  Missing data in multiple variables is a common issue. We investigate the
applicability of the framework of graphical models for handling missing data to
a complex longitudinal pharmacological study of children with HIV treated with
an efavirenz-based regimen as part of the CHAPAS-3 trial. Specifically, we
examine whether the causal effects of interest, defined through static
interventions on multiple continuous variables, can be recovered (estimated
consistently) from the available data only. So far, no general algorithms are
available to decide on recoverability, and decisions have to be made on a
case-by-case basis. We emphasize sensitivity of recoverability to even the
smallest changes in the graph structure, and present recoverability results for
three plausible missingness directed acyclic graphs (m-DAGs) in the CHAPAS-3
study, informed by clinical knowledge. Furthermore, we propose the concept of
"closed missingness mechanisms" and show that under these mechanisms an
available case analysis is admissible for consistent estimation for any type of
statistical and causal query, even if the underlying missingness mechanism is
of missing not at random (MNAR) type. Both simulations and theoretical
considerations demonstrate how, in the assumed MNAR setting of our study, a
complete or available case analysis can be superior to multiple imputation, and
estimation results vary depending on the assumed missingness DAG. Our analyses
are possibly the first to show the applicability of missingness DAGs (m-DAGs)
to complex longitudinal real-world data, while highlighting the sensitivity
with respect to the assumed causal model.
