Design of sequential experiments with covariate information

Abstract

Randomized experiments are considered the gold standard of study designs. When averaged over all possible randomizations, the treatment effect is free from bias and can also have a causal interpretation. In experiments involving human participants, it is common for participants to become available sequentially over time. Covariate information, such as age and sex, is taken and a treatment is assigned soon after. In this sequential setting, there are two main dangers of allocating treatments completely at random: replication of treatments may be unbalanced, and replication of treatments may be unbalanced for covariates. Both problems can lead to imprecision in the estimate of the treatment effect.

Covariate-adaptive schemes allocate treatments to patients to minimize some measure of imbalance in treatments and covariates. Minimization is a method commonly used in clinical trials which is appropriate for binary covariates. Alternatively, sequential optimal design based methodology allocates treatments to minimize the variance of the treatment effect under a specified model. We extend the optimal design based methodology to a nonmyopic setting, where treatment allocation for the current patient depends not only on the treatments and covariates of the patients in the study, but also the impact of possible future treatment assignments. The number of possible future decisions considered is called the horizon. Our simulation studies shows that there are very few examples with binary treatment where the non-myopic approach offers benefit over the myopic approach. One main limitation of the nonmyopic approach is that it involves computationally expensive recursive formulae which can only be implemented in limited contexts, for example for discrete treatments and for a horizon of no more than five. This motivated the development of a pseudo-nonmyopic approach which has a similar aim to the nonmyopic approach, but does not involve recursion. The horizon can be up until the end of the trial and the approach can also be used for continuous treatments.

We apply the sequential nonmyopic and pseudo-nonmyopic framework in the setting of personalized medicine. A trial for personalized medicine aims to identify effective combinations of treatments and biomarkers. In this context, our main result from simulations is that the pseudo-nonmyopic approach is more efficient than the myopic approach in the logistic model case with continuous treatment where there is a large interaction between the treatment and biomarker. In particular, this benefit is more pronounced when the biomarker relevant in the interaction is rare.

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Identifiers

ORCID for Peter W.F. Smith: orcid.org/0000-0003-4423-5410

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