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Abstract:
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Precision medicine is an emerging medical paradigm that focuses on the most effective treatment strategy tailored for individual patients. In optimal treatment decision making, a crucial question is to fi nd variables that have qualitative treatment effects, namely the prescriptive variables. Gunter et al. (2011) gives a formal defi nition of the marginal qualitative interaction between a single covariate and treatment. In this paper, we first introduce the notion of conditional qualitative treatment effects (CQTE) of a set of variables given another set of variables and provide a class of equivalent representations for the null hypothesis of no CQTE. The proposed defi nition of CQTE does not assume any parametric form for the optimal treatment rule and plays an important role for assessing the incremental value of a set of new variables in optimal treatment decision making conditional on an existing set of prescriptive variables. We then propose novel testing procedures for no CQTE based on kernel estimation of the conditional contrast functions. We show that our test statistics have asymptotically correct size and non-negligible power against some nonstandard local alternative.
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