Variance prior specification for a basket trial design using Bayesian hierarchical modeling

Abstract

Background: In the era of targeted therapies, clinical trials in oncology are rapidly evolving, wherein patients from multiple diseases are now enrolled and treated according to their genomic mutation(s). In such trials, known as basket trials, the different disease cohorts form the different baskets for inference. Several approaches have been proposed in the literature to efficiently use information from all baskets while simultaneously screening to find individual baskets where the drug works. Most proposed methods are developed in a Bayesian paradigm that requires specifying a prior distribution for a variance parameter, which controls the degree to which information is shared across baskets. Methods: A common approach used to capture the correlated binary endpoints across baskets is Bayesian hierarchical modeling. We evaluate a Bayesian adaptive design in the context of a non-randomized basket trial and investigate three popular prior specifications: an inverse-gamma prior on the basket-level variance, a uniform prior and half-t prior on the basket-level standard deviation. Results: From our simulation study, we can see that the inverse-gamma prior is highly sensitive to the input hyperparameters. When the prior mean value of the variance parameter is set to be near zero [Formula: see text], this can lead to unacceptably high false-positive rates [Formula: see text] in some scenarios. Thus, use of this prior requires a fully comprehensive sensitivity analysis before implementation. Alternatively, we see that a prior that places sufficient mass in the tail, such as the uniform or half-t prior, displays desirable and robust operating characteristics over a wide range of prior specifications, with the caveat that the upper bound of the uniform prior and the scale parameter of the half-t prior must be larger than 1. Conclusion: Based on the simulation results, we recommend that those involved in designing basket trials that implement hierarchical modeling avoid using a prior distribution that places a majority of the density mass near zero for the variance parameter. Priors with this property force the model to share information regardless of the true efficacy configuration of the baskets. Many commonly used inverse-gamma prior specifications have this undesirable property. We recommend to instead consider the more robust uniform prior or half-t prior on the standard deviation.

Reporting of master protocols towards a standardized approach: A systematic review

“…While basket trial definitions (n = 35) [[1], [2], [3], [4], [5],11,13,15,18,[23], [24], [25], [26], [27], [28], [29], [30], [31], [32], [33], [34], [35], [36], [37], [38], [39], [40], [41], [42], [43], [44], [45], [46], [47], [48]] were consistent on some aspects, such as that basket trials study multiple disease types (n = 34), other features such as the number of interventions to be studied were inconsistent. Approximately half of the reviewed publications (n = 18) [1,2,4,5,11,13,15,25,30,31,33,35,38,39,41,42,45,49] specified that basket trials are designed to evaluate a single intervention, while around a third (n = 10) [3,18,23,[26], [27], [28], [29],36,40,43] stated that they can evaluate multiple interventions. The remaining definitions (n = 7) specified both [37,44,47] or neither [32,34,46,48].…”

“…The remaining definitions (n = 7) specified both [37,44,47] or neither [32,34,46,48]. The number of biomarkers or subgroups studied in a basket trial also varied, with the majority of definitions describing these studies as including only a single biomarker (n = 25) [1,[3], [4], [5],11,13,15,23,[26], [27], [28], [29],[31], [32], [33], [34], [35],[37], [38], [39], [40], [41], [42], [43],45] and considerably fewer including multiple (n = 5) [2,18,25,30,49]. Three basket trials specified the need for seamless design [3,4,39] and one for common control [41].…”

“…2) [[1], [2], [3], [4], [5],11,13,15,18,19,27,28,[31], [32], [33],35,36,38,[45], [46], [47],[50], [51], [52], [53], [54]]. For example, the majority described umbrella trials as limited to a single disease (n = 21) [[1], [2], [3],11,13,15,18,27,[31], [32], [33],35,36,38,[45], [46], [47],[50], [51], [52], [53]], while a single publication proposed the opposite [19]. The remaining four trials specified both [4] or neither [5,28,54].…”

The Evolution of Master Protocol Clinical Trial Designs: A Systematic Literature Review

“…A basket trial design using Bayesian hierarchical modeling to borrow information on the treatment effect across different patient subpopulations was proposed by Liu et al 217 In a simulation study, Cunanan et al 218 found that the Bayesian hierarchical model as proposed by Berry et al 219 can have heavily inflated error rates. Cunanan et al 220 further investigated the effect of different priors for the variance parameter in Bayesian hierarchical models, which is directly linked to how much information is shared across subpopulations, on the type 1 error rate. To better control the type 1 error in Bayesian hierarchical models attributable to inappropriately determining the degree of information borrowing, Chu and Yuan 221 proposed a calibrated Bayesian hierarchical model for basket trials in which the shrinkage parameter is defined as a (through simulation calibrated) function of a treatment effect similarity measure.…”

A Bayesian basket trial design accounting for uncertainties of homogeneity and heterogeneity of treatment effect among subpopulations

“…Recently, modifications and improvements of the BHM approach have been proposed. Cunanan et al 19 adequately investigated prior specifications on the variance parameter that controls the degree of borrowing information on the response rate across subpopulations. However, BHM assumes that the treatment effect for each subpopulation is exchangeable and localizes around a common mean of distribution on the treatment effect.…”