Graphical Models for Recovering Probabilistic and Causal Queries from Missing Data

Mohan, Karthika; Pearl, Judea

doi:10.21236/ada614408

Cited by 30 publications

(36 citation statements)

References 21 publications

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“…As Mealli and Rubin ( 5 ) noted, MAR is not an assumption about conditional independencies between variables, as is often thought, but about the nondependence of a function on one of its arguments. This is difficult to assess on the basis of substantive knowledge ( 6 ), which is crucial in the multivariable missingness setting ( 7 – 9 ). In particular, the stringency of MAR in general problems with multivariable missingness is poorly understood ( 4 – 6 , 10 , 11 ).…”

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confidence: 99%

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

Moreno‐Betancur

Lee

Leacy

et al. 2018

American Journal of Epidemiology

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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.

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confidence: 99%

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

Moreno‐Betancur

Lee

Leacy

et al. 2018

American Journal of Epidemiology

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“…These definitions are associated to conditional independence statements on the random variables under investigation and therefore are typically easier to interpret in applications. Much of the recent work by Pearl and his co‐authors (Pearl & Mohan, ; Mohan et al ., Mohan & Pearl, ; Mohan & Pearl, ; Mohan & Pearl ; Mohan & Pearl, ) adopts the variable‐based framework to investigate under what conditions a missingness mechanism is testable or a probabilistic/causal query on the data is recoverable given that the data are corrupted by missingness.…”

Section: Discussionmentioning

confidence: 99%

“…Another recently developed branch of the literature considers a third group of definitions relying on the existence of always‐observed auxiliary information (Pearl & Mohan, ; Mohan et al , ). These definitions are termed variable‐based or graph‐based as they enable the use of graphical tools like missingness‐graphs that are directed acyclic graphs including missingness indicators in their set of nodes (Mohan & Pearl, ; Mohan et al , ). In this paper, we denote these definitions by adding the prefix VB‐, which stands for ‘variable‐based’.…”

Section: Introductionmentioning

confidence: 99%

“…Mohan et al () use missingness graphs to explore recoverability of probabilistic queries. Mohan & Pearl (), Mohan & Pearl () and Daniel et al () focus also on recoverability of causal relations. Potthoff et al () show that whether data are missing according to their variable‐based definition of missing at random, which they term MAR+, can be tested when at least two variables have missing values.…”

Section: Introductionmentioning

confidence: 99%

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Missing Data: A Unified Taxonomy Guided by Conditional Independence

Doretti

Geneletti

Stanghellini

2017

Int Statistical Rev

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Summary Recent work (Seaman et al., ; Mealli & Rubin, ) attempts to clarify the not always well‐understood difference between realised and everywhere definitions of missing at random (MAR) and missing completely at random. Another branch of the literature (Mohan et al., ; Pearl & Mohan, ) exploits always‐observed covariates to give variable‐based definitions of MAR and missing completely at random. In this paper, we develop a unified taxonomy encompassing all approaches. In this taxonomy, the new concept of ‘complementary MAR’ is introduced, and its relationship with the concept of data observed at random is discussed. All relationships among these definitions are analysed and represented graphically. Conditional independence, both at the random variable and at the event level, is the formal language we adopt to connect all these definitions. Our paper covers both the univariate and the multivariate case, where attention is paid to monotone missingness and to the concept of sequential MAR. Specifically, for monotone missingness, we propose a sequential MAR definition that might be more appropriate than both everywhere and variable‐based MAR to model dropout in certain contexts.

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“…For example, PðX; Y; Z; R z Þ is recoverable in Figure 4(a) since the graph is in ðMÞ (it is also in MAR) and this distribution advertises the conditional independence Z \ \ R z jXY. Yet, Z \ \ R z jXY is not testable by any data in which the probability of observing Z is non-zero (for all x; y) [33,37]. Any such data can be construed as if generated by the model in Figure 4(a), where the independence holds.…”

Section: Definition 5 (Testability)mentioning

confidence: 99%

The Deductive Approach to Causal Inference

Pearl

2014

Journal of Causal Inference

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This paper reviews concepts, principles, and tools that have led to a coherent mathematical theory that unifies the graphical, structural, and potential outcome approaches to causal inference. The theory provides solutions to a number of pending problems in causal analysis, including questions of confounding control, policy analysis, mediation, missing data, and the integration of data from diverse studies.

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Graphical Models for Recovering Probabilistic and Causal Queries from Missing Data

Cited by 30 publications

References 21 publications

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

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

Missing Data: A Unified Taxonomy Guided by Conditional Independence

The Deductive Approach to Causal Inference

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