\begin{abstract} Tie-breaker designs (TBDs), in which subjects with extreme values are assigned treatment deterministically and those in the middle are randomized, are intermediate between regression discontinuity designs (RDDs) and randomized controlled trials (RCTs). TBDs thus provide a convenient mechanism by which to trade off between the treatment benefit of an RDD and the statistical efficiency gains of an RCT. We study a model where the expected response is one multivariate regression for treated subjects and another one for control subjects. For a given set of subject data we show how to use convex optimization to choose treatment probabilities that optimize a prospective $D$-optimality condition (expected information gain) adapted from Bayesian optimal design. We can incorporate economically motivated linear constraints on those treatment probabilities as well as monotonicity constraints that have a strong ethical motivation. Our condition can be used in two scenarios: known covariates with random treatments, and random covariates with random treatments. We find that optimality for the treatment effect coincides with optimality for the whole regression, and that the RCT satisfies moment conditions for optimality. For Gaussian data we can find optimal linear scorings of subjects, one for statistical efficiency and another for short term treatment benefit. We apply the convex optimization solution to some real emergency triage data from MIMIC.
翻译:\ begin{ apptract} 断层设计(TBDs), 在其中,极端值的主体被指定为确定性的治疗对象,中间的主体被随机确定,介于回归性不连续设计(RDDs)和随机控制试验(RCTs)之间。 因此,TBDs 提供了一个方便的机制,可以将RDD的治疗效益与RCT的统计效率增益进行交换。 我们研究一种模型,预期的反应是处理对象的多变量回归,而控制对象的模型。 对于一套特定的主题数据,我们展示了如何使用 convex优化来选择治疗概率,以优化预期的美元-最优性条件(预期的信息增益)从巴伊斯的最佳设计中加以调整。 我们可以将出于经济动机的线性限制纳入这些治疗概率以及具有强烈道德动机的单一性限制。 我们的状况可以在两种情况下使用: 已知的随机处理对象的三角变量, 以及随机处理对象的随机变异。 对于一组数据, 我们发现治疗效果的最佳性效果与最优化的治疗方法相吻合, 将一个最优性为最优化的 最优化的 最优性 水平数据 。