TY - JOUR

T1 - Optimal design to discriminate between rival copula models for a bivariate binary response

AU - Deldossi, Laura

AU - Osmetti, Silvia Angela

AU - Tommasi, Chiara

PY - 2019

Y1 - 2019

N2 - 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.

AB - 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.

KW - Bivariate logistic model

KW - Copula models

KW - Cox’s test

KW - Efficacy–toxicity response

KW - KL-optimality

KW - Optimal experimental design

KW - Statistics and Probability

KW - Statistics, Probability and Uncertainty

KW - Bivariate logistic model

KW - Copula models

KW - Cox’s test

KW - Efficacy–toxicity response

KW - KL-optimality

KW - Optimal experimental design

KW - Statistics and Probability

KW - Statistics, Probability and Uncertainty

UR - http://hdl.handle.net/10807/130926

UR - http://www.springerlink.com/content/1133-0686

U2 - 10.1007/s11749-018-0595-1

DO - 10.1007/s11749-018-0595-1

M3 - Article

VL - 28

SP - 147

EP - 165

JO - TEST

JF - TEST

SN - 1133-0686

ER -