Minimax Crossover Designs
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In crossover experiments, two broad types of treatment effects are typically considered: direct effects that capture the immediate impact of the treatment, and carryover effects that capture the lagged impact of past treatments. Existing approaches to optimal crossover design usually minimize a criterion that relies on an outcome model, and on assumptions that carryover effects are limited, say, to one or two time periods. The former assumption relies on correct specification, which is usually untenable, whereas the latter assumption is problematic when long-range carryover effects are expected, and are of primary interest. In this paper, we derive minimax optimal designs to estimate both direct and carryover effects simultaneously. In contrast to prior work, our minimax designs do not require specifying a model for the outcomes, relying instead on invariance assumptions. This allows us to address problems with arbitrary carryover lag, such as those encountered in digital experimentation.
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