Comment on “Blessings of Multiple Causes”

(This comment has been updated to respond to Wang and Blei's rejoinder [arXiv:1910.07320].) The premise of the deconfounder method proposed in "Blessings of Multiple Causes" by Wang and Blei [arXiv:1805.06826], namely that a variable that renders multiple causes conditionally independent also controls for unmeasured multi-cause confounding, is incorrect. This can be seen by noting that no fact about the observed data alone can be informative about ignorability, since ignorability is compatible with any observed data distribution. Methods to control for unmeasured confounding may be valid with additional assumptions in specific settings, but they cannot, in general, provide a checkable approach to causal inference, and they do not, in general, require weaker assumptions than the assumptions that are commonly used for causal inference. While this is outside the scope of this comment, we note that much recent work on applying ideas from latent variable modeling to causal inference problems suffers from similar issues.

[1]  D. Reich,et al.  Principal components analysis corrects for stratification in genome-wide association studies , 2006, Nature Genetics.

[2]  J. Robins.  Data, Design, and Background Knowledge in Etiologic Inference , 2001, Epidemiology.

[3]  Christopher Winship,et al.  Endogenous Selection Bias: The Problem of Conditioning on a Collider Variable. , 2014, Annual review of sociology.

[4]  J. Pearl,et al.  Measurement bias and effect restoration in causal inference , 2014 .

[5]  Peter Spirtes,et al.  Introduction to Causal Inference , 2010, J. Mach. Learn. Res..

[6]  James M. Robins,et al.  On the Validity of Covariate Adjustment for Estimating Causal Effects , 2010, UAI.

[7]  H. Strasser.  Efficient and adaptive estimation for semiparametric models - P. J. Bickel; Ch. A. J. Klaassen; Ya 'acov Ritov; J. A. Wellner. , 1997 .

[8]  J. Kmenta.  Mostly Harmless Econometrics: An Empiricist's Companion , 2010 .

[9]  J. Pearl.  Causality: Models, Reasoning and Inference , 2000 .

[10]  O. Kallenberg.  Foundations of Modern Probability , 2021, Probability Theory and Stochastic Modelling.

[11]  K. Do,et al.  Efficient and Adaptive Estimation for Semiparametric Models. , 1994 .

[12]  Johannes Textor,et al.  A Complete Generalized Adjustment Criterion , 2015, UAI.

[13]  S. Cole,et al.  Illustrating bias due to conditioning on a collider. , 2010, International journal of epidemiology.

[14]  Alexander D'Amour,et al.  On Multi-Cause Causal Inference with Unobserved Confounding: Counterexamples, Impossibility, and Alternatives , 2019, ArXiv.

[15]  T. Hastie,et al.  CONFOUNDER ADJUSTMENT IN MULTIPLE HYPOTHESIS TESTING. , 2015, Annals of statistics.

[16]  David M. Blei,et al.  The Blessings of Multiple Causes , 2018, Journal of the American Statistical Association.