title: Limitations of individual causal models, causal graphs, and ignorability assumptions, as illustrated by random confounding and design unfaithfulness.
abstract: We describe how ordinary interpretations of causal models and causal graphs fail to capture important distinctions among ignorable allocation mechanisms for subject selection or allocation. We illustrate these limitations in the case of random confounding and designs that prevent such confounding. In many experimental designs individual treatment allocations are dependent, and explicit population models are needed to show this dependency. In particular, certain designs impose unfaithful covariate-treatment distributions to prevent random confounding, yet ordinary causal graphs cannot discriminate between these unconfounded designs and confounded studies. Causal models for populations are better suited for displaying these phenomena than are individual-level models, because they allow representation of allocation dependencies as well as outcome dependencies across individuals. Nonetheless, even with this extension, ordinary graphical models still fail to capture distinctions between hypothetical superpopulations (sampling distributions) and observed populations (actual distributions), although potential-outcome models can be adapted to show these distinctions and their consequences.
authors: Department of Epidemiology, UCLA School of Public Health, University of California, Los Angeles, CA, USA.|Department of Statistics, UCLA College of Letters and Science, University of California, Los Angeles, CA, USA.
authors: Sander
authors: S
authors: Greenland
authors: Department of Epidemiology and Biostatistics, School of Public Health, Tehran University of Medical Sciences, PO Box: 14155-6446, Tehran, Iran. mansournia_ma@yahoo.com.
authors: Mohammad Ali
authors: MA
authors: Mansournia
mesh_terms: D015984:Causality; D015986:Confounding Factors, Epidemiologic; D006801:Humans; D015233:Models, Statistical; D011897:Random Allocation; D016032:Randomized Controlled Trials as Topic; D012107:Research Design; D015983:Selection Bias
keywords: Causal graphs; Confounding; Directed acyclic graphs; Ignorability; Inverse probability weighting; Unfaithfulness