LAUSR

In this Reply we will discuss the reason why we left out a scenario where missingness is dependent of the outcome and show that our simulation results are consistent when there is a non-null treatment effect. Regarding the first point, we agree with the authors that a complete case analysis will results in bias when data are missing at random and the missingness in covariates is dependent on the outcome. This can also be shown in a missingness graph (Fig. 1a). In this scenario, a complete case analysis will result in bias since the missing indicator R and the outcome Y cannot be d-separated. In fact, complete case analysis will result in bias in any situation when missingness in covariates (R) and the outcome (Y) cannot be conditionally d-separated even when the treatment effect is homogeneous. This can happen in three different scenarios: