The regression discontinuity (RD) design is a widely utilized approach for assessing treatment effects. It involves assigning treatment based on the value of an observed covariate in relation to a fixed threshold. Although the RD design has been widely employed across various problems, its application to specific data types has received limited attention. For instance, there has been little research on utilizing the RD design when the outcome variable exhibits zero-inflation. This study introduces a novel RD estimator using local likelihood, which overcomes the limitations of the local linear regression model, a popular approach for estimating treatment effects in RD design, by considering the data type of the outcome variable. To determine the optimal bandwidth, we propose a modified Ludwig-Miller cross validation method. A set of simulations is carried out, involving binary, count, and zero-inflated outcome variables, to showcase the superior performance of the suggested method over local linear regression models. Subsequently, the proposed local likelihood model is employed on HIV care data, where antiretroviral therapy eligibility is determined by a CD4 count threshold. A comparison is made between the results obtained using the local likelihood model and those obtained using local linear regression.

中文翻译：

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在回归不连续性设计中利用局部可能性：调查南非抗逆转录病毒治疗资格对保留临床艾滋病毒护理的影响

断点回归 (RD) 设计是一种广泛使用的评估治疗效果的方法。它涉及根据观察到的协变量相对于固定阈值的值来分配治疗。尽管RD设计已广泛应用于各种问题，但其在特定数据类型上的应用受到的关注有限。例如，当结果变量呈现零通胀时，很少有关于利用 RD 设计的研究。本研究引入了一种使用局部似然的新型 RD 估计器，它通过考虑结果变量的数据类型，克服了局部线性回归模型的局限性，局部线性回归模型是 RD 设计中估计治疗效果的流行方法。为了确定最佳带宽，我们提出了一种改进的 Ludwig-Miller 交叉验证方法。进行了一组模拟，涉及二元、计数和零膨胀结果变量，以展示所建议的方法相对于局部线性回归模型的优越性能。随后，所提出的局部似然模型应用于 HIV 护理数据，其中抗逆转录病毒治疗资格由 CD4 计数阈值确定。将使用局部似然模型获得的结果与使用局部线性回归获得的结果进行比较。