Utilizing local likelihood in regression discontinuity design: Investigating the impact of antiretroviral therapy eligibility on retention in clinical HIV care in South Africa

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.