Abstract
I present an overview of two methods controversies that are central to analysis and inference: That surrounding causal modeling as reflected in the “causal inference” movement, and that surrounding null bias in statistical methods as applied to causal questions. Human factors have expanded what might otherwise have been narrow technical discussions into broad philosophical debates. There seem to be misconceptions about the requirements and capabilities of formal methods, especially in notions that certain assumptions or models (such as potential-outcome models) are necessary or sufficient for valid inference. I argue that, once these misconceptions are removed, most elements of the opposing views can be reconciled. The chief problem of causal inference then becomes one of how to teach sound use of formal methods (such as causal modeling, statistical inference, and sensitivity analysis), and how to apply them without generating the overconfidence and misinterpretations that have ruined so many statistical practices.
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Notes
The same comment may well apply to physical sciences, but those are far outside my scope.
In these papers, “identification” has its strict statistical meaning of estimability rather than its more recent epidemiologic meaning of qualitative identification, as in Schwartz et al. (2016) and VanderWeele (2016).
Apart from invertible equation systems, which do not exist in realistic models for health and social phenomena.
In a common notation, knowing the treatment indicator X is positively associated with the outcome indicator Y0 under X=0 yet unassociated with the observed outcome Yobs leads us to infer that Y1 > Y0 for some observed unit.
In terms of potential outcomes Yx indexed by drug dose x, we would infer that the unobserved variable Y40 is sometimes greater than Y0 even though Pr(X=40) = 0.
In notation: With Yx the potential outcome and Yobs its measurement, we can have Yobs ≠ Yx yet still infer that Y1 ≠ Y0 for some unit.
Adding confusion, the term ‘consistency' is already well established for unrelated concepts such as estimator convergence and freedom from contradiction.
Even more startling is that temporality (cause preceding effect) is not necessary in some counterfactual accounts of causation (Price 1996).
In logic this syntactical structure is called a theory, and the interpretations that follow that structure are called models of the theory. I instead call this structure a model, which I think more in line with common usage in statistics and applied sciences.
This fact is one way of seeing why quantum physics has defied classical causal explanations: Robins et al. (2015) show that potential-outcome models obey Bell’s inequality, whose observed violations conflict with local definiteness (local realism, local hidden variables) and local causal diagrams (Gill 2014).
Notably, similar concerns about untestable mathematical theory arise in hard sciences like physics (Ellis and Silk 2014).
When in addition to the causal graph we can assume faithfulness (open paths imply association), the number of logically possible structures is reduced drastically – to the point that a certain limited type of conditional causal identification can be enabled (Spirtes et al. 2001; Robins et al. 2003).
One measure of the evidence against a model (whether causal or not) supplied by the P-value p from a test of its fit is the binary information or surprisal −log2(p).
The retrolental-fibroplasia controversy provides one such case study (Greenland 1991).
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Acknowledgements
I am deeply indebted to many colleagues for extensive comments and correspondence on the initial draft of this paper, including Alex Broadbent, Jan Vandenbroucke, Neil Pearce, Ashley Naimi, Jay Kaufman, Sharon Schwartz, Nicolle Gatto, Ulka Campbell, George Maldonado, Alfredo Morabia, James Robins, and Tyler VanderWeele. Any errors that remain are solely my responsibility.
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Greenland, S. For and Against Methodologies: Some Perspectives on Recent Causal and Statistical Inference Debates. Eur J Epidemiol 32, 3–20 (2017). https://doi.org/10.1007/s10654-017-0230-6
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DOI: https://doi.org/10.1007/s10654-017-0230-6