Optimal Design of Controlled Experiments for Personalized Decision Making in the Presence of Observational Covariates
Optimal Design of Controlled Experiments for Personalized Decision Making in the Presence of Observational Covariates
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DOI：
10.51387/23-nejsds22
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发表时间：
2023
期刊：
影响因子：
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通讯作者：
Yezhuo Li;Qiong Zhang;A. Khademi;Boshi Yang
中科院分区：
文献类型：
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作者：
Yezhuo Li;Qiong Zhang;A. Khademi;Boshi Yang
受控实验广泛应用于临床试验或IT公司的用户行为研究等许多领域。近年来，研究实验设计问题以促进个性化决策成为一个热点。在本文中，我们调查的问题，多个治疗分配的最优设计的个性化决策的观察协变量与实验单位（通常，患者或用户）的存在。我们假设分配给治疗的受试者的反应遵循线性模型，该模型包括协变量和治疗之间的相互作用，以促进精确决策。我们将最优目标定义为不同治疗和不同协变量值的估计个性化治疗效果的最大方差。最优设计是通过最小化这个目标来获得的。在半定规划的原始优化问题，我们使用YALMIP和MOSEK为基础的优化求解器提供最优设计。数值研究提供了最优设计的质量进行评估。
Controlled experiments are widely applied in many areas such as clinical trials or user behavior studies in IT companies. Recently, it is popular to study experimental design problems to facilitate personalized decision making. In this paper, we investigate the problem of optimal design of multiple treatment allocation for personalized decision making in the presence of observational covariates associated with experimental units (often, patients or users). We assume that the response of a subject assigned to a treatment follows a linear model which includes the interaction between covariates and treatments to facilitate precision decision making. We define the optimal objective as the maximum variance of estimated personalized treatment effects over different treatments and different covariates values. The optimal design is obtained by minimizing this objective. Under a semi-definite program reformulation of the original optimization problem, we use a YALMIP and MOSEK based optimization solver to provide the optimal design. Numerical studies are provided to assess the quality of the optimal design.