Significant evidence has become available that emphasizes the importance of personalization in medicine. In fact, it has become a common belief that personalized medicine is the future of medicine. The core of personalized medicine is the ability to design clinical trials that investigate the role of patient covariates on treatment effects. In this work, we study the optimal design of two-armed clinical trials to maximize accuracy of statistical models where the interaction between patient covariates and treatment effect are incorporated to enable precision medication. Such a modeling extension leads to significant complexities for the produced optimization problems because they include optimization over design and covariates concurrently. We take a robust optimization approach and minimize (over design) the maximum (over population) variance of interaction effect between treatment and patient covariates. This results in a min-max bi-level mixed integer nonlinear programming problem, which is notably challenging to solve. To address this challenge, we introduce a surrogate model by approximating the objective function for which we propose two solution approaches. The first approach provides an exact solution based on reformulation and decomposition techniques. In the second approach, we provide a lower bound for the inner optimization problem and solve the outer optimization problem over the lower bound. We test our proposed algorithms with synthetic and real-world data sets and compare it with standard (re-)randomization methods. Our numerical analysis suggests that the lower bounding approach provides high-quality solutions across a variety of settings.
We consider applying multi-armed bandits to model-assisted designs for dose-finding clinical trials. Multi-armed bandits are very simple and powerful methods to determine actions to maximize a reward in a limited number of trials. Among the multi-armed bandits, we first consider the use of Thompson sampling which determines actions based on random samples from a posterior distribution. In the small sample size, as shown in dose-finding trials, because the tails of posterior distribution are heavier and random samples are too much variability, we also consider an application of regularized Thom…
This article proposes a novel adaptive design algorithm that can be used to find optimal treatment allocations in N-of-1 clinical trials. This new methodology uses two Laplace approximations to provide a computationally efficient estimate of population and individual random effects within a repeated measures, adaptive design framework. Given the efficiency of this approach, it is also adopted for treatment selection to target the collection of data for the precise estimation of treatment effects. To evaluate this approach, we consider both a simulated and motivating N-of-1 clinical trial from …
Response-adaptive designs allow the randomization probabilities to change during the course of a trial based on cumulated response data, so that a greater proportion of patients can be allocated to the better performing treatments. A major concern over the use of response-adaptive designs in practice, particularly from a regulatory viewpoint, is controlling the type I error rate. In particular, we show that the naive z-test can have an inflated type I error rate even after applying a Bonferroni correction. Simulation studies have often been used to demonstrate error control, but do not provide…
Multi-armed bandit problems (MABPs) are a special type of optimal control problem well suited to model resource allocation under uncertainty in a wide variety of contexts. Since the first publication of the optimal solution of the classic MABP by a dynamic index rule, the bandit literature quickly diversified and emerged as an active research topic. Across this literature, the use of bandit models to optimally design clinical trials became a typical motivating application, yet little of the resulting theory has ever been used in the actual design and analysis of clinical trials. To this end, w…
The objective of this paper is to develop statistical methodology for planning and evaluating three-armed non-inferiority trials for general retention of effect hypotheses, where the endpoint of interest may follow any (regular) parametric distribution family. This generalizes and unifies specific results for binary, normally and exponentially distributed endpoints. We propose a Wald-type test procedure for the retention of effect hypothesis (RET), which assures that the test treatment maintains at least a proportion $Δ$ of reference treatment effect compared to placebo. At this, we distinguis…
The most common objective for response adaptive clinical trials is to seek to ensure that patients within a trial have a high chance of receiving the best treatment available by altering the chance of allocation on the basis of accumulating data. Approaches which yield good patient benefit properties suffer from low power from a frequentist perspective when testing for a treatment difference at the end of the study due to the high imbalance in treatment allocations. In this work we develop an alternative pairwise test for treatment difference on the basis of allocation probabilities of the cov…
In clinical trials, response-adaptive randomization (RAR) has the appealing ability to assign more subjects to better-performing treatments based on interim results. The traditional RAR strategy alters the randomization ratio on a patient-by-patient basis; this has been heavily criticized for bias due to time-trends. An alternate approach is blocked RAR, which groups patients together in blocks and recomputes the randomization ratio in a block-wise fashion; the final analysis is then stratified by block. However, the typical blocked RAR design divides patients into equal-sized blocks, which is…
This PhD thesis covers breakthroughs in several areas of adaptive experiment design: (i) (Chapter 2) Novel clinical trial designs and statistical methods in the era of precision medicine. (ii) (Chapter 3) Multi-armed bandit theory, with applications to learning healthcare systems and clinical trials. (iii) (Chapter 4) Bandit and covariate processes, with finite and non-denumerable set of arms. (iv) (Chapter 5) A rigorous framework for simulation-based verification of adaptive design properties.
University of Florida（佛罗里达大学）；Emerging Pathogens Institute（新兴病原体研究所）
Bacterial infections are responsible for high mortality worldwide. Antimicrobial resistance underlying the infection, and multifaceted patient's clinical status can hamper the correct choice of antibiotic treatment. Randomized clinical trials provide average treatment effect estimates but are not ideal for risk stratification and optimization of therapeutic choice, i.e., individualized treatment effects (ITE). Here, we leverage large-scale electronic health record data, collected from Southern US academic clinics, to emulate a clinical trial, i.e., 'target trial', and develop a machine learnin…
Traditionally, the major objective in phase I trials is to identify a working-dose for subsequent studies, whereas the major endpoint in phase II and III trials is treatment efficacy. The dose sought is typically referred to as the maximum tolerated dose (MTD). Several statistical methodologies have been proposed to select the MTD in cancer phase I trials. In this manuscript, we focus on a Bayesian adaptive design, known as escalation with overdose control (EWOC). Several aspects of this design are discussed, including large sample properties of the sequence of doses selected in the trial, cho…
Adaptive seamless designs combine confirmatory testing, a domain of phase III trials, with features such as treatment or subgroup selection, typically associated with phase II trials. They promise to increase the efficiency of development programmes of new drugs, e.g. in terms of sample size and / or development time. It is well acknowledged that adaptive designs are more involved from a logistical perspective and require more upfront planning, often in form of extensive simulation studies, than conventional approaches. Here we present a framework for adaptive treatment and subgroup selection …
Statistical methodology plays a crucial role in drug regulation. Decisions by the FDA or EMA are typically made based on multiple primary studies testing the same medical product, where the two-trials rule is the standard requirement, despite a number of shortcomings. A new approach is proposed for this task based on the (weighted) harmonic mean of the squared study-specific test statistics. Appropriate scaling ensures that, for any number of independent studies, the null distribution is a $χ^2$-distribution with one degree of freedom. This gives rise to a new method for combining one-sided $p…
We consider the problem of selecting the optimal subgroup to treat when data on covariates is available from a randomized trial or observational study. We distinguish between four different settings including (i) treatment selection when resources are constrained, (ii) treatment selection when resources are not constrained, (iii) treatment selection in the presence of side effects and costs, and (iv) treatment selection to maximize effect heterogeneity. We show that, in each of these cases, the optimal treatment selection rule involves treating those for whom the predicted mean difference in o…
Randomly censored survival data are frequently encountered in applied sciences including biomedical or reliability applications and clinical trial analyses. Testing the significance of statistical hypotheses is crucial in such analyses to get conclusive inference but the existing likelihood based tests, under a fully parametric model, are extremely non-robust against outliers in the data. Although, there exists a few robust parameter estimators (e.g., M-estimators and minimum density power divergence estimators) given randomly censored data, there is hardly any robust testing procedure availab…
Comparison of Simulation-Guided Design to Closed-Form Power Calculations in Planning a Cluster Randomized Trial with Covariate-Constrained Randomization: A Case Study in Rural Chad
