Pith. sign in

REVIEW 3 major objections 5 minor 63 references

This paper claims that powering a SMART to compare treatment strategies can be done by simulating realistic synthetic trials from pilot data, without the restrictive formulas of current calculators.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

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

T0 review · deepseek-v4-flash

2026-08-01 06:47 UTC pith:U7VYJ7II

load-bearing objection The paper fills a real gap in SMART power analysis, but its effect-size calibration is mathematically wrong, so the reported power curves do not correspond to the stated effect size. the 3 major comments →

arxiv 2607.21751 v1 pith:U7VYJ7II submitted 2026-07-23 stat.OT

Simulation-based Power Analysis for Sequential Multiple Assignment Randomized Trials

Niki Z. Petrakos , Erica E. M. Moodie , Nicolas Savy , Manon de Raad , Eric Belzile , Sylvie Lambert This is my paper
classification stat.OT
keywords SMARTdynamic treatment regimepower analysissample sizesimulationsynthetic datapilot trialresponder status
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The paper proposes a simulation-based way to determine sample size for the third aim of a SMART: comparing two treatment strategies that begin with different first-stage treatments. Instead of relying on sample-size formulas that assume equal response rates, equal arm sizes, and fixed effect sizes, the method fits generative models to pilot SMART data, augmented with external baseline data, and simulates full trials. By repeating many simulated trials at different sample sizes, it estimates power and lets trialists compare alternative design decisions, such as a stricter definition of 'responder,' before committing to the full trial. The authors show their sample-size estimates track a standard calculator at large effect sizes but diverge at small effect sizes, where the simulation captures the gap between fixed and observed effect sizes. If sound, this gives SMARTs a way to be powered for the treatment-sequence comparisons they are designed to answer.

Core claim

The paper's central claim is that the effect-size calibration equation can inject a known standardized effect into synthetically generated SMART data. After fitting regression-based generative models to pilot data, coefficients are chosen so that the difference between two embedded dynamic treatment regimes equals a target standardized effect, with response probabilities to the two stage-1 treatments entering the constraint. Once calibrated, the simulation pipeline generates full SMART data sets: baseline covariates from a flexible multivariate model, treatments by the trial's randomization scheme, intermediate tailoring variables by regression, responder status by the design's definition, s

What carries the argument

The load-bearing machinery is the sequential synthetic-data generator—a flexible multivariate model (an R-vine copula) for baseline covariates followed by regression models for post-randomization variables, with multiple imputation handling missingness—plus the effect-size calibration identity: the standardized effect equals a linear combination of outcome-model coefficients and response probabilities. This identity converts a chosen effect size into a constraint on the outcome-model coefficients, so every simulated trial contains a known 'true' effect even as response probabilities fluctuate with the random synthetic data.

Load-bearing premise

In the effect-size derivation (Section 4.3.2, Equations 3–4), the math assumes the average baseline and intermediate characteristics are the same for responders and non-responders, so those characteristics cancel out of the effect-size formula; but response status is defined from those very characteristics, so the cancellation generally does not hold.

What would settle it

Generate a synthetic cohort under the paper's procedure using the calibrated coefficients, then compute the actual standardized mean difference in the outcome between the two compared strategies. If that observed difference systematically diverges from the nominal effect size, especially when responder groups differ in baseline covariates, the calibration identity is not delivering the effect size the power curve claims.

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

If this is right

  • A trialist can power a full-scale SMART for an aim-3 comparison, including strategies with different first-stage treatments, without assuming equal response rates or equal arm sizes.
  • Design choices such as the responder definition can be varied in simulation, and the required sample size can be compared across designs before finalizing a protocol.
  • Stage-specific attrition is built into simulated trials rather than approximated by a single drop-out inflation factor.
  • At large expected effect sizes, results match a standard sample-size calculator, so the calculator remains adequate there; at small effect sizes the simulation reveals when the fixed effect size is not the effect size the trial would actually observe.
  • Because response rates vary across simulated data sets, the resulting power curve reflects uncertainty around the true effect size rather than an exact value.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same generative pipeline should extend to aim-4 comparisons (estimating the optimal dynamic treatment regime) if the test statistic is changed to account for correlated strategy outcomes, a direction the paper notes but does not develop.
  • The effect-size calibration assumes that average baseline and stage-1 characteristics are identical for responders and non-responders, which is only approximately true when response status is a deterministic function of those characteristics; a robust version would model the conditional means directly.
  • Because external data enter only at baseline, post-baseline realism is bounded by pilot sample size; borrowing external post-baseline data or increasing pilot size would reduce parameter uncertainty.
  • The design-comparison logic suggests a testable extension: pre-specify several candidate responder definitions, run the fixed-data-generating-mechanism investigation, and select the design with the largest expected effect size—an empirical decision rule that could be automated.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 5 minor

Summary. The manuscript proposes a simulation-based power analysis for SMARTs that compares embedded dynamic treatment regimes beginning with different stage-1 treatments (aim 3). The procedure uses pilot SMART data, augmented at baseline by external data, to fit a sequence of generative models (R-vine copula at baseline; regressions post-baseline) and generates synthetic SMART data with attrition. For power calculations, the outcome generation model is modified by calibrating β4 so that Equation (4) yields a pre-specified standardized effect size δ between two strategies (A vs. C). Two investigations are presented: fixing the data-generating mechanism and predicting δ under competing responder-status designs, and fixing δ while re-calibrating per design. Results are compared with the SMARTsize calculator. The central claim is that this is the first simulation-based tool for SMART aim-3 comparisons that avoids the simplifying assumptions of existing calculators.

Significance. If the calibration procedure were valid, the paper would fill a real methodological gap: there is little simulation-based support for powering SMARTs to compare EDTRs with different stage-1 treatments, and the sequential generative framework is a natural and flexible way to leverage pilot data. The authors provide reproducible code, describe the synthetic-data pipeline in detail, and make a reasonable comparison against SMARTsize. These are genuine strengths. However, the validity of the entire procedure rests on Equation (4) and the calibration of β4. As detailed below, this equation is derived under an incorrect conditional-expectation calculation, so the synthetic data do not necessarily contain the intended effect size. The reported power curves and sample-size estimates are therefore not for the effect size the authors claim, and the competing-design comparison in Figure 2 inherits the same flaw.

major comments (3)
  1. [§4.3.2, Eqs. (3)–(4)] The derivation of Equation (4) is invalid. In the second line of Eq. (3), E[Y | A1, A2, R1=r1] is expanded using the outcome model Y = β0 + β1X + β2A1 + β3I(A2=1) + β4I(A2=2) + ε, but the manuscript then replaces E[X | A1, R1] with the unconditional E[X] and treats this as common to both A1=1 and A1=0. This is not justified: X explicitly includes stage-1 tailoring variables Z11 and Z12, and Table 3 shows that these are generated as linear regressions on X and A1. Hence E[Z11 | A1=1] ≠ E[Z11 | A1=0] and similarly for Z12. The strategy-A mean contains β1E[X | A1=1] while the strategy-C mean contains β1E[X | A1=0], so the A−C contrast in Eq. (4) is missing the term β1(E[X | A1=1] − E[X | A1=0]). Because β1 is a fitted coefficient from the pilot data, this omitted term is generally nonzero and need not be small. Consequently, the calibrated β4 does not guarantee that the synthetic data have
  2. [§4.4 and Fig. 2] The 'predicted' effect sizes for Designs II and III are computed using the same flawed Equation (4), with p0 and p1 set to the synthetic response probabilities and β2, β3, β4 set to the values calibrated for Design I. Since Eq. (4) omits the A1-dependent covariate means, the δ distributions shown in the right-hand panel of Figure 2 are not estimates of a true effect size under competing designs; they are deterministic functions of the same misspecified model used to calibrate β4. The conclusion that 'Design II yields the largest effect size' and the corresponding power curves therefore are not supported. The observation that the effect size is driven by p1 is also a mathematical consequence of the form of Eq. (4) rather than an empirical finding about the synthetic data.
  3. [§4.5 and Table 1] The second investigation, which fixes δ and varies the data-generating mechanism per design, also relies on the calibration formula in Eq. (4): β4 is recalculated for each design using the same expression. Because that expression is incorrect, the recalibrated β4 values do not produce the nominal δ in the synthetic data. The sample-size comparisons with SMARTsize in Table 1 and Figure 3 are therefore not anchored to the intended effect size. This problem is independent of the choice of β2 and β3; it is intrinsic to replacing conditional covariate means with unconditional means. The Appendix derivations for the other strategy pairs (A vs. D, B vs. C, B vs. D) repeat the same simplification and are invalid for the same reason.
minor comments (5)
  1. [Appendix B.2, Table 4 caption] The caption says the table corresponds to the 'first investigation' but parenthetically describes 'a different data generating mechanism was used for each design (i.e., β4 was re-defined per design)', which is the second investigation described in §4.5. The caption is internally inconsistent and should be corrected.
  2. [§4.3.2, after Eq. (4)] The sentence beginning 'This requires fixing the values of S, p0, p1' lists S=Ŝr as an empirical estimate from the real pilot data and p0, p1 as empirical estimates from the synthetic data. It is not explained why p's are taken from synthetic data rather than from the pilot design when the goal is to specify a target effect size; using simulation-dependent p's makes the 'fixed' δ a stochastic target.
  3. [§4.3.1 and Table 3] The generative model for Design II responder status is listed in Table 3 as using 'Baseline HADS, X1, Z11, Z12', while the Design II definition in §4.4 refers only to DT and HADS decreases. The role of baseline HADS beyond its inclusion in X1 is unclear; please clarify.
  4. [Figure 10 caption] The caption states the RCT data are displayed in 'peach' twice; the synthetic data appear to be labeled peach as well. The color legend for this figure needs to be checked.
  5. [§4.4, first paragraph] The response probabilities are denoted with a superscript rI (e.g., p̂^{rI}_1 = 0.52), and later synthetic probabilities are denoted p̂^{sI}_1. The notation is clear but somewhat heavy; a short summary table of all design-specific response rates would help readability.

Circularity Check

1 steps flagged

Effect sizes for competing designs are computed from the same calibration equation used to force δ under Design I, so the reported design ordering is forced by construction.

specific steps
  1. fitted input called prediction [Section 4.3.2 (Eq. 4) and Section 4.4 (Fig. 2)]
    "Then, to ensure a data-generating standardized effect size of δ in the synthetic data (such that the power calculation is valid), select β2, β3, β4 such that the above equality holds. ... Now fixing these β0, β1, β2, β3 as the fitted values and β4 as β̂4 calculated from Equation 4, calculate the value of δ for Design II and Design III using Equation 4 with p1, p0 set as p̂sII0, p̂sII1 and p̂sIII0, p̂sIII1, respectively."

    Equation 4 is first inverted to choose β̂4 so that Design I has δ=0.2. The same equation is then evaluated at Designs II and III response probabilities to produce the 'expected effect size' distributions shown in Figure 2. The ordering (Design II largest, then III, then I) is therefore an algebraic consequence of the calibration equation and the response probabilities, not an independent empirical estimate from generated outcome data. Additionally, Eq. 4 was obtained by replacing E[X|A1,R1] with the unconditional E[X], even though X includes stage-1 tailoring variables Z11 and Z12 whose generation depends on A1 (Table 3); consequently, the calibrated quantity is not the actual strategy-mean difference defined in Eq. 1, and the 'predicted' δs are values of a misspecified identity by constru

full rationale

The paper's central simulation-based sample-size estimation is largely self-contained: synthetic data are generated from fitted models, the two-sample t-test is applied, and results are benchmarked against the external SMARTsize calculator, with discrepancies attributed to fixed-versus-observed effect sizes. That core power calculation is not circular. The circularity arises in the first advertised mode—'fixing the data generating mechanism and estimating effect size under different designs'—where the effect sizes for Designs II and III are not simulated but computed from Eq. 4, the very equation used to calibrate β4 under Design I. The conclusion that Design II yields the largest effect size is thus forced by the calibration scheme rather than discovered from synthetic outcome data. A separate correctness concern (not counted as circularity by itself) is that Eq. 4 drops the A1-dependent covariate terms in X, so the calibrated δ may not equal the true standardized strategy-mean difference; this reinforces that the design-comparison 'predictions' are properties of the calibration equation rather than of the actual data-generating process.

Axiom & Free-Parameter Ledger

5 free parameters · 5 axioms · 0 invented entities

The central claim rests on a chain of fitted quantities (β coefficients, response probabilities, variance estimate, dropout rates), all derived from a very small pilot (n=48). The most serious issue is the implicit axiom that covariate means cancel in the response-stratified contrast, which is false and breaks the effect-size calibration. The competing-design predictions further depend on the invariance of treatment effects across designs, which is assumed without evidence.

free parameters (5)
  • β4 (stage-2 treatment effect for A2=2) = Calibrated per simulation/imputation via Eq. 4 to enforce target δ; exact values not reported
    β4 is solved from Equation (4) to make the standardized effect equal δ in the synthetic data. This is a parameter fitted to the pilot data and recalibrated, and it directly determines the power curves.
  • β2, β3 (stage-1 and A2=1 treatment effects) = Estimated from 48-patient pilot SMART via regression; values not reported
    These coefficients are fit to the pilot data and are load-bearing in Equation (4). Their uncertainty and possible bias directly affect the calibrated effect size and the competing-design predictions.
  • Ŝr (standardizing variance in δ definition) = Empirical estimate from pilot data
    S is used to convert the mean difference into the standardized effect δ. If the actual variance of the generated outcomes differs from Ŝr, the true standardized effect in the synthetic data differs from the nominal δ.
  • p̂s0, p̂s1 (response rates per design) = Estimated from synthetic data; vary per simulation run and design
    The response probabilities enter directly into Equation (4) and are used to calibrate β4 and to compute predicted δ for competing designs. They are not fixed parameters but data-dependent quantities, adding another layer of variability.
  • Dropout probabilities at T1 and T2 = 0.06 and 0.07 (three dropouts each from pilot)
    Attrition is simulated by Bernoulli draws with probabilities equal to the observed pilot drop-out rates. These estimates come from six total dropouts and are used to impose missingness on the synthetic data, affecting the analyzed sample and power.
axioms (5)
  • domain assumption The R-vine copula and sequential regression generative models recapitulate the target population distribution.
    The entire synthetic data generation relies on these models, fit to a 48-patient pilot and augmented external data, faithfully representing the distribution of the future full-scale SMART population (Section 4.1, 4.3.1).
  • domain assumption External data augmentation via 'static borrowing' does not bias the baseline covariate distribution.
    The baseline data are a mixture of pilot SMART data and an external RCT; the method assumes that after applying inclusion/exclusion criteria, the augmented sample is representative of the target population (Section 3).
  • ad hoc to paper The outcome model coefficients β2, β3, β4 are invariant across different responder-status definitions (Designs I-III).
    In Section 4.4, the same fitted β coefficients are used to compute effect sizes under Designs II and III; this assumes that changing the responder definition does not change the treatment effects, which is a strong and untested assumption.
  • ad hoc to paper E[X | A1, R] = E[X], so covariate terms cancel in the effect-size contrast.
    Equation (3)-(4) replace the conditional mean of X given response status with the unconditional mean. Since R is a deterministic function of X and Z11, this is generally false and is the central mathematical flaw of the calibration step.
  • ad hoc to paper Recalibrating β4 per simulation run based on the synthetic response probabilities yields a meaningful power curve.
    The paper states p̂s0 and p̂s1 change per simulation run and β4 is chosen accordingly, meaning the true treatment effect is not fixed across simulated trials. The power calculation then mixes different data-generating mechanisms, which is non-standard.

pith-pipeline@v1.3.0-alltime-deepseek · 28554 in / 16387 out tokens · 156318 ms · 2026-08-01T06:47:34.510094+00:00 · methodology

0 comments
read the original abstract

Sequential Multiple Assignment Randomized Trials (SMARTs) provide evidence for treatment sequences based on patient profiles, which is relevant in chronic disease settings. Sample size formulae implemented in calculators are the primary tool available to power SMARTs, though they require strong assumptions. We propose a simulation-based procedure omitting these assumptions, instead generating realistic synthetic SMART data by fitting models to real pilot data, to power SMARTs to compare treatment strategies. The proposed framework powers designs in two ways: by fixing the data generating mechanism and estimating effect size under different designs, or by fixing effect size and varying operational decisions within the SMART. Comparing our results to a calculator (SMARTsize), estimated sample sizes at varying power levels were similar at larger fixed effect sizes, whereas a discrepancy was apparent at smaller effect sizes due to differences between fixed and observed effect sizes in the simulated trials. The simulation-based procedure's ability to capture this effect size fluctuation is advantageous for smaller expected effect sizes, as it is essential to ensure adequate sample size to avoid a type II error. In providing flexible tools to power competing SMART designs, the full potential of SMARTs to build treatment sequences can be better realized.

Figures

Figures reproduced from arXiv: 2607.21751 by Erica E. M. Moodie, Eric Belzile, Manon de Raad, Nicolas Savy, Niki Z. Petrakos, Sylvie Lambert.

Figure 1
Figure 1. Figure 1: Flowchart showing the pilot cancer SMART design, with labels for each of the four potential strategies (Strategy A in red, B in purple, C in blue, D in green). The symbols R in boxes represent points of treatment (re-)randomization. The external data source is an RCT that compared a novel telephone-delivered depression self-care intervention, called CanDirect, to usual care among cancer patients (McCusker … view at source ↗
Figure 2
Figure 2. Figure 2: On the left: power curves for Design I (the original pilot design) as well as the two competing designs (Design II in green, Design III in purple), under a fixed data generating mechanism (setting δ = 0.2 under Design I). On the right: distribution of computed values of δ using Equation 4, setting β parameters in the outcome generation model for Design II and Design III to be equal to the values of β under… view at source ↗
Figure 3
Figure 3. Figure 3: Power curves for Design I (the original pilot design) as well as the two competing designs (Design II in green, Design III in purple), for different effect sizes (δ = 0.2 depicted by a solid line, δ = 0.5 depicted by a dashed line). 6 Discussion and Conclusion We have proposed a novel simulation-based procedure to power designs for a full-scale SMART, comparing EDTRs that differ in stage 1 treatment. The s… view at source ↗
Figure 4
Figure 4. Figure 4: Univariate density plot of age in the baseline Cancer SMART complete cases (pink), the RCT complete cases (peach), and one synthetic data set (blue). 0% 20% 40% 60% 80% Female Male Sex Percent Data SMART RCT Synthetic [PITH_FULL_IMAGE:figures/full_fig_p024_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Univariate density plot of sex in the baseline Cancer SMART complete cases (pink), the RCT complete cases (peach), and one synthetic data set (blue). 24 [PITH_FULL_IMAGE:figures/full_fig_p024_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Univariate density plot of language in the baseline Cancer SMART complete cases (pink), the RCT complete cases (peach), and one synthetic data set (blue). 0% 20% 40% 60% Not Single Single Marital Status Percent Data SMART RCT Synthetic [PITH_FULL_IMAGE:figures/full_fig_p025_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Univariate density plot of marital status in the baseline Cancer SMART complete cases (pink), the RCT complete cases (peach), and one synthetic data set (blue). Data were coarsened so that categories better matched across the internal and external data (i.e., Married and Common Law were merged as Not Single, while Separated, Divorced, Widowed, and Single/Never Married were merged as Single). The Single/Nev… view at source ↗
Figure 8
Figure 8. Figure 8: Univariate density plot of highest level of education in the Cancer SMART complete cases (pink), the RCT complete cases (peach), and one synthetic data set (blue). Two of the categories in the SMART data were merged to better match the RCT: Undergraduate University Degree and Graduate Diploma were merged as University. Both the SMART and the RCT originally had missing education values. 0% 20% 40% 60% 80% C… view at source ↗
Figure 9
Figure 9. Figure 9: Univariate density plot of country of birth in the Cancer SMART complete cases (pink), the RCT complete cases (peach), and one synthetic data set (blue). The RCT originally had missing country of birth values whereas this variable was completely observed in the SMART. 26 [PITH_FULL_IMAGE:figures/full_fig_p026_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Univariate density plot of (continuous) HADS anxiety score at baseline in the Cancer SMART complete cases (pink), the RCT complete cases (peach), and one synthetic data set (peach). The RCT originally had missing values for this variable blue this variable was completely observed in the SMART. 27 [PITH_FULL_IMAGE:figures/full_fig_p027_10.png] view at source ↗

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

63 extracted references

  1. [1]

    2014 , journal = "

    Lambert, Sylvie D and Pallant, Julie F and Clover, Kerrie and Britton, Benjamin and King, Madeleine T and Carter, Gregory , title =. 2014 , journal = "

    2014

  2. [2]

    Lambert, Sylvie D and Moodie, Erica E. M. and McCusker, Jane and Lokhorst, Marion and Harris, Cheryl and Langmuir, Tori and Belzile, Eric and Laizner, Andrea Maria and Brahim, Lydia Ould and Wasserman, Sydney and Chehayeb, Sarah and Vickers, Michael and Duncan, Lindsay and Esplen, Mary Jane and Maheu, Christine and Howell, Doris and de Raad, Manon , title...

    2025

  3. [3]

    2021 , journal = "

    McCusker, Jane and Jones, Jennifer M and Li, Madeline and Faria, Rosana and Yaffe, Mark J and Lambert, Sylvie D and Ciampi, Antonio and Belzile, Eric and de Raad, Manon , title =. 2021 , journal = "

    2021

  4. [4]

    2001 , journal = "

    Kroenke, Kurt and Spitzer, Robert L and Williams, Janet B W , title =. 2001 , journal = "

    2001

  5. [5]

    2011 , journal = "

    Thekkumpurath, Parvez and Walker, Jane and Butcher, Isabella and Hodges, Laura and Kleiboer, Annet and O'Connor, Mark and Wall, Lucy and Murray, Gordon and Kroenke, Kurt and Sharpe, Michael , title =. 2011 , journal = "

    2011

  6. [6]

    2004 , journal = "

    Eton, David T and Cella, David and Yost, Kathleen J and Yount, Susan E and Peterman, Amy H and Neuberg, Donna S and Sledge, George W and Wood, William C , title =. 2004 , journal = "

    2004

  7. [7]

    1983 , journal = "

    Zigmond, A S and Snaith, R P , title =. 1983 , journal = "

    1983

  8. [8]

    Lovibond, S H and Lovibond, P F , title =

  9. [9]

    2025 , journal = "

    Petrakos, Niki Z and Moodie, Erica E M and Savy, Nicolas , title =. 2025 , journal = "

    2025

  10. [10]

    2025 , note = "

    Petrakos, Niki Z and Moodie, Erica E M and Savy, Nicolas , title =. 2025 , note = "

    2025

  11. [11]

    2005 , journal = "

    Murphy, Susan A , title =. 2005 , journal = "

    2005

  12. [12]

    2007 , journal = "

    Collins, Linda M and Murphy, Susan A and Strecher, Victor , title =. 2007 , journal = "

    2007

  13. [13]

    2014 , journal = "

    Lavori, Philip W and Dawson, Ree , title =. 2014 , journal = "

    2014

  14. [14]

    2011 , journal = "

    Chuang-Stein, Christy and Kirby, Simon and Hirsch, Ian and Atkinson, Gary , title =. 2011 , journal = "

    2011

  15. [15]

    2019 , journal = "

    Van Norman, Gail A , title =. 2019 , journal = "

    2019

  16. [16]

    2010 , journal = "

    Paul, Steven M and Mytelka, Daniel S and Dunwiddie, Christopher T and Persinger, Charles C and Munos, Bernard H and Lindborg, Stacy R and Schacht, Aaron L , title =. 2010 , journal = "

    2010

  17. [17]

    2016 , journal = "

    Van Norman, Gail A , title =. 2016 , journal = "

    2016

  18. [18]

    Causality and Psychopathology:

    Oetting, A I and Levy, J A and Weiss, R D and Murphy, S A , title =. Causality and Psychopathology:. 2007 , pages =

    2007

  19. [19]

    2025 , journal = "

    Jayawardana, Kaushala S and Dymock, Michael and Mahar, Robert K and Marsh, Julie A and Lee, Katherine J , title =. 2025 , journal = "

    2025

  20. [20]

    2018 , journal = "

    Thorlund, Kristian and Haggstrom, Jonas and Park, Jay J H and Mills, Edward J , title =. 2018 , journal = "

    2018

  21. [21]

    Adaptive Designs for Clinical Trials of Drugs and Biologics: Guidance for Industry , institution =

  22. [22]

    Adaptive Designs for Clinical Trials of Drugs and Biologics: Guidance for Industry , note =

  23. [23]

    2019 , note =

    Adaptive Designs for Clinical Trials of Drugs and Biologics:. 2019 , note =

    2019

  24. [24]

    2019 , address =

    Adaptive Designs for Clinical Trials of Drugs and Biologics:. 2019 , address =

    2019

  25. [25]

    2019 , journal = "

    Mayer, Cristiana and Perevozskaya, Inna and Leonov, Sergei and Dragalin, Vladimir and Pritchett, Yili and Bedding, Alun and Hartford, Alan and Fardipour, Parvin and Cicconetti, Greg , title =. 2019 , journal = "

    2019

  26. [26]

    2008 , journal = "

    Westfall, Peter H and Tsai, Kuenhi and Ogenstad, Stephan and Tomoiaga, Alin and Moseley, Scott and Lu, Yonggang , title =. 2008 , journal = "

    2008

  27. [27]

    2020 , journal = "

    Artman, William J and Nahum-Shani, Inbal and Wu, Tianshuang and Mckay, James R and Ertefaie, Ashkan , title =. 2020 , journal = "

    2020

  28. [28]

    2024 , url =

    Seewald, Nick and Williams, Augustus and Ye, Beiqin and Kidwell, Kelley M , title =. 2024 , url =

    2024

  29. [29]

    2017 , journal = "

    NeCamp, Timothy and Kilbourne, Amy and Almirall, Daniel , title =. 2017 , journal = "

    2017

  30. [30]

    2024 , journal = "

    Dziak, John J and Almirall, Daniel and Dempsey, Walter and Stanger, Catherine and Nahum-Shani, Inbal , title =. 2024 , journal = "

    2024

  31. [31]

    2016 , journal = "

    Kim, Hwanwoo and Ionides, Edward and Almirall, Daniel , title =. 2016 , journal = "

    2016

  32. [32]

    2012 , journal = "

    Almirall, Daniel and Compton, Scott N and Gunlicks-Stoessel, Meredith and Duan, Naihua and Murphy, Susan A , title =. 2012 , journal = "

    2012

  33. [33]

    2016 , journal = "

    Gunlicks-Stoessel, Meredith and Mufson, Laura and Westervelt, Ana and Almirall, Daniel and Murphy, Susan A , title =. 2016 , journal = "

    2016

  34. [34]

    2009 , journal = "

    Auyeung, S Freda and Long, Qi and Royster, Erica Bruce and Murthy, Smitha and McNutt, Marcia D and Lawson, David and Miller, Andrew and Manatunga, Amita and Musselman, Dominique L , title =. 2009 , journal = "

    2009

  35. [35]

    2023 , journal = "

    Lorenzoni, Giulia and Petracci, Elisabetta and Scarpi, Emanuela and Baldi, Ileana and Gregori, Dario and Nanni, Oriana , title =. 2023 , journal = "

    2023

  36. [36]

    2020 , journal = "

    Petracci, Elisabetta and Scarpi, Emanuela and Passardi, Alessandro and Biggeri, Annibale and Milandri, Carlo and Vecchia, Stefano and Gelsomino, Fabio and Tassinari, Davide and Tamberi, Stefano and Bernardini, Ilaria and Accettura, Caterina and Frassineti, Giovanni Luca and Amadori, Dino and Nanni, Oriana , title =. 2020 , journal = "

    2020

  37. [37]

    2025 , journal = "

    Freeman, Nikki L B and Browder, Sydney E and Rowland, Bryce and Jones, Emily P and Hoch, Margaret and Kim, Alice and Zhou, Christina W and Kahkoska, Anna R and McGinigle, Katharine L and Ivanova, Anastasia and Kosorok, Michael R and Anstrom, Kevin J , title =. 2025 , journal = "

    2025

  38. [38]

    2020 , journal = "

    Seewald, Nicholas J and Kidwell, Kelley M and Nahum-Shani, Inbal and Wu, Tianshuang and McKay, James R and Almirall, Daniel , title =. 2020 , journal = "

    2020

  39. [39]

    2022 , journal = "

    Bigirumurame, Theophile and Uwimpuhwe, Germaine and Wason, James , title =. 2022 , journal = "

    2022

  40. [40]

    2025 , journal = "

    Kim, Jongjin and Morales, Juan Francisco and Kang, Sanghoon and Klose, Marian and Willcocks, Rebecca J and Daniels, Michael J and Belfiore-Oshan, Ramona and Walter, Glenn A and Rooney, William D and Vandenborne, Krista and Kim, Sarah , title =. 2025 , journal = "

    2025

  41. [41]

    2024 , journal = "

    Ferstad, Johannes O and Prahalad, Priya and Maahs, David M and Zaharieva, Dessi P and Fox, Emily and Desai, Manisha and Johari, Ramesh and Scheinker, David , title =. 2024 , journal = "

    2024

  42. [42]

    2021 , journal = "

    Yan, Xiaoxi and Matchar, David B and Sivapragasam, Nirmali and Ansah, John P and Goel, Aastha and Chakraborty, Bibhas , title =. 2021 , journal = "

    2021

  43. [43]

    2019 , journal = "

    Pappalardo, Francesco and Russo, Giulia and Tshinanu, Flora Musuamba and Viceconti, Marco , title =. 2019 , journal = "

    2019

  44. [44]

    2024 , journal = "

    Friedrich, Sarah and Friede, Tim , title =. 2024 , journal = "

    2024

  45. [45]

    2018 , journal = "

    Kidwell, Kelley M and Seewald, Nicholas J and Tran, Qui and Kasari, Connie and Almirall, Daniel , title =. 2018 , journal = "

    2018

  46. [46]

    2023 , journal = "

    Franceschini, Marco and Boffa, Angelo and Pignotti, Elettra and Andriolo, Luca and Zaffagnini, Stefano and Filardo, Giuseppe , title =. 2023 , journal = "

    2023

  47. [47]

    2023 , address =

    Considerations for the Design and Conduct of Externally Controlled Trials for Drug and Biological Products:. 2023 , address =

    2023

  48. [48]

    2024 , journal = "

    Damone, Emily M and Zhu, Jiawen and Pang, Herbert and Li, Xiao and Zhao, Yinqi and Kwiatkowski, Evan and Carey, Lisa A and Ibrahim, Joseph G , title =. 2024 , journal = "

    2024

  49. [49]

    2023 , journal = "

    Yang, Peng and Zhao, Yuansong and Nie, Lei and Vallejo, Jonathon and Yuan, Ying , title =. 2023 , journal = "

    2023

  50. [50]

    2020 , journal = "

    Zhu, Ming and Sridhar, Saranya and Hollingsworth, Rosalind and Chit, Ayman and Kimball, Tammy and Murmello, Kerry and Greenberg, Michael and Gurunathan, Sanjay and Chen, Josh , title =. 2020 , journal = "

    2020

  51. [51]

    2018 , journal = "

    Lim, Jessica and Walley, Rosalind and Yuan, Jiacheng and Liu, Jeen and Dabral, Abhishek and Best, Nicky and Grieve, Andrew and Hampson, Lisa and Wolfram, Josephine and Woodward, Phil and Yong, Florence and Zhang, Xiang and Bowen, Ed , title =. 2018 , journal = "

    2018

  52. [52]

    2021 , journal = "

    Burger, Hans Ulrich and Gerlinger, Christoph and Harbron, Chris and Koch, Armin and Posch, Martin and Rochon, Justine and Schiel, Anja , title =. 2021 , journal = "

    2021

  53. [53]

    2019 , journal = "

    Lin, Junjing and Gamalo-Siebers, Margaret and Tiwari, Ram , title =. 2019 , journal = "

    2019

  54. [54]

    2020 , journal = "

    Wang, Chenguang and Lu, Nelson and Chen, Wei-Chen and Li, Heng and Tiwari, Ram and Xu, Yunling and Yue, Lilly Q , title =. 2020 , journal = "

    2020

  55. [55]

    2023 , journal = "

    Fu, Chenqi and Pang, Herbert and Zhou, Shouhao and Zhu, Jiawen , title =. 2023 , journal = "

    2023

  56. [56]

    2012 , journal = "

    Little, Roderick J and D'Agostino, Ralph and Cohen, Michael L and Dickersin, Kay and Emerson, Scott S and Farrar, John T and Frangakis, Constantine and Hogan, Joseph W and Molenberghs, Geert and Murphy, Susan A and Neaton, James D and Rotnitzky, Andrea and Scharfstein, Daniel and Shih, Weichung J and Siegel, Jay P and Stern, Hal , title =. 2012 , journal = "

    2012

  57. [57]

    2024 , journal = "

    Jeffers, Angela and Konrad, Kathryn and Larson, Gary and Allen-Moyer, Katherine and Cunny, Helen and Shockley, Keith , title =. 2024 , journal = "

    2024

  58. [58]

    2020 , journal = "

    Annunziata, Maria Antonietta and Muzzatti, Barbara and Bidoli, Ettore and Flaiban, Cristiana and Bomben, Francesca and Piccinin, Marika and Gipponi, Katiuscia Maria and Mariutti, Giulia and Busato, Sara and Mella, Sara , title =. 2020 , journal = "

    2020

  59. [59]

    2018 , journal = "

    Rombach, Ines and Jenkinson, Crispin and Gray, Alastair M and Murray, David W and Rivero-Arias, Oliver , title =. 2018 , journal = "

    2018

  60. [60]

    2023 , journal = "

    Wang, Xinru and Chakraborty, Bibhas , title =. 2023 , journal = "

    2023

  61. [61]

    2018 , journal = "

    Hariton, Eduardo and Locascio, Joseph J , title =. 2018 , journal = "

    2018

  62. [62]

    Case Studies in Innovative Clinical Trials , editor =

    Lambert, Sylvie D and Brahim, Lydia O and Moodie, Erica E M , title =. Case Studies in Innovative Clinical Trials , editor =. 2023 , pages =

    2023

  63. [63]

    2026 , journal = "

    Lambert, Sylvie D and Wasserman, Sydney and Bédard, Mélanie and Brahim, Lydia O and Frati, Francesca and Moodie, Erica E M , title =. 2026 , journal = "

    2026