  Research in oncology has changed the focus from histological properties of
tumors in a specific organ to a specific genomic aberration potentially shared
by multiple cancer types. This motivates the basket trial, which assesses the
efficacy of treatment simultaneously on multiple cancer types that have a
common aberration. Although the assumption of homogeneous treatment effects
seems reasonable given the shared aberration, in reality, the treatment effect
may vary by cancer type, and potentially only a subgroup of the cancer types
respond to the treatment. Various approaches have been proposed to increase the
trial power by borrowing information across cancer types, which, however, tend
to inflate the type I error rate. In this paper, we review some representative
Bayesian information borrowing methods for the analysis of early-phase basket
trials. We then propose a novel method called the Bayesian hierarchical model
with a correlated prior (CBHM), which conducts more flexible borrowing across
cancer types according to sample similarity. We did simulation studies to
compare CBHM with independent analysis and three information borrowing
approaches: the conventional Bayesian hierarchical model, the EXNEX approach
and Liu's two-stage approach. Simulation results show that all information
borrowing approaches substantially improve the power of independent analysis if
a large proportion of the cancer types truly respond to the treatment. Our
proposed CBHM approach shows an advantage over the existing information
borrowing approaches, with a power similar to that of EXNEX or Liu's approach,
but the potential to provide substantially better control of type I error rate.
