论文标题
最佳打决策设计的一般表征
A general characterization of optimal tie-breaker designs
论文作者
论文摘要
胜利者设计以短期收益的统计设计目标进行了贸易，从优先分配二进制治疗的二进制治疗，为较高的运行变量$ x $的二进制治疗。设计目标是在两行回归模型中预期信息矩阵的任何连续函数，而短期增益表示为运行变量和处理指标之间的协方差。我们调查了如何在外部限制接受治疗的受试者的数量下指示指示治疗概率作为$ x $函数的设计功能，以优化这些竞争目标。我们的结果包括敏锐的存在和唯一性保证，同时满足了在$ x $中不受约束的道德上吸引人的要求。在这样的约束下，总是存在一个最佳的设计功能，该功能在单个不连续性下方和之上恒定。如果运行变量分布不是对称的，或者接受治疗的受试者的一部分不是$ 1/2 $，那么我们的最佳设计在不牺牲短期收益的情况下可以改善$ d $ dypimational的目标，而欧文和瓦里安（2020）（2020年）将治疗率的三个级别的打preative级设计为0美元，$ 0 $，$ 1/2 $，$ 1/2 $。我们使用Head Start的数据（一项幼儿政府干预计划）来说明我们的最佳设计。
Tie-breaker designs trade off a statistical design objective with short-term gain from preferentially assigning a binary treatment to those with high values of a running variable $x$. The design objective is any continuous function of the expected information matrix in a two-line regression model, and short-term gain is expressed as the covariance between the running variable and the treatment indicator. We investigate how to specify design functions indicating treatment probabilities as a function of $x$ to optimize these competing objectives, under external constraints on the number of subjects receiving treatment. Our results include sharp existence and uniqueness guarantees, while accommodating the ethically appealing requirement that treatment probabilities are non-decreasing in $x$. Under such a constraint, there always exists an optimal design function that is constant below and above a single discontinuity. When the running variable distribution is not symmetric or the fraction of subjects receiving the treatment is not $1/2$, our optimal designs improve upon a $D$-optimality objective without sacrificing short-term gain, compared to the three level tie-breaker designs of Owen and Varian (2020) that fix treatment probabilities at $0$, $1/2$, and $1$. We illustrate our optimal designs with data from Head Start, an early childhood government intervention program.
