Canonical Causal Diagrams to Guide the Treatment of Missing Data in Epidemiologic Studies

Abstract

With incomplete data, the "missing at random" (MAR) assumption is widely understood to enable unbiased estimation with appropriate methods. While the need to assess the plausibility of MAR and to perform sensitivity analyses considering "missing not at random" (MNAR) scenarios has been emphasized, the practical difficulty of these tasks is rarely acknowledged. With multivariable missingness, what MAR means is difficult to grasp, and in many MNAR scenarios unbiased estimation is possible using methods commonly associated with MAR. Directed acyclic graphs (DAGs) have been proposed as an alternative framework for specifying practically accessible assumptions beyond the MAR-MNAR dichotomy. However, there is currently no general algorithm for deciding how to handle the missing data given a specific DAG. Here we construct "canonical" DAGs capturing typical missingness mechanisms in epidemiologic studies with incomplete data on exposure, outcome, and confounding factors. For each DAG, we determine whether common target parameters are "recoverable," meaning that they can be expressed as functions of the available data distribution and thus estimated consistently, or whether sensitivity analyses are necessary. We investigate the performance of available-case and multiple-imputation procedures. Using data from waves 1-3 of the Longitudinal Study of Australian Children (2004-2008), we illustrate how our findings can guide the treatment of missing data in point-exposure studies.

Figure 1.

Canonical complete-data directed acyclic graph (c-DAG) for a general point-exposure study. For illustration, we provide under each node heading the variables involved in an example study of maternal mental illness and child behavior that used data from waves 1–3 of the Longitudinal Study of Australian Children (2004–2008). SDQ, Strengths and Difficulties Questionnaire.

Figure 2.

Canonical missingness directed acyclic graphs (m-DAGs) for a general point-exposure study. These 10 m-DAGs were identified as providing the most general forms of all essentially distinct extensions of the m-DAG shown in panel A (referred to as “m-DAG A”) in terms of recoverability. To illustrate how each m-DAG extends m-DAG A, the additional arrows are indicated with a heavier line. In the text and tables, we refer to each m-DAG according to its figure locant (m-DAG A, m-DAG B, etc.).

Figure 3.

Assessment of the existence of an arrow from each incomplete variable to each missingness indicator in the example from the Longitudinal Study of Australian Children (2004–2008), drawing from evidence in the literature (, –45). SDQ, Strengths and Difficulties Questionnaire.