In a tie-breaker design (TBD), subjects with high values of a running variable are given some (usually desirable) treatment, subjects with low values are not, and subjects in the middle are randomized. TBDs are intermediate between regression discontinuity designs (RDDs) and randomized controlled trials (RCTs). TBDs allow a tradeoff between the resource allocation efficiency of an RDD and the statistical efficiency of an RCT. We study a model where the expected response is one multivariate regression for treated subjects and another for control subjects. We propose a prospective D-optimality, analogous to Bayesian optimal design, to understand design tradeoffs without reference to a specific data set. For given covariates, we show how to use convex optimization to choose treatment probabilities that optimize this criterion. We can incorporate a variety of constraints motivated by economic and ethical considerations. In our model, D-optimality for the treatment effect coincides with D-optimality for the whole regression, and, without constraints, an RCT is globally optimal. We show that a monotonicity constraint favoring more deserving subjects induces sparsity in the number of distinct treatment probabilities. We apply the convex optimization solution to a semi-synthetic example involving triage data from the MIMIC-IV-ED database.

翻译：在平局决胜设计中，运行变量取值较高的受试者被给予某种（通常为理想的）处理，取值较低的受试者则不予处理，而处于中间区间的受试者则被随机分配处理。平局决胜设计介于断点回归设计与随机对照试验之间。它允许在断点回归设计的资源配置效率与随机对照试验的统计效率之间进行权衡。我们研究了一个模型，其中受试者的期望响应对于处理组是一个多元回归，对于对照组则是另一个多元回归。我们提出了一种前瞻性D最优性准则，类似于贝叶斯最优设计，旨在无需参照特定数据集即可理解设计权衡。对于给定的协变量，我们展示了如何利用凸优化来选择优化此准则的处理概率。我们可以纳入由经济与伦理考量驱动的多种约束条件。在我们的模型中，处理效应的D最优性与整个回归的D最优性一致，并且在无约束条件下，随机对照试验是全局最优的。我们证明，一项倾向于更值得受试者的单调性约束会导致不同处理概率的数量具有稀疏性。我们将凸优化解应用于一个涉及MIMIC-IV-ED数据库中分诊数据的半合成示例。