All your data are always missing: incorporating bias due to measurement error into the potential outcomes framework.

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Causal Effect Inference with Deep Latent-Variable Models (2017, neutral): “The general idea is that in many cases one should first attempt to infer the joint distribution p(X,Z) between the proxy and the hidden confounders, and then use that knowledge to adjust for the hidden confounders [55, 41, 32, 37, 12].”
Deconfounding Reinforcement Learning in Observational Settings (2018, methodology): “However, using proxy variables to correctly recover causal eﬀects requires strict mathematical assumptions (Louizos et al., 2017; Edwards et al., 2015; Kuroki and Pearl, 2014; Miao et al., 2018; Pearl, 2012; Wooldridge, 2009) and, in practice, we do not know whether or not the available data meets…”
Policy Evaluation with Latent Confounders via Optimal Balance (2019, methodology): “As in our problem setup, much of this work is based on the model of using an identified latent variable model for the proxies [9, 27, 34, 37, 43].”