  Basket trials have emerged as a new class of efficient approaches in oncology
to evaluate a new treatment in several patient subgroups simultaneously. In
this paper, we extend the key ideas to disease areas outside of oncology,
developing a robust Bayesian methodology for randomised, placebo-controlled
basket trials with a continuous endpoint to enable borrowing of information
across subtrials with similar treatment effects. After adjusting for
covariates, information from a complementary subtrial can be represented into a
commensurate prior for the parameter that underpins the subtrial under
consideration. We propose using distributional discrepancy to characterise the
commensurability between subtrials for appropriate borrowing of information
through a spike-and-slab prior, which is placed on the prior precision factor.
When the basket trial has at least three subtrials, commensurate priors for
point-to-point borrowing are combined into a marginal predictive prior,
according to the weights transformed from the pairwise discrepancy measures. In
this way, only information from subtrial(s) with the most commensurate
treatment effect is leveraged. The marginal predictive prior is updated to a
robust posterior by the contemporary subtrial data to inform decision making.
Operating characteristics of the proposed methodology are evaluated through
simulations motivated by a real basket trial in chronic diseases. The proposed
methodology has advantages compared to other selected Bayesian analysis models,
for (i) identifying the most commensurate source of information, and (ii)
gauging the degree of borrowing from specific subtrials. Numerical results also
suggest that our methodology can improve the precision of estimates and,
potentially, the statistical power for hypothesis testing.
