Regression discontinuity design (RDD) is a quasi-experimental approach used to estimate the causal effects of an intervention assigned based on a cutoff criterion. RDD exploits the idea that close to the cutoff units below and above are similar; hence, they can be meaningfully compared. Consequently, the causal effect can be estimated only locally at the cutoff point. This makes the cutoff point an essential element of RDD. However, especially in medical applications, the exact cutoff location may not always be disclosed to the researcher, and even when it is, the actual location may deviate from the official one. As we illustrate on the application of RDD to the HIV treatment eligibility data, estimating the causal effect at an incorrect cutoff point leads to meaningless results. Moreover, since the cutoff criterion often acts as a guideline rather than as a strict rule, the location of the cutoff may be unclear from the data. The method we present can be applied both as an estimation and validation tool in RDD. We use a Bayesian approach to incorporate prior knowledge and uncertainty about the cutoff location in the causal effect estimation. At the same time, our Bayesian model LoTTA is fitted globally to the whole data, whereas RDD is a local, boundary point estimation problem. In this work we address a natural question that arises: how to make Bayesian inference more local to render a meaningful and powerful estimate of the treatment effect?

翻译：断点回归设计（RDD）是一种准实验方法，用于估计基于断点标准分配干预的因果效应。RDD利用接近断点的上下单元具有相似性的原理，从而可以进行有意义的比较。因此，因果效应只能在断点处进行局部估计。这使得断点成为RDD的核心要素。然而，特别是在医学应用中，确切的断点位置可能并不总是向研究者公开，即使公开，实际位置也可能与官方位置存在偏差。正如我们在HIV治疗资格数据中应用RDD所展示的，在错误的断点处估计因果效应会导致无意义的结果。此外，由于断点标准通常作为指导原则而非严格规则，断点的位置在数据中可能并不明确。本文提出的方法可作为RDD中的估计和验证工具。我们采用贝叶斯方法，在因果效应估计中纳入关于断点位置的先验知识和不确定性。同时，我们的贝叶斯模型LoTTA全局拟合整个数据，而RDD属于局部边界点估计问题。本研究解决了一个自然产生的问题：如何使贝叶斯推断更具局部性，从而获得有意义且有效的治疗效果估计？