Shared Keyboard: An improved Bayesian design for phase I clinical trials via Beta kernel process

Model-assisted interval designs such as the Keyboard design are transparent and easy to implement in phase I oncology trials. However, interim decisions based solely on data from the current dose may overlook informative signals from neighbouring doses, leading to unnecessary escalation or de-escalation. We propose the shared Keyboard design, a Bayesian model-assisted design that replaces the independent beta--binomial updating scheme at each dose with a posterior induced by a Beta kernel process using kernel-weighted pseudo-counts. The design preserves the decision structure of the Keyboard design while enabling controlled borrowing across nearby doses. To prioritise overdose control, we propose an asymmetric kernel that assigns greater weight to toxicities observed at higher doses during escalation. We further extend the proposed design to accommodate adaptive dose insertion when the initial dose grid is inadequate and time-to-event outcomes when late-onset toxicities are present. Extensive simulation studies demonstrate substantial improvements in both accuracy and safety for identifying the maximum tolerated dose. In settings involving dose insertion, the proposed design identifies inserted target doses more effectively than adaptive dose modification while maintaining a comparable modification rate.

BKP: An R Package for Beta Kernel Process Modeling

We present BKP, a user-friendly and extensible R package that implements the Beta Kernel Process (BKP) -- a fully nonparametric and computationally efficient framework for modeling spatially varying binomial probabilities. The BKP model combines localized kernel-weighted likelihoods with conjugate beta priors, resulting in closed-form posterior inference without requiring latent variable augmentation or intensive MCMC sampling. The package supports binary and aggregated binomial responses, allows flexible choices of kernel functions and prior specification, and provides loss-based kernel hyperparameter tuning procedures. In addition, BKP extends naturally to the Dirichlet Kernel Process (DKP) for modeling spatially varying multinomial or compositional data. To our knowledge, this is the first publicly available R package for implementing BKP-based methods. We illustrate the use of BKP through several synthetic and real-world datasets, highlighting its interpretability, accuracy, and scalability. The package aims to facilitate practical application and future methodological development of kernel-based beta modeling in statistics and machine learning.