  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?
