Information-regret compromise in covariate-adaptive treatment allocation

Abstract : Covariate-adaptive treatment allocation is considered in the situation when a compromise must be made between information (about the dependency of the probability of success of each treatment upon influential covariates) and cost (in terms of number of subjects receiving the poorest treatment). Information is measured through a design criterion for parameter estimation, the cost is additive and is related to the success probabilities. Within the framework of approximate design theory, the determination of optimal allocations forms a compound design problem. We show that when the covariates are i.i.d. with a probability measure µ, its solution possesses strong similarities with the construction of optimal design measures bounded by µ. We characterize optimal designs through an Equivalence Theorem and construct a covariate-adaptive sequential allocation strategy that converges to the optimum. Our new optimal designs can be used as benchmarks for other, more usual, allocation methods. A response-adaptive implementation is possible for practical applications with unknown model parameters. Several illustrative examples are provided.
Type de document :
Article dans une revue
Annals of Statistics, Institute of Mathematical Statistics, 2017, 45 (5), pp.2046 - 2073. 〈10.1214/16-AOS1518〉
Liste complète des métadonnées

Littérature citée [40 références]  Voir  Masquer  Télécharger

https://hal.archives-ouvertes.fr/hal-01246252
Contributeur : Luc Pronzato <>
Soumis le : jeudi 2 novembre 2017 - 11:55:11
Dernière modification le : mercredi 8 novembre 2017 - 01:15:21

Fichier

AOS1518.pdf
Fichiers éditeurs autorisés sur une archive ouverte

Identifiants

Collections

Relations

Citation

Asya Metelkina, Luc Pronzato. Information-regret compromise in covariate-adaptive treatment allocation. Annals of Statistics, Institute of Mathematical Statistics, 2017, 45 (5), pp.2046 - 2073. 〈10.1214/16-AOS1518〉. 〈hal-01246252v2〉

Partager

Métriques

Consultations de la notice

16

Téléchargements de fichiers

3