Sequential modeling for a class of reference‐based imputation methods in clinical trials with quantitative or binary outcomes

We consider treatment effect estimation in a randomized clinical trial with longitudinally measured quantitative or categorical outcomes. To handle missing data, we usually assume missing at random and then conduct sensitivity analysis for missing not at random. In the literature, several reference-based imputation methods, including "jump to reference" (J2R) and "copy reference" (CR), have been commonly used for conducting sensitivity analysis. J2R assumes the mean effect profile of patients who discontinue the investigative treatment jumps to that of the patients in the reference group after discontinuation, while CR assumes the conditional mean effect profile given the status prior to the time of discontinuation copies that of the patients in the reference group after discontinuation. In this article, we propose a novel, wide class of reference-based imputation methods for conducting sensitivity analysis, which includes J2R and CR as two extreme ends. The framework is motivated by the thought that the investigative treatment may have no, partially, or fully carried-over effect after deviation from the assigned treatment (eg, discontinue the assigned treatment or change to a different treatment). Further, we show that the proposed reference-based imputation methods can be implemented through sequential modeling. This property ensures that the methods can be applied to clinical trials with either quantitative or categorical outcomes. We use both causal-inference arguments and numerical examples to demonstrate the performance of the proposed methods.