Missing data are a common occurrence in epidemiological studies and may impact
study conclusions due to potential bias and loss of statistical power. It is
widely understood that if the data are ``missing at random'' (MAR) -- an
assumption allowing the probability of missing data to depend on observed values
-- then unbiased estimation is possible with appropriate methods. While the need
to assess the plausibility of this assumption has been emphasised, the practical
difficulty of these tasks and the stringency of MAR in the context of multiple
incomplete variables are rarely acknowledged. Further, while MAR is sufficient,
it is certainly not necessary: in a wide range of ``missing not at random''
(MNAR) scenarios unbiased estimation of certain parameters is possible.
Recent developments in the computer science literature suggest that directed
acyclic graphs (DAGs) could be an intuitive tool for stating and assessing
finer-grained assumptions, beyond the MAR-MNAR dichotomy. However, as we show,
translating the assumptions in a given generic DAG to a decision about the
missing data method is a surprisingly complex problem requiring a case-by-case
treatment. Seeking a balance between detail and feasibility, we constructed
eight ``canonical'' DAGs representing broad categories of missingness mechanisms
that could be encountered in a typical point-exposure epidemiological study with
incomplete exposure, outcome and confounders. For each DAG, we derived
mathematically whether unbiased estimation of some common target parameters is
possible using common procedures, or if sensitivity analyses are necessary.
These DAGs and findings can be readily used by epidemiologists to articulate
their assumptions, and choose a strategy to handle missing data depending on
their target parameter. We use numerical simulations and the Longitudinal Study
of Australian Children for illustration.