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In sequential experiments, subjects become available for the study over aperiod of time, and covariates are often measured at the time of arrival. Weconsider the setting where the sample size is fixed but covariate values areunknown until subjects enrol. Given a model for the outcome, a sequentialoptimal design approach can be used to allocate treatments to minimize thevariance of the treatment effect. We extend existing optimal design methodologyso it can be used within a nonmyopic framework, where treatment allocation forthe current subject depends not only on the treatments and covariates of thesubjects already enrolled in the study, but also the impact of possible futuretreatment assignments. The nonmyopic approach is computationally expensive asit requires recursive formulae. We propose a pseudo-nonmyopic approach whichhas a similar aim to the nonmyopic approach, but does not involve recursion andinstead relies on simulations of future possible decisions. Our simulationstudies show that the myopic approach is the most efficient for the logisticmodel case with a single binary covariate and binary treatment.

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