Nonmyopic and pseudo-nonmyopic approaches to optimal sequential design in the presence of covariates
Nonmyopic and pseudo-nonmyopic approaches to optimal sequential design in the presence of covariates
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 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 estimator 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 within a specified horizon. The nonmyopic approach requires recursive formulae and suffers from the curse of dimensionality. We propose a pseudo-nonmyopic approach which has a similar aim to the nonmyopic approach, but does not involve recursion and instead relies on simulating trajectories of future possible decisions. Our simulation studies show that for the simple case of a logistic regression with a single binary covariate and a binary treatment, and a more realistic case with four binary covariates, binary treatment and treatment–covariate interactions, the nonmyopic and pseudo-nonmyopic approaches provide no competitive advantage over the myopic approach, both in terms of the size of the estimated treatment effect and also the efficiency of the designs. Results are robust to the size of the horizon used in the nonmyopic approach, and the number of simulated trajectories used in the pseudo-nonmyopic approach.
Design of experiments, coordinate exchange, dynamic programming, optimal design, sequential design
Tackney, Mia Sato
37c4aac1-b47d-4e1e-aa75-3ca45844b82e
Woods, David
ae21f7e2-29d9-4f55-98a2-639c5e44c79c
Shpitser, Ilya
4d295b9b-39e8-417f-b38d-fbb5d7df6992
Tackney, Mia Sato
37c4aac1-b47d-4e1e-aa75-3ca45844b82e
Woods, David
ae21f7e2-29d9-4f55-98a2-639c5e44c79c
Shpitser, Ilya
4d295b9b-39e8-417f-b38d-fbb5d7df6992
Tackney, Mia Sato, Woods, David and Shpitser, Ilya
(2022)
Nonmyopic and pseudo-nonmyopic approaches to optimal sequential design in the presence of covariates.
Journal of Statistical Computation and Simulation.
(doi:10.1080/00949655.2022.2113788).
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 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 estimator 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 within a specified horizon. The nonmyopic approach requires recursive formulae and suffers from the curse of dimensionality. We propose a pseudo-nonmyopic approach which has a similar aim to the nonmyopic approach, but does not involve recursion and instead relies on simulating trajectories of future possible decisions. Our simulation studies show that for the simple case of a logistic regression with a single binary covariate and a binary treatment, and a more realistic case with four binary covariates, binary treatment and treatment–covariate interactions, the nonmyopic and pseudo-nonmyopic approaches provide no competitive advantage over the myopic approach, both in terms of the size of the estimated treatment effect and also the efficiency of the designs. Results are robust to the size of the horizon used in the nonmyopic approach, and the number of simulated trajectories used in the pseudo-nonmyopic approach.
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Accepted/In Press date: 12 August 2022
e-pub ahead of print date: 15 September 2022
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Publisher Copyright:
© 2022 Informa UK Limited, trading as Taylor & Francis Group.
Keywords:
Design of experiments, coordinate exchange, dynamic programming, optimal design, sequential design
Identifiers
Local EPrints ID: 470416
URI: http://eprints.soton.ac.uk/id/eprint/470416
ISSN: 0094-9655
PURE UUID: 1c6f08e7-b126-4f67-a51b-cb4230396a2f
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Date deposited: 10 Oct 2022 16:54
Last modified: 17 Mar 2024 07:31
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Author:
Mia Sato Tackney
Author:
Ilya Shpitser
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