Nonmyopic and pseudo-nonmyopic approaches to optimal sequential design in the presence of covariates

TL;DR

This paper develops nonmyopic and pseudo-nonmyopic sequential design methods for treatment allocation in studies with covariates, aiming to optimize treatment effect estimation while addressing computational challenges.

Contribution

It introduces a pseudo-nonmyopic approach that approximates nonmyopic design without recursion, enhancing computational feasibility in sequential experiments.

Findings

Pseudo-nonmyopic approach reduces computational complexity.

Myopic approach is most efficient for logistic models with binary covariates.

Extended optimal design methodology for nonmyopic treatment allocation.

Abstract

In sequential experiments, subjects become available for the study over a period of time, and covariates are often measured at the time of arrival. We consider the setting where the sample size is fixed but covariate values are unknown until subjects enrol. Given a model for the outcome, a sequential optimal design approach can be used to allocate treatments to minimize the variance of the treatment effect. We extend existing optimal design methodology so it can be used within a nonmyopic framework, where treatment allocation for the current subject depends not only on the treatments and covariates of the subjects already enrolled in the study, but also the impact of possible future treatment assignments. The nonmyopic approach is computationally expensive as it requires recursive formulae. We propose a pseudo-nonmyopic approach which has a similar aim to the nonmyopic approach, but does not involve recursion and instead relies on simulations of future possible decisions. Our simulation studies show that the myopic approach is the most efficient for the logistic model case with a single binary covariate and binary treatment.