arXiv subjects

Stef Baas

Publications and source records attributed to Stef Baas.

12 recordsLinked to original sources

arXiv2026

Adaptive clinical trials based on design-optimal e-values with automatic curtailment: An application to single-arm trials with binary data

The e-value is gaining traction as a robust alternative to p-values and Bayes factors for quantifying statistical evidence. e-values are a promising method for adaptive clinical trials due to their anytime-validity: e-values ensure type I error rate control at any stopping time, facilitating repeated interim analyses, complex stopping rules, and valid inference under protocol deviations. The e-value literature focuses mostly on asymptotic optimality; however, sample sizes in clinical trials are often limited. To this end, we investigate e-value-based designs with finite-horizon optimality for single-arm multi-stage clinical trials with binary data. This setting is relevant in early-phase cancer trials, but it also facilitates an accessible introduction to the betting interpretation of e-values, which we use to construct e-values that either (1) maximize statistical power, or (2) minimize the expected sample size, with or without constraints on the minimum power. We construct these designs through (constrained) dynamic programming based on the currently observed e-value, the maximum sample size, and the pre-specified significance level. Using exact calculations, we show that, next to robustness, e-value-based designs can provide competitive operating characteristics to standard (non-)adaptive designs with and without futility stopping and outperform growth-rate-optimal e-values in finite samples. In addition, small e-values automatically indicate trial continuation is futile, e.g., an e-value of zero indicates the impossibility of an efficacy conclusion. Hence, e-value-based designs provide a viable alternative to the current state-of-the-art in single-arm binary trials, warranting extension to other adaptive clinical trial settings such as multi-arm multi-stage and response-adaptive designs.

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arXiv2025

Informed Burn-In Decisions in RAR: Harmonizing Adaptivity and Inferential Precision Based on Study Setting

Response-Adaptive Randomization (RAR) is recognized for its potential to deliver improvements in patient benefit. However, the utility of RAR is contingent on regularization methods to mitigate early instability and preserve statistical integrity. A standard regularization approach is the ''burn-in'' period, an initial phase of equal randomization before treatment allocation adapts based on accrued data. The length of this burn-in is a critical design parameter, yet its selection remains unsystematic and improvised, as no established guideline exists. A poorly chosen length poses significant risks: one that is too short leads to high estimation bias and type-I error rate inflation, while one that is too long impedes the intended patient and power benefits of using adaptation. The challenge of selecting the burn-in generalizes to a fundamental question: what is the statistically appropriate timing for the first adaptation? We introduce the first systematic framework for determining burn-in length. This framework synthesizes core factors - total sample size, problem difficulty, and two novel metrics (reactivity and expected final allocation error) - into a single, principled formula. Simulation studies, grounded in real-world designs, demonstrate that lengths derived from our formula successfully stabilize the trial. The formula identifies a ''sweet spot'' that mitigates type-I error rate inflation and mean-squared error, preserving the advantages of higher power and patient benefit. This framework moves researchers from conjecture toward a systematic, reliable approach.

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arXiv2025

A computational method for type I error rate control in power-maximizing response-adaptive randomization

Maximizing statistical power in experimental design often involves imbalanced treatment allocation, but several challenges hinder its practical adoption: (1) the misconception that equal allocation always maximizes power, (2) when only targeting maximum power, more than half the participants may be expected to obtain inferior treatment, and (3) response-adaptive randomization (RAR) targeting maximum statistical power may inflate type I error rates substantially. Recent work identified issue (3) and proposed a novel allocation procedure combined with the asymptotic score test. Instead, the current research focuses on finite-sample guarantees. First, we analyze the power for traditional power-maximizing RAR procedures under exact tests, including a novel generalization of Boschloo's test. Second, we evaluate constrained Markov decision process (CMDP) RAR procedures under exact tests. These procedures target maximum average power under constraints on pointwise and average type I error rates, with averages taken across the parametric space. A combination of the unconditional exact test and the CMDP procedure protecting allocations to the superior arm gives the best performance, providing substantial power gains over equal allocation while allocating more participants in expectation to the superior treatment. Future research could focus on the randomization test, in which CMDP procedures exhibited lower power compared to other examined RAR procedures.

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arXiv2025

Is 1:1 Always Most Powerful? Why Careful Determination of Allocation Ratios Matters in Trial Design

The principle of allocating an equal number of patients to each arm in a randomized controlled trial remains widely believed to be optimal for maximising statistical power. However, this long-held belief only holds true if the treatment groups have equal outcome variances, a condition that is often not met or, is simply not assessed in practice. This paper reasserts the fact that a departure from a 1:1 ratio can maintain or improve statistical power while increasing the benefits to participants. The benefit is particularly self-evident for binary and time-to-event endpoints, where variances are determined by the assumed success or event rates. To illustrate this, we present two case studies: a small-scale metastatic melanoma trial with a binary endpoint and a larger trial evaluating virtual reality for pain reduction with a continuous endpoint. Our simulations compare equal randomisation, preplanned fixed unequal randomisation, and response-adaptive randomisation targeting Neyman allocation. Results show that unequal allocation can increase the proportion of patients receiving the superior treatment without reducing power, with modest power gains observed in both binary and continuous settings, highlighting the practical relevance of optimised allocation strategies across trial types and sizes.

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arXiv2025

A burn-in(g) question: How long should an initial equal randomization stage be before Bayesian response-adaptive randomization?

Response-adaptive randomization (RAR) can increase participant benefit in clinical trials, but also complicates statistical analysis. The burn-in period (a non-adaptive initial stage) is commonly used to mitigate this disadvantage, yet guidance on its optimal duration is scarce. To address this critical gap, this paper introduces an exact evaluation approach to investigate how the burn-in length impacts statistical operating characteristics of two-arm binary Bayesian RAR (BRAR) designs. We show that (1) commonly used calibration and asymptotic tests show substantial type I error rate inflation for BRAR designs without a burn-in period, and increasing the total burn-in length to more than half the trial size reduces but does not fully mitigate type I error rate inflation, necessitating exact tests; (2) exact tests conditioning on total successes show the highest average and minimum power up to large burn-in lengths; (3) the burn-in length substantially influences power and participant benefit, which are often not maximized at the maximum or minimum possible burn-in length; (4) the test statistic influences the type I error rate and power; (5) estimation bias decreases quicker in the burn-in length for larger treatment effects and increases for larger trial sizes under the same burn-in length. Our approach is illustrated by re-designing the ARREST trial.

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arXiv2025

An integer programming-based approach to construct exact two-sample binomial tests with maximum power

Traditional hypothesis tests for differences between binomial proportions are at risk of being too liberal (Wald test) or overly conservative (Fisher's exact test). This problem is exacerbated in small samples. Regulators favour exact tests, which provide robust type I error control, even though they may have lower power than non-exact tests. To target an exact test with high power, we extend and evaluate an overlooked approach, proposed in 1969, which determines the rejection region through a binary decision for each outcome vector and uses integer programming to, in line with the Neyman-Pearson paradigm, find an optimal decision boundary that maximizes a power objective subject to type I error constraints. Despite only evaluating the type I error rate for a finite parameter set, our approach guarantees type I error control over the full parameter space. Our results show that the test maximizing average power exhibits remarkable robustness, often showing highest power among comparators while maintaining exact type I error control. The method can be further tailored to prior beliefs by using a weighted average. The findings highlight both the method's practical utility and how techniques from combinatorial optimization can improve statistical methodology.

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arXiv2024

Thompson, Ulam, or Gauss? Multi-criteria recommendations for posterior probability computation methods in Bayesian response-adaptive trials

Bayesian adaptive designs enable flexible clinical trials by adapting features based on accumulating data. Among these, Bayesian Response-Adaptive Randomization (BRAR) skews patient allocation towards more promising treatments based on interim data. Implementing BRAR requires the relatively quick evaluation of posterior probabilities. However, the limitations of existing closed-form solutions mean trials often rely on computationally intensive approximations which can impact accuracy and the scope of scenarios explored. While faster Gaussian approximations exist, their reliability is not guaranteed. Critically, the approximation method used is often poorly reported, and the literature lacks practical guidance for selecting and comparing these methods, particularly regarding the trade-offs between computational speed, inferential accuracy, and their implications for patient benefit. In this paper, we focus on BRAR trials with binary endpoints, developing a novel algorithm that efficiently and exactly computes these posterior probabilities, enabling a robust assessment of existing approximation methods in use. Leveraging these exact computations, we establish a comprehensive benchmark for evaluating approximation methods based on their computational speed, patient benefit, and inferential accuracy. Our comprehensive analysis, conducted through a range of simulations in the two-armed case and a re-analysis of the three-armed Established Status Epilepticus Treatment Trial, reveals that the exact calculation algorithm is often the fastest, even for up to 12 treatment arms. Furthermore, we demonstrate that commonly used approximation methods can lead to significant power loss and Type I error rate inflation. We conclude by providing practical guidance to aid practitioners in selecting the most appropriate computation method for various clinical trial settings.

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arXiv2024

Exact statistical analysis for response-adaptive clinical trials: A general and computationally tractable approach

Response-adaptive clinical trial designs allow targeting a given objective by skewing the allocation of participants to treatments based on observed outcomes. Response-adaptive designs face greater regulatory scrutiny due to potential type I error rate inflation, which limits their uptake in practice. Existing approaches for type I error control either only work for specific designs, have a risk of Monte Carlo/approximation error, are conservative, or computationally intractable. To this end, a general and computationally tractable approach is developed for exact analysis in two-arm response-adaptive designs with binary outcomes. This approach can construct exact tests for designs using either a randomized or deterministic response-adaptive procedure. The constructed conditional and unconditional exact tests generalize Fisher's and Barnard's exact tests, respectively. Furthermore, the approach allows for complexities such as delayed outcomes, early stopping, or allocation of participants in blocks. The efficient implementation of forward recursion allows for testing of two-arm trials with 1,000 participants on a standard computer. Through an illustrative computational study of trials using randomized dynamic programming it is shown that, contrary to what is known for equal allocation, the conditional exact Wald test based on total successes has, almost uniformly, higher power than the unconditional exact Wald test. Two real-world trials with the above-mentioned complexities are re-analyzed to demonstrate the value of the new approach in controlling type I errors and/or improving the statistical power.

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arXiv2024

Constrained Markov decision processes for response-adaptive procedures in clinical trials with binary outcomes

A constrained Markov decision process (CMDP) approach is developed for response-adaptive procedures in clinical trials with binary outcomes. The resulting CMDP class of Bayesian response -- adaptive procedures can be used to target a certain objective, e.g., patient benefit or power while using constraints to keep other operating characteristics under control. In the CMDP approach, the constraints can be formulated under different priors, which can induce a certain behaviour of the policy under a given statistical hypothesis, or given that the parameters lie in a specific part of the parameter space. A solution method is developed to find the optimal policy, as well as a more efficient method, based on backward recursion, which often yields a near-optimal solution with an available optimality gap. Three applications are considered, involving type I error and power constraints, constraints on the mean squared error, and a constraint on prior robustness. While the CMDP approach slightly outperforms the constrained randomized dynamic programming (CRDP) procedure known from literature when focussing on type I and II error and mean squared error, showing the general quality of CRDP, CMDP significantly outperforms CRDP when the focus is on type I and II error only.

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arXiv2023

A stochastic programming approach for dynamic allocation of bed capacity and assignment of patients to collaborating hospitals during pandemic outbreaks

Sustaining regular and infectious care during an infectious outbreak requires adequate management support for capacity allocation for regular and infectious patients. During the COVID-19 pandemic, hospitals faced severe challenges, including uncertainty concerning the number of infectious patients needing hospitalization and too little regional cooperation. This led to inefficient usage of healthcare capacity. To better prepare for future pandemics, we have developed a decision support system for central regional decision-making on opening and closing (regular care) hospital rooms for infectious patients and assigning new infectious patients to regional hospitals. Since the relabeling of rooms takes some lead time, we make decisions with a stochastic lookahead approach using stochastic programming with sample average approximation based on scenarios of the number of occupied infectious beds and infectious patients needing hospitalization. The lookahead approach produces high-quality decisions by measuring the impact of current decisions on future costs, such as costs for bed shortages, unused beds for infectious patients, and opening and closing rooms. Our simulation study applied to a COVID-19 scenario in the Netherlands, demonstrates that the stochastic lookahead approach outperforms a deterministic approach as well as other heuristic decision rules such as hospitals acting individually and implementing a pandemic unit, i.e., one hospital is designated to take all regional infectious patients until full. Our approach is very flexible and capable of tuning the model parameters to take into account the characteristics of future, yet unknown, pandemics, and supports sustaining regular care by minimizing the strain of infectious care on the available number of beds for regular care.

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arXiv2023

A Sampling-Based Method for Gittins Index Approximation

A sampling-based method is introduced to approximate the Gittins index for a general family of alternative bandit processes. The approximation consists of a truncation of the optimization horizon and support for the immediate rewards, an optimal stopping value approximation, and a stochastic approximation procedure. Finite-time error bounds are given for the three approximations, leading to a procedure to construct a confidence interval for the Gittins index using a finite number of Monte Carlo samples, as well as an epsilon-optimal policy for the Bayesian multi-armed bandit. Proofs are given for almost sure convergence and convergence in distribution for the sampling based Gittins index approximation. In a numerical study, the approximation quality of the proposed method is verified for the Bernoulli bandit and Gaussian bandit with known variance, and the method is shown to significantly outperform Thompson sampling and the Bayesian Upper Confidence Bound algorithms for a novel random effects multi-armed bandit.

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arXiv2022

Bayesian Covariance Structure Modeling of Multi-Way Nested Data

A Bayesian multivariate model with a structured covariance matrix for multi-way nested data is proposed. This flexible modeling framework allows for positive and for negative associations among clustered observations, and generalizes the well-known dependence structure implied by random effects. A conjugate shifted-inverse gamma prior is proposed for the covariance parameters which ensures that the covariance matrix remains positive definite under posterior analysis. A numerically efficient Gibbs sampling procedure is defined for balanced nested designs, and is validated using two simulation studies. For a top-layer unbalanced nested design, the procedure requires an additional data augmentation step. The proposed data augmentation procedure facilitates sampling latent variables from (truncated) univariate normal distributions, and avoids numerical computation of the inverse of the structured covariance matrix. The Bayesian multivariate (linear transformation) model is applied to two-way nested interval-censored event times to analyze differences in adverse events between three groups of patients, who were randomly allocated to treatment with different stents (BIO-RESORT). The parameters of the structured covariance matrix represent unobserved heterogeneity in treatment effects and are examined to detect differential treatment effects.

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