Antonios Daletzakis

Therapeutic advancements in oncology have shifted towards targeted therapy based on genomic aberrations. This necessitates innovative statistical approaches in clinical trials, particularly in master protocol studies. Basket trials, a type of master protocol, evaluate a single treatment across cohorts sharing a genomic aberration but differing in tumor histology. While offering operational advantages, basket trial analysis presents statistical inference challenges. These trials help determine for which tumor histology the treatment is promising enough to advance to confirmatory evaluation and often use Bayesian designs to support decisions. Beyond decision-making, estimating cohort-specific response rates is crucial for designing subsequent trials. This study compares seven Bayesian estimation methods for basket trials with binary outcomes against the (frequentist) sample proportion estimate through simulations. The goal is to estimate cohort-specific response rates, focusing on bias, mean squared error, and information borrowing. Various scenarios are examined, including homogeneous, heterogeneous, and clustered response rates across cohorts. Results show trade-offs in bias and precision, highlighting the importance of method selection. Berry's method performs best with limited heterogeneity. No clear winner emerges in general cases, with performance affected by shrinkage, bias, and the choice of priors and tuning parameters. Challenges include computational complexity, parameter tuning, and the lack of clear guidance on selection. Researchers should consider these factors when designing and analyzing basket trials.

The duration of response (DoR) is defined as the time from the onset of response to treatment up to progression of disease or death due to any reason, whichever occurs earlier. The expected DoR could be a suitable estimand to measure the efficacy of a treatment but is in practice difficult to estimate, since patients' follow‐up times are often right‐censored. Instead, the restricted mean duration of response (RMDoR) is often used. The RMDoR in a time is equal to the expected DoR restricted to the interval . In this paper, we consider the behaviour of the RMDoR as a function of and its suitability as a measure to quantify the efficacy of a treatment. Besides, we focus on the estimation of the RMDoR. In oncology, the events response to treatment and progression of disease are typically detected through time‐scheduled scans and are therefore interval‐censored. We describe multiple estimators for the RMDoR that deal with the interval censoring in different ways and study the performance of these estimators in single arm trials and randomised controlled trials.

In early phase clinical studies in oncology, Simon's two-stage designs are widely used. The trial design could be made more efficient by stopping early in the second stage when the required number of responses is reached, or when it has become clear that this target can no longer be met (a form of non-stochastic curtailment). Early stopping, however, will affect proper estimation of the response rate. We propose a uniformly minimum-variance unbiased estimator (UMVUE) for the response rate in this setting. The estimator is proven to be UMVUE using the Rao-Blackwell theorem. We evaluate the estimator's properties in terms of bias and mean squared error, both analytically and via simulations. We derive confidence intervals based on sample space orderings, and assess the coverage. For various design options, we evaluate the reduction in expected sample size as a function of the true response rate. Our method provides a solution for estimating response rates in case of a non-stochastic curtailment Simon's two-stage design.