arXiv subjects

James Willard

Publications and source records attributed to James Willard.

4 recordsLinked to original sources

arXiv2024

Bayesian Optimization for Identification of Optimal Biological Dose Combinations in Personalized Dose-Finding Trials

Early phase, personalized dose-finding trials for combination therapies seek to identify patient-specific optimal biological dose (OBD) combinations, which are defined as safe dose combinations that maximize therapeutic benefit for a specific covariate pattern. Given the small sample sizes which are typical of these trials, it is challenging for traditional parametric approaches to identify OBD combinations across multiple dosing agents and covariate patterns. To address these challenges, we propose a Bayesian optimization approach to dose-finding which incorporates efficacy and toxicity information into the sequential search strategy. Independent Gaussian processes are used to model the efficacy and toxicity surfaces, and an acquisition function is utilized to define the dose-finding strategy. Furthermore, we define an adaptive stopping rule using the posterior entropy for the location of the OBD. This work is motivated by a personalized dose-finding trial which considers a dual-agent therapy for obstructive sleep apnea (OSA), where OBD combinations are tailored to OSA severity. Via a simulation study, the approach is first investigated across varying degrees of response heterogeneity for both efficacy and toxicity, and then a collection of final designs for the OSA trial are compared. We demonstrate that the proposed approach toward personalized dose-finding yields good performance under the considered scenarios.

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arXiv2023

Bayesian Optimization for Personalized Dose-Finding Trials with Combination Therapies

Identification of optimal dose combinations in early phase dose-finding trials is challenging, due to the trade-off between precisely estimating the many parameters required to flexibly model the possibly non-monotonic dose-response surface, and the small sample sizes in early phase trials. This difficulty is even more pertinent in the context of personalized dose-finding, where patient characteristics are used to identify tailored optimal dose combinations. To overcome these challenges, we propose the use of Bayesian optimization for finding optimal dose combinations in standard ("one size fits all") and personalized multi-agent dose-finding trials. Bayesian optimization is a method for estimating the global optima of expensive-to-evaluate objective functions. The objective function is approximated by a surrogate model, commonly a Gaussian process, paired with a sequential design strategy to select the next point via an acquisition function. This work is motivated by an industry-sponsored problem, where focus is on optimizing a dual-agent therapy in a setting featuring minimal toxicity. To compare the performance of the standard and personalized methods under this setting, simulation studies are performed for a variety of scenarios. Our study concludes that taking a personalized approach is highly beneficial in the presence of heterogeneity.

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arXiv2023

Estimating the Sampling Distribution of Posterior Decision Summaries in Bayesian Clinical Trials

Bayesian inference and the use of posterior or posterior predictive probabilities for decision making have become increasingly popular in clinical trials. The current practice in Bayesian clinical trials relies on a hybrid Bayesian-frequentist approach where the design and decision criteria are assessed with respect to frequentist operating characteristics such as power and type I error rate conditioning on a given set of parameters. These operating characteristics are commonly obtained via simulation studies. The utility of Bayesian measures, such as ``assurance", that incorporate uncertainty about model parameters in estimating the probabilities of various decisions in trials has been demonstrated recently. However, the computational burden remains an obstacle toward wider use of such criteria. In this article, we propose methodology which utilizes large sample theory of the posterior distribution to define parametric models for the sampling distribution of the posterior summaries used for decision making. The parameters of these models are estimated using a small number of simulation scenarios, thereby refining these models to capture the sampling distribution for small to moderate sample size. The proposed approach toward the assessment of conditional and marginal operating characteristics and sample size determination can be considered as simulation-assisted rather than simulation-based. It enables formal incorporation of uncertainty about the trial assumptions via a design prior and significantly reduces the computational burden for the design of Bayesian trials in general.

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arXiv2022

Covariate Adjustment in Bayesian Adaptive Randomized Controlled Trials

In conventional randomized controlled trials, adjustment for baseline values of covariates known to be at least moderately associated with the outcome increases the power of the trial. Recent work has shown particular benefit for more flexible frequentist designs, such as information adaptive and adaptive multi-arm designs. However, covariate adjustment has not been characterized within the more flexible Bayesian adaptive designs, despite their growing popularity. We focus on a subclass of these which allow for early stopping at an interim analysis given evidence of treatment superiority. We consider both collapsible and non-collapsible estimands, and show how to obtain posterior samples of marginal estimands from adjusted analyses. We describe several estimands for three common outcome types. We perform a simulation study to assess the impact of covariate adjustment using a variety of adjustment models in several different scenarios. This is followed by a real world application of the compared approaches to a COVID-19 trial with a binary endpoint. For all scenarios, it is shown that covariate adjustment increases power and the probability of stopping the trials early, and decreases the expected sample sizes as compared to unadjusted analyses.

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