## The Annals of Statistics

### 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 $\mu$, its solution possesses some similarities with the construction of optimal design measures bounded by $\mu$. 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.

#### Article information

Source
Ann. Statist., Volume 45, Number 5 (2017), 2046-2073.

Dates
Revised: September 2016
First available in Project Euclid: 31 October 2017

https://projecteuclid.org/euclid.aos/1509436827

Digital Object Identifier
doi:10.1214/16-AOS1518

Mathematical Reviews number (MathSciNet)
MR3718161

Zentralblatt MATH identifier
06821118

Subjects
Primary: 62K05: Optimal designs
Secondary: 62P10: Applications to biology and medical sciences

#### Citation

Metelkina, Asya; Pronzato, Luc. Information-regret compromise in covariate-adaptive treatment allocation. Ann. Statist. 45 (2017), no. 5, 2046--2073. doi:10.1214/16-AOS1518. https://projecteuclid.org/euclid.aos/1509436827

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#### Supplemental materials

• Supplement to “Information-regret compromise in covariate-adaptive treatment allocation”. In this Supplement, we give the proofs of Theorems 2.1, 2.2 and 4.1.