The New England Journal of Statistics in Data Science

The MiniPDX model is a cost-effective preclinical platform that replicates human tumor microenvironments in mice, enabling rapid drug response evaluation in precision oncology. In contrast, the patient-derived xenograft (PDX) model offers a more comprehensive but slower and costlier approach by engrafting human tumors into immunodeficient mice to evaluate efficacy in a physiologically relevant context. In this study, we present an integrated Bayesian framework that supports both separate and joint analyses of MiniPDX and PDX data. Our models borrow information across biomarker-defined subgroups and between assays, improving the efficiency and precision of drug effect estimation. Furthermore, we implement an adaptive sample size re-estimation procedure for MiniPDX experiments, allowing for more flexible designs and optimized resource utilization. Together, these methods provide a Bayesian framework that improves estimation efficiency for small-sample MiniPDX and PDX experiments and offers a principled adaptive sample-size rule, helping to identify biomarker-defined subpopulations with distinct predictive profiles for treatment response.

Phase I oncology trials aim to identify a safe dose—often the maximum tolerated dose (MTD)—for subsequent studies. Conventional designs focus on population-level toxicity modeling, with recent attention on leveraging pharmacokinetic (PK) data to improve dose selection. We propose the Precision Dose-Finding (PDF) design, a novel Bayesian phase I framework that integrates individual patient PK profiles into the dose-finding process. By incorporating patient-specific PK parameters (such as volume of distribution ${V_{i}}$ and elimination rate ${k_{i}}$), PDF models toxicity risk at the individual level, in contrast to traditional methods that ignore inter-patient variability. The trial is structured in two stages: an initial training stage to update model parameters using cohort-based dose escalation, and a subsequent test stage in which doses for new patients are chosen based on each patient’s own PK-predicted toxicity probability. This two-stage approach enables truly personalized dose assignment while maintaining rigorous safety oversight. Extensive simulation studies demonstrate the feasibility of PDF and suggest that it provides improved safety and dosing precision relative to the continual reassessment method (CRM). The PDF design thus offers a refined dose-finding strategy that tailors the MTD to individual patients, aligning phase I trials with the ideals of precision medicine.

The phase III BNT162b2 mRNA COVID-19 vaccine trial is based on a Bayesian design and analysis, and the main evidence of vaccine efficacy is presented in Bayesian statistics. Confusion and mistakes arise in the presentation of the Bayesian results. Some key statistics, such as Bayesian credible intervals, are mislabeled and stated as confidence intervals. Posterior probabilities of the vaccine efficacy are not reported as the main results. We illustrate the main differences in the reporting of Bayesian analysis results for a clinical trial and provide four recommendations. We argue that statistical evidence from a Bayesian trial, when presented properly, is easier to interpret and directly addresses the main clinical questions, thereby better supporting regulatory decision making. We also recommend using the abbreviation “BI” to represent Bayesian credible interval as a differentiation to “CI” which stands for confidence interval.

We consider a formal statistical design that allows simultaneous enrollment of a main cohort and a backfill cohort of patients in a dose-finding trial. The goal is to accumulate more information at various doses to facilitate dose optimization. The proposed design, called Bi3+3, combines the simple dose-escalation algorithm in the i3+3 design and a model-based inference under the framework of probability of decisions (POD), both previously published. As a result, Bi3+3 provides a simple algorithm for backfilling patients to lower doses in a dose-finding trial once these doses exhibit safety profile in patients. The POD framework allows dosing decisions to be made when some backfill patients are still being followed with incomplete toxicity outcomes, thereby potentially expediting the clinical trial. At the end of the trial, Bi3+3 uses both toxicity and efficacy outcomes to estimate an optimal biological dose (OBD). The proposed inference is based on a dose-response model that takes into account either a monotone or plateau dose-efficacy relationship, which are frequently encountered in modern oncology drug development. Simulation studies show promising operating characteristics of the Bi3+3 design in comparison to existing designs.

Clinical trials usually involve sequential patient entry. When designing a clinical trial, it is often desirable to include a provision for interim analyses of accumulating data with the potential for stopping the trial early. We review Bayesian sequential clinical trial designs based on posterior probabilities, posterior predictive probabilities, and decision-theoretic frameworks. A pertinent question is whether Bayesian sequential designs need to be adjusted for the planning of interim analyses. We answer this question from three perspectives: a frequentist-oriented perspective, a calibrated Bayesian perspective, and a subjective Bayesian perspective. We also provide new insights into the likelihood principle, which is commonly tied to statistical inference and decision making in sequential clinical trials. Some theoretical results are derived, and numerical studies are conducted to illustrate and assess these designs.

Phase I trials investigate the toxicity profile of a new treatment and identify the maximum tolerated dose for further evaluation. Most phase I trials use a binary dose-limiting toxicity endpoint to summarize the toxicity profile of a dose. In reality, reported toxicity information is much more abundant, including various types and grades of adverse events. Building upon the i3+3 design (Liu et al., 2020), we propose the Ti3+3 design, in which the letter “T” represents “total” toxicity. The proposed design takes into account multiple toxicity types and grades by computing the toxicity burden at each dose. The Ti3+3 design aims to achieve desirable operating characteristics using a simple statistics framework that utilizes“toxicity burden interval” (TBI). Simulation results show that Ti3+3 demonstrates comparable performance with existing more complex designs.