Treatment Comparison for a Single Arm Study Utilizing External Control: Performing Inference when Imputing Potential Outcomes.

Non-randomized comparative studies are often used to compare treatment effects between an investigational product and a control when randomization is not feasible or difficult in practice. A typical situation is that the product is investigated in a single-arm study, and the control data are collected in an external data source. For such a situation, we propose an alternative approach to draw inference on the treatment effect difference. First, a potential outcome model (POM) for the outcome under control treatment is built based on the external control data source. Next, the POM is utilized to impute outcomes of subjects in the single-arm study as if they were treated with the control treatment. Then the inference on the treatment effect difference can be made by comparing imputed outcomes (for the control) and observed outcomes (for the investigational product). The main purpose of this paper is to provide a proof of concept regarding how to perform inference on the treatment effect between the investigational product and the control under this scenario. We illustrate our approach by assuming the endpoint to follow a normal distribution and the POM to be a linear regression model.