5 research outputs found
Dose Selection Balancing Efficacy and Toxicity Using Bayesian Model Averaging
Successful pharmaceutical drug development requires finding correct doses
that provide an optimum balance between efficacy and toxicity. Competing
responses to dose such as efficacy and toxicity often will increase with dose,
and it is important to identify a range of doses to provide an acceptable
efficacy response (minimum effective dose) while not causing unacceptable
intolerance or toxicity (maximum tolerated dose). How this should be done is
not self-evident. Relating efficacy to dose conditionally on possible toxicity
may be problematic because whether toxicity occurs will not be known when a
dose for a patient needs to be chosen. Copula models provide an appealing
approach for incorporating an efficacy-toxicity association when the functional
forms of the efficacy and toxicity dose-response models are known but may be
less appealing in practice when the functional forms of the dose-response
models and the particular copula association model are unknown. This paper
explores the use of the BMA-Mod Bayesian model averaging framework that
accommodates efficacy and toxicity responses to provide a statistically valid,
distributionally flexible, and operationally practical model-agnostic strategy
for predicting efficacy and toxicity outcomes both in terms of expected
responses and in terms of predictions for individual patients. The performance
of the approach is evaluated via simulation when efficacy and toxicity outcomes
are considered marginally, when they are associated via gaussian and
Archimedean copulas, and when they are expressed in terms of clinically
meaningful categories. In all cases, the BMA-Mod strategy identified consistent
ranges of acceptable doses.Comment: 23 pages, 14 figures. R code, annotated session log, and datasets
available from [email protected]
Optimal design to discriminate between rival copula models for a bivariate binary response
We consider a bivariate logistic model for a binary response, and we assume that two rival dependence structures are possible. Copula functions are very useful tools to model different kinds of dependence with arbitrary marginal distributions. We consider Clayton and Gumbel copulae as competing association models. The focus is on applications in testing a new drug looking at both efficacy and toxicity outcomes. In this context, one of the main goals is to find the dose which maximizes the probability of efficacy without toxicity, herein called P-optimal dose. If the P-optimal dose changes under the two rival copulae, then it is relevant to identify the proper association model. To this aim, we propose a criterion (called PKL) which enables us to find the optimal doses to discriminate between the rival copulae, subject to a constraint that protects patients against dangerous doses. Furthermore, by applying the likelihood ratio test for non-nested models, via a simulation study we confirm that the PKL-optimal design is really able to discriminate between the rival copulae
Design of experiments for bivariate binary responses modelled by Copula functions
Optimal design for generalized linear models has primarily focused on univariate data. Often experiments are performed that have multiple dependent responses described by regression type models, and it is of interest and of value to design the experiment for all these responses. This requires a multivariate distribution underlying a pre-chosen model for the data. Here, we consider the design of experiments for bivariate binary data which are dependent. We explore Copula functions which provide a rich and flexible class of structures to derive joint distributions for bivariate binary data. We present methods for deriving optimal experimental designs for dependent bivariate binary data using Copulas, and demonstrate that, by including the dependence between responses in the design process, more efficient parameter estimates are obtained than by the usual practice of simply designing for a single variable only. Further, we investigate the robustness of designs with respect to initial parameter estimates and Copula function, and also show the performance of compound criteria within this bivariate binary setting