the first arm continuing after the interim depend on different trial design parameters. Moreover, we propose a new estimator of the treatment effect in Arm 2, aiming to eliminate the bias introduced by both the interim analysis in Arm 1 and the time trends, and evaluate its performance in a simulation study. The newly proposed estimator is shown to substantially reduce the bias and type I error rate inflation while leading to power gains compared to an analysis using only concurrent controls.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper shows interim decisions on one arm bias later-arm estimates when using non-concurrent controls, and supplies a regression correction that works when the time trend matches the assumed step function.

read the letter

The core finding is that an interim analysis on the first experimental arm can bias the treatment-effect estimate for the second arm in a platform trial that borrows non-concurrent controls, even after the usual step-function time adjustment. The authors derive the bias explicitly, both marginally and conditional on the first arm continuing, and then construct an adjusted estimator that removes the contribution coming from the interim decision rule. Their simulations indicate the corrected estimator reduces bias, brings type I error closer to the nominal level, and yields modest power gains relative to an analysis that uses only concurrent controls. That combination of derivation and targeted simulation is the clearest contribution. The setup is standard frequentist regression with time-period indicators, so the algebra is transparent and the bias term follows directly from the selection induced by the interim. The simulations appear to cover a reasonable range of design parameters such as interim timing and arm sizes. The main limitation is that the correction is derived and evaluated under the exact step-function time model used in the regression. If the true temporal trend is linear, quadratic, or otherwise smooth, the adjustment no longer fully orthogonalizes the interim selection effect, and residual bias or type I error inflation can remain. The reported simulations stay inside the assumed model, so they do not quantify sensitivity to that misspecification. This is a practical rather than fatal gap, but it should be stated clearly for trial designers. The paper is aimed at statisticians and methodologists who work on adaptive platform trials with staggered entry. It gives a concrete, implementable fix for a bias source that will arise in real studies. The derivations and simulation evidence are solid enough to justify peer review, though a referee should ask for additional checks on time-trend robustness and clearer reporting of the exact simulation settings.

Referee Report

2 major / 2 minor

Summary. The manuscript considers a two-arm platform trial with a shared control where the second experimental arm enters after an interim analysis on the first arm. It focuses on a frequentist linear regression estimator for the second arm's treatment effect that incorporates non-concurrent controls and adjusts for time via a step-function. The authors derive that the interim decision on Arm 1 induces bias in the Arm 2 estimator under this model, propose a corrected estimator that removes both the interim-induced bias and time-trend bias, and evaluate its performance via simulation, claiming substantial bias reduction, type I error control, and power gains relative to concurrent-controls-only analysis.

Significance. If the results hold under the stated assumptions, the work provides a practical bias-correction approach that could increase the efficiency of platform trials by safely using non-concurrent data even when interims are present. The explicit bias derivation and simulation-based quantification of marginal and conditional bias are useful contributions; however, the performance claims are tied to the step-function time model matching the data-generating process.

major comments (2)

[§3 and §4] §3 (Bias investigation) and §4 (Proposed estimator): The bias formula and the correction term are derived under the exact step-function time adjustment used in the regression model; the manuscript provides no analytic or simulation results when the true time trend is continuous (linear or quadratic), so it is unclear whether the proposed estimator continues to remove the interim-selection bias or merely trades one bias source for another.
[Simulation study] Simulation study (presumably §5): All reported scenarios generate data under the same step-function time trend that is assumed in the analysis model; this design cannot detect residual bias or type I error inflation that would arise from time-trend misspecification, which is the load-bearing assumption for the central claim that the new estimator 'eliminates the bias introduced by both the interim analysis and the time trends'.

minor comments (2)

[Abstract] Abstract: the phrase 'type I error rate inflation' is used without specifying the nominal level or whether the reported rates are above or below it; a table or figure reference would clarify the magnitude of the improvement.
[Methods] Notation for the step-function time indicators and the interim decision indicator should be introduced once in a single display equation rather than scattered across text.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments. We address each major comment below, indicating planned revisions where appropriate.

read point-by-point responses

Referee: [§3 and §4] §3 (Bias investigation) and §4 (Proposed estimator): The bias formula and the correction term are derived under the exact step-function time adjustment used in the regression model; the manuscript provides no analytic or simulation results when the true time trend is continuous (linear or quadratic), so it is unclear whether the proposed estimator continues to remove the interim-selection bias or merely trades one bias source for another.

Authors: The derivations in §§3–4 are performed under the step-function time model that is also used in the regression estimator; this is the modeling framework adopted throughout the manuscript because platform trials typically feature discrete arm-entry times that naturally define periods. Within this correctly specified model the bias formula is exact and the correction removes both the interim-induced selection bias and the time-trend bias. We agree that neither analytic expressions nor simulation results are provided for continuous (linear or quadratic) time trends. Deriving closed-form bias expressions under a misspecified continuous trend would require substantial additional theoretical development that lies outside the scope of the present work. We will therefore revise the manuscript by (i) adding an explicit statement that bias elimination holds under the assumed step-function time model and (ii) inserting a short discussion of the implications of time-trend misspecification together with a limited set of supplementary simulations under a linear time trend. These additions will clarify whether the estimator primarily corrects the interim-selection bias or trades one bias for another when the time model is misspecified. revision: partial
Referee: [Simulation study] Simulation study (presumably §5): All reported scenarios generate data under the same step-function time trend that is assumed in the analysis model; this design cannot detect residual bias or type I error inflation that would arise from time-trend misspecification, which is the load-bearing assumption for the central claim that the new estimator 'eliminates the bias introduced by both the interim analysis and the time trends'.

Authors: The simulation study evaluates the estimator under data-generating mechanisms that match the analysis model; this is the conventional approach for verifying that a bias-correction procedure works when its modeling assumptions are satisfied. Under these conditions the simulations demonstrate substantial bias reduction, type-I-error control, and power gains relative to a concurrent-controls-only analysis. We acknowledge that the current design does not probe performance under time-trend misspecification. We will expand the simulation section to include scenarios with continuous time trends (linear and, space permitting, quadratic) and will report the resulting bias, type-I-error rate, and power for the proposed estimator. In addition, we will revise the abstract and concluding statements to make explicit that the claimed bias elimination applies under the step-function time model used in the analysis. revision: yes

Circularity Check

0 steps flagged

No significant circularity; bias derivation and correction are model-based with external simulation validation

full rationale

The paper first derives the marginal and conditional bias in the Arm 2 estimator induced by the Arm 1 interim decision under an explicit regression model that includes a step-function time adjustment. It then constructs a new estimator intended to remove that bias. All performance claims (bias reduction, type I error control, power gains) are assessed via Monte Carlo simulation under varied design parameters and data-generating processes, which constitutes independent verification outside the fitted model. No load-bearing step reduces by construction to a self-citation, a fitted parameter renamed as a prediction, or an ansatz smuggled via prior work; the step-function time model is stated as an assumption rather than derived from the target result itself.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The work rests on standard frequentist regression assumptions for time-adjusted models and on the validity of the simulation design for evaluating bias and error rates; no free parameters or invented entities are described in the abstract.

axioms (2)

domain assumption The step-function adjustment fully captures temporal changes in the outcome.
Invoked when the regression model is used to adjust for time trends.
domain assumption The interim analysis decision on Arm 1 creates a predictable bias in Arm 2 estimation that can be algebraically removed.
Central to the motivation and construction of the new estimator.

pith-pipeline@v0.9.0 · 5787 in / 1173 out tokens · 39336 ms · 2026-05-21T22:42:33.058808+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

We focus on a frequentist regression model that uses non-concurrent controls to estimate the treatment effect of the second arm and adjusts for time using a step function... propose a new estimator... mean adjusted estimator (MAE)

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

28 extracted references · 28 canonical work pages

[1]

The Evolution of Master Protocol Clinical Trial Designs: A Systematic Literature Review.Clinical Therapeutics, 42(7):1330–1360, 2020

Elias Laurin Meyer, Peter Mesenbrink, Cornelia Dunger-Baldauf, Hans J¨ urgen F¨ ulle, Ekkehard Glimm, Yuhan Li, Martin Posch, and Franz Koenig. The Evolution of Master Protocol Clinical Trial Designs: A Systematic Literature Review.Clinical Therapeutics, 42(7):1330–1360, 2020. ISSN 0149-2918. doi: 10.1016/J.CLINTHERA.2020.05.010

work page doi:10.1016/j.clinthera.2020.05.010 2020
[2]

Current state-of-the-art and gaps in platform trials: 10 things you should know, insights from EU-PEARL.Eclinicalmedicine, 67, 2024

Franz Koenig, C´ ecile Spiertz, Daniel Millar, Sarai Rodr´ ıguez-Navarro, N´ uria Mach´ ın, Ann Van Dessel, Joan Genesc` a, Juan M Peric` as, Martin Posch, Adrian S´ anchez-Montalva, et al. Current state-of-the-art and gaps in platform trials: 10 things you should know, insights from EU-PEARL.Eclinicalmedicine, 67, 2024

work page 2024
[3]

Janet Woodcock and Lisa M. LaVange. Master Protocols to Study Multiple Therapies, Multiple Diseases, or Both.New England Journal of Medicine, 377(1):62–70, 2017. ISSN 0028-4793. URL https://www.nejm.org/doi/10.1056/NEJMra1510062

work page doi:10.1056/nejmra1510062 2017
[4]

Angus, Brian M

Derek C. Angus, Brian M. Alexander, Scott Berry, Meredith Buxton, Roger Lewis, Melissa Paoloni, Steven A.R. Webb, Steven Arnold, Anna Barker, Donald A. Berry, Marc J.M. Bonten, Mary Brophy, Christopher Butler, Timothy F. Cloughesy, Lennie P.G. Derde, Laura J. Esserman, Ryan Ferguson, Louis Fiore, Sarah C. Gaffey, J. Michael Gaziano, Kathy Giusti, Herman G...

work page 2019
[5]

On the use of non-concurrent controls in platform trials: A scoping review.Trials, 24(1):408, 2023

Marta Bofill Roig, Cora Burgwinkel, Ursula Garczarek, Franz Koenig, Martin Posch, Quynh Nguyen, and Katharina Hees. On the use of non-concurrent controls in platform trials: A scoping review.Trials, 24(1):408, 2023

work page 2023
[6]

Dodd, Boris Freidlin, and Edward L

Lori E. Dodd, Boris Freidlin, and Edward L. Korn. Platform Trials — Beware the Noncomparable Control Group.New England Journal of Medicine, 384(16):1572–1573, 2021. ISSN 0028-4793. doi: 10.1056/nejmc2102446. 18

work page doi:10.1056/nejmc2102446 2021
[7]

Food and Drug Administration

U.S. Food and Drug Administration. Master protocols for drug and biological product development - guidance for industry. 2023. https://www.fda.gov/media/174976/download

work page 2023
[8]

Including non-concurrent control patients in the analysis of platform trials: Is it worth it?BMC Medical Research Methodology, 20(1):1–12, 2020

Kim May Lee and James Wason. Including non-concurrent control patients in the analysis of platform trials: Is it worth it?BMC Medical Research Methodology, 20(1):1–12, 2020. ISSN 14712288. doi: 10.1186/s12874-020-01043-6

work page doi:10.1186/s12874-020-01043-6 2020
[9]

On model-based time trend adjustments in platform trials with non-concurrent controls.BMC medical research methodology, 22(1): 1–16, 2022

Marta Bofill Roig, Pavla Krotka, Carl-Fredrik Burman, Ekkehard Glimm, Stefan M Gold, Katharina Hees, Peter Jacko, Franz Koenig, Dominic Magirr, Peter Mesenbrink, et al. On model-based time trend adjustments in platform trials with non-concurrent controls.BMC medical research methodology, 22(1): 1–16, 2022

work page 2022
[10]

Statistical mod- eling to adjust for time trends in adaptive platform trials utilizing non-concurrent controls.Biometrical Journal, 67(3):e70059, 2025

Pavla Krotka, Martin Posch, Mohamed Gewily, G¨ unter H¨ oglinger, and Marta Bofill Roig. Statistical mod- eling to adjust for time trends in adaptive platform trials utilizing non-concurrent controls.Biometrical Journal, 67(3):e70059, 2025

work page 2025
[11]

Analysis of adaptive platform trials using a network approach

Ian C Marschner and I Manjula Schou. Analysis of adaptive platform trials using a network approach. Clinical Trials, 19(5):479–489, 2022. doi: 10.1177/17407745221112001. URL https://doi.org/10. 1177/17407745221112001

work page doi:10.1177/17407745221112001 2022
[12]

Treatment comparisons in adaptive platform trials adjusting for temporal drift.Statistics in Biopharmaceutical Research, 16(3):361–370, 2024

Beibei Guo, Li Wang, and Ying Yuan. Treatment comparisons in adaptive platform trials adjusting for temporal drift.Statistics in Biopharmaceutical Research, 16(3):361–370, 2024

work page 2024
[13]

The bayesian time machine: Accounting for temporal drift in multi-arm platform trials.Clinical Trials, 19(5):490–501,

Benjamin R Saville, Donald A Berry, Nicholas S Berry, Kert Viele, and Scott M Berry. The bayesian time machine: Accounting for temporal drift in multi-arm platform trials.Clinical Trials, 19(5):490–501,

work page
[14]

URLhttps://doi.org/10.1177/17407745221112013

doi: 10.1177/17407745221112013. URLhttps://doi.org/10.1177/17407745221112013

work page doi:10.1177/17407745221112013
[15]

Robust meta-analytic-predictive priors in clinical trials with historical control information.Biometrics, 70(4):1023–1032, 2014

Heinz Schmidli, Sandro Gsteiger, Satrajit Roychoudhury, Anthony O’Hagan, David Spiegelhalter, and Beat Neuenschwander. Robust meta-analytic-predictive priors in clinical trials with historical control information.Biometrics, 70(4):1023–1032, 2014. doi: 10.1111/BIOM.12242

work page doi:10.1111/biom.12242 2014
[16]

Seaman III, Tomoyuki Kakizume, and Heinz Schmidli

Sebastian Weber, Yue Li, John W. Seaman III, Tomoyuki Kakizume, and Heinz Schmidli. Applying Meta-Analytic-Predictive Priors with the R Bayesian Evidence Synthesis Tools.Journal of Statistical Software, 100(19):1–32, 2021. doi: 10.18637/jss.v100.i19. URL https://www.jstatsoft.org/index. php/jss/article/view/v100i19

work page doi:10.18637/jss.v100.i19 2021
[17]

Treatment-control comparisons in platform trials including non-concurrent controls.Statistics in Biopharmaceutical Research, (just-accepted):1–29, 2025

Marta Bofill Roig, Pavla Krotka, Katharina Hees, Franz Koenig, Dominic Magirr, Peter Jacko, Tom Parke, and Martin Posch. Treatment-control comparisons in platform trials including non-concurrent controls.Statistics in Biopharmaceutical Research, (just-accepted):1–29, 2025

work page 2025
[18]

A multi-arm multi-stage platform design that allows preplanned addition of arms while still controlling the family-wise error.Statistics in Medicine, 43(19):3613–3632, 2024

Peter Greenstreet, Thomas Jaki, Alun Bedding, Chris Harbron, and Pavel Mozgunov. A multi-arm multi-stage platform design that allows preplanned addition of arms while still controlling the family-wise error.Statistics in Medicine, 43(19):3613–3632, 2024

work page 2024
[19]

Springer Series in Pharmaceutical Statistics, 2016

Gernot Wassmer and Werner Brannath.Group Sequential and Confirmatory Adaptive Designs in Clinical Trials. Springer Series in Pharmaceutical Statistics, 2016. ISBN 978-3-319-32560-6. URL http://link.springer.com/10.1007/978-3-319-32562-0

work page doi:10.1007/978-3-319-32562-0 2016
[20]

Conditional bias of point estimates following a group sequential test.Journal of Biopharmaceutical Statistics, 14(2):505–530, 2004

Xiaoyin Fan, David L DeMets, and KK Gordon Lan. Conditional bias of point estimates following a group sequential test.Journal of Biopharmaceutical Statistics, 14(2):505–530, 2004

work page 2004
[21]

Point estimation following a two-stage group sequential trial

Michael J Grayling and James MS Wason. Point estimation following a two-stage group sequential trial. Statistical Methods in Medical Research, 32(2):287–304, 2023

work page 2023
[22]

Point estimation for adaptive trial designs I: A methodological review.Statistics in medicine, 42(2):122–145, 2023

David S Robertson, Babak Choodari-Oskooei, Munya Dimairo, Laura Flight, Philip Pallmann, and Thomas Jaki. Point estimation for adaptive trial designs I: A methodological review.Statistics in medicine, 42(2):122–145, 2023

work page 2023
[23]

On the bias of maximum likelihood estimation following a sequential test.Biometrika, 73(3):573–581, 1986

John Whitehead. On the bias of maximum likelihood estimation following a sequential test.Biometrika, 73(3):573–581, 1986. 19

work page 1986
[24]

Parameter estimation following group sequential hypothesis testing.Biometrika, 77(4):875–892, 1990

Scott S Emerson and Thomas R Fleming. Parameter estimation following group sequential hypothesis testing.Biometrika, 77(4):875–892, 1990

work page 1990
[25]

Unbiased estimation following a group sequential test.Biometrika, 86(1):71–78, 1999

Aiyi Liu and WJ Hall. Unbiased estimation following a group sequential test.Biometrika, 86(1):71–78, 1999

work page 1999
[26]

Confidence intervals for a normal mean following a group sequential test.Biometrics, pages 247–254, 1989

Myron N Chang. Confidence intervals for a normal mean following a group sequential test.Biometrics, pages 247–254, 1989

work page 1989
[27]

Exact confidence intervals following a group sequential trial: A comparison of methods.Biometrika, 75(4):723–729, 1988

Gary L Rosner and Anastasios A Tsiatis. Exact confidence intervals following a group sequential trial: A comparison of methods.Biometrika, 75(4):723–729, 1988. 20 A Derivation of the bias of the model-based treatment effect estimator for Arm 2 Let ¯yks denote the sample mean in arm k and period s. Assume there is a stepwise time trend in the platform tria...

work page 1988
[28]

¯y11 −¯y01 |¯y11 −¯y01 ≥c 1 ·σ r 1 n11 + 1 n01 # −E

Hence, the sample means in period 1 ¯y01 and ¯y11 follow normal distributions with means µ0 and µ1, respectively. In period 2, the sample means ¯y02, ¯y12, and ¯y22 follow normal distributions with means µ0 + λ, µ1 + λ, and µ2 + λ, respectively. Denote by Z11 = ( ¯y11 −¯y01)/σ p 1/n11 + 1/n01 the Z-statistic from the interim analysis of Arm 1. The arm is ...

work page

[1] [1]

The Evolution of Master Protocol Clinical Trial Designs: A Systematic Literature Review.Clinical Therapeutics, 42(7):1330–1360, 2020

Elias Laurin Meyer, Peter Mesenbrink, Cornelia Dunger-Baldauf, Hans J¨ urgen F¨ ulle, Ekkehard Glimm, Yuhan Li, Martin Posch, and Franz Koenig. The Evolution of Master Protocol Clinical Trial Designs: A Systematic Literature Review.Clinical Therapeutics, 42(7):1330–1360, 2020. ISSN 0149-2918. doi: 10.1016/J.CLINTHERA.2020.05.010

work page doi:10.1016/j.clinthera.2020.05.010 2020

[2] [2]

Current state-of-the-art and gaps in platform trials: 10 things you should know, insights from EU-PEARL.Eclinicalmedicine, 67, 2024

Franz Koenig, C´ ecile Spiertz, Daniel Millar, Sarai Rodr´ ıguez-Navarro, N´ uria Mach´ ın, Ann Van Dessel, Joan Genesc` a, Juan M Peric` as, Martin Posch, Adrian S´ anchez-Montalva, et al. Current state-of-the-art and gaps in platform trials: 10 things you should know, insights from EU-PEARL.Eclinicalmedicine, 67, 2024

work page 2024

[3] [3]

Janet Woodcock and Lisa M. LaVange. Master Protocols to Study Multiple Therapies, Multiple Diseases, or Both.New England Journal of Medicine, 377(1):62–70, 2017. ISSN 0028-4793. URL https://www.nejm.org/doi/10.1056/NEJMra1510062

work page doi:10.1056/nejmra1510062 2017

[4] [4]

Angus, Brian M

Derek C. Angus, Brian M. Alexander, Scott Berry, Meredith Buxton, Roger Lewis, Melissa Paoloni, Steven A.R. Webb, Steven Arnold, Anna Barker, Donald A. Berry, Marc J.M. Bonten, Mary Brophy, Christopher Butler, Timothy F. Cloughesy, Lennie P.G. Derde, Laura J. Esserman, Ryan Ferguson, Louis Fiore, Sarah C. Gaffey, J. Michael Gaziano, Kathy Giusti, Herman G...

work page 2019

[5] [5]

On the use of non-concurrent controls in platform trials: A scoping review.Trials, 24(1):408, 2023

Marta Bofill Roig, Cora Burgwinkel, Ursula Garczarek, Franz Koenig, Martin Posch, Quynh Nguyen, and Katharina Hees. On the use of non-concurrent controls in platform trials: A scoping review.Trials, 24(1):408, 2023

work page 2023

[6] [6]

Dodd, Boris Freidlin, and Edward L

Lori E. Dodd, Boris Freidlin, and Edward L. Korn. Platform Trials — Beware the Noncomparable Control Group.New England Journal of Medicine, 384(16):1572–1573, 2021. ISSN 0028-4793. doi: 10.1056/nejmc2102446. 18

work page doi:10.1056/nejmc2102446 2021

[7] [7]

Food and Drug Administration

U.S. Food and Drug Administration. Master protocols for drug and biological product development - guidance for industry. 2023. https://www.fda.gov/media/174976/download

work page 2023

[8] [8]

Including non-concurrent control patients in the analysis of platform trials: Is it worth it?BMC Medical Research Methodology, 20(1):1–12, 2020

Kim May Lee and James Wason. Including non-concurrent control patients in the analysis of platform trials: Is it worth it?BMC Medical Research Methodology, 20(1):1–12, 2020. ISSN 14712288. doi: 10.1186/s12874-020-01043-6

work page doi:10.1186/s12874-020-01043-6 2020

[9] [9]

On model-based time trend adjustments in platform trials with non-concurrent controls.BMC medical research methodology, 22(1): 1–16, 2022

Marta Bofill Roig, Pavla Krotka, Carl-Fredrik Burman, Ekkehard Glimm, Stefan M Gold, Katharina Hees, Peter Jacko, Franz Koenig, Dominic Magirr, Peter Mesenbrink, et al. On model-based time trend adjustments in platform trials with non-concurrent controls.BMC medical research methodology, 22(1): 1–16, 2022

work page 2022

[10] [10]

Statistical mod- eling to adjust for time trends in adaptive platform trials utilizing non-concurrent controls.Biometrical Journal, 67(3):e70059, 2025

Pavla Krotka, Martin Posch, Mohamed Gewily, G¨ unter H¨ oglinger, and Marta Bofill Roig. Statistical mod- eling to adjust for time trends in adaptive platform trials utilizing non-concurrent controls.Biometrical Journal, 67(3):e70059, 2025

work page 2025

[11] [11]

Analysis of adaptive platform trials using a network approach

Ian C Marschner and I Manjula Schou. Analysis of adaptive platform trials using a network approach. Clinical Trials, 19(5):479–489, 2022. doi: 10.1177/17407745221112001. URL https://doi.org/10. 1177/17407745221112001

work page doi:10.1177/17407745221112001 2022

[12] [12]

Treatment comparisons in adaptive platform trials adjusting for temporal drift.Statistics in Biopharmaceutical Research, 16(3):361–370, 2024

Beibei Guo, Li Wang, and Ying Yuan. Treatment comparisons in adaptive platform trials adjusting for temporal drift.Statistics in Biopharmaceutical Research, 16(3):361–370, 2024

work page 2024

[13] [13]

The bayesian time machine: Accounting for temporal drift in multi-arm platform trials.Clinical Trials, 19(5):490–501,

Benjamin R Saville, Donald A Berry, Nicholas S Berry, Kert Viele, and Scott M Berry. The bayesian time machine: Accounting for temporal drift in multi-arm platform trials.Clinical Trials, 19(5):490–501,

work page

[14] [14]

URLhttps://doi.org/10.1177/17407745221112013

doi: 10.1177/17407745221112013. URLhttps://doi.org/10.1177/17407745221112013

work page doi:10.1177/17407745221112013

[15] [15]

Robust meta-analytic-predictive priors in clinical trials with historical control information.Biometrics, 70(4):1023–1032, 2014

Heinz Schmidli, Sandro Gsteiger, Satrajit Roychoudhury, Anthony O’Hagan, David Spiegelhalter, and Beat Neuenschwander. Robust meta-analytic-predictive priors in clinical trials with historical control information.Biometrics, 70(4):1023–1032, 2014. doi: 10.1111/BIOM.12242

work page doi:10.1111/biom.12242 2014

[16] [16]

Seaman III, Tomoyuki Kakizume, and Heinz Schmidli

Sebastian Weber, Yue Li, John W. Seaman III, Tomoyuki Kakizume, and Heinz Schmidli. Applying Meta-Analytic-Predictive Priors with the R Bayesian Evidence Synthesis Tools.Journal of Statistical Software, 100(19):1–32, 2021. doi: 10.18637/jss.v100.i19. URL https://www.jstatsoft.org/index. php/jss/article/view/v100i19

work page doi:10.18637/jss.v100.i19 2021

[17] [17]

Treatment-control comparisons in platform trials including non-concurrent controls.Statistics in Biopharmaceutical Research, (just-accepted):1–29, 2025

Marta Bofill Roig, Pavla Krotka, Katharina Hees, Franz Koenig, Dominic Magirr, Peter Jacko, Tom Parke, and Martin Posch. Treatment-control comparisons in platform trials including non-concurrent controls.Statistics in Biopharmaceutical Research, (just-accepted):1–29, 2025

work page 2025

[18] [18]

A multi-arm multi-stage platform design that allows preplanned addition of arms while still controlling the family-wise error.Statistics in Medicine, 43(19):3613–3632, 2024

Peter Greenstreet, Thomas Jaki, Alun Bedding, Chris Harbron, and Pavel Mozgunov. A multi-arm multi-stage platform design that allows preplanned addition of arms while still controlling the family-wise error.Statistics in Medicine, 43(19):3613–3632, 2024

work page 2024

[19] [19]

Springer Series in Pharmaceutical Statistics, 2016

Gernot Wassmer and Werner Brannath.Group Sequential and Confirmatory Adaptive Designs in Clinical Trials. Springer Series in Pharmaceutical Statistics, 2016. ISBN 978-3-319-32560-6. URL http://link.springer.com/10.1007/978-3-319-32562-0

work page doi:10.1007/978-3-319-32562-0 2016

[20] [20]

Conditional bias of point estimates following a group sequential test.Journal of Biopharmaceutical Statistics, 14(2):505–530, 2004

Xiaoyin Fan, David L DeMets, and KK Gordon Lan. Conditional bias of point estimates following a group sequential test.Journal of Biopharmaceutical Statistics, 14(2):505–530, 2004

work page 2004

[21] [21]

Point estimation following a two-stage group sequential trial

Michael J Grayling and James MS Wason. Point estimation following a two-stage group sequential trial. Statistical Methods in Medical Research, 32(2):287–304, 2023

work page 2023

[22] [22]

Point estimation for adaptive trial designs I: A methodological review.Statistics in medicine, 42(2):122–145, 2023

David S Robertson, Babak Choodari-Oskooei, Munya Dimairo, Laura Flight, Philip Pallmann, and Thomas Jaki. Point estimation for adaptive trial designs I: A methodological review.Statistics in medicine, 42(2):122–145, 2023

work page 2023

[23] [23]

On the bias of maximum likelihood estimation following a sequential test.Biometrika, 73(3):573–581, 1986

John Whitehead. On the bias of maximum likelihood estimation following a sequential test.Biometrika, 73(3):573–581, 1986. 19

work page 1986

[24] [24]

Parameter estimation following group sequential hypothesis testing.Biometrika, 77(4):875–892, 1990

Scott S Emerson and Thomas R Fleming. Parameter estimation following group sequential hypothesis testing.Biometrika, 77(4):875–892, 1990

work page 1990

[25] [25]

Unbiased estimation following a group sequential test.Biometrika, 86(1):71–78, 1999

Aiyi Liu and WJ Hall. Unbiased estimation following a group sequential test.Biometrika, 86(1):71–78, 1999

work page 1999

[26] [26]

Confidence intervals for a normal mean following a group sequential test.Biometrics, pages 247–254, 1989

Myron N Chang. Confidence intervals for a normal mean following a group sequential test.Biometrics, pages 247–254, 1989

work page 1989

[27] [27]

Exact confidence intervals following a group sequential trial: A comparison of methods.Biometrika, 75(4):723–729, 1988

Gary L Rosner and Anastasios A Tsiatis. Exact confidence intervals following a group sequential trial: A comparison of methods.Biometrika, 75(4):723–729, 1988. 20 A Derivation of the bias of the model-based treatment effect estimator for Arm 2 Let ¯yks denote the sample mean in arm k and period s. Assume there is a stepwise time trend in the platform tria...

work page 1988

[28] [28]

¯y11 −¯y01 |¯y11 −¯y01 ≥c 1 ·σ r 1 n11 + 1 n01 # −E

Hence, the sample means in period 1 ¯y01 and ¯y11 follow normal distributions with means µ0 and µ1, respectively. In period 2, the sample means ¯y02, ¯y12, and ¯y22 follow normal distributions with means µ0 + λ, µ1 + λ, and µ2 + λ, respectively. Denote by Z11 = ( ¯y11 −¯y01)/σ p 1/n11 + 1/n01 the Z-statistic from the interim analysis of Arm 1. The arm is ...

work page