A Bayesian Semiparametric Approach to Intermediate Variables in Causal Inference

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Principal causal effect identification and surrogate end point evaluation by multiple trials (2015, methodology): “ dichotomizing the endpoint (Ding et al., 2011). However, it is non-trivial to deal with a continuous surrogate endpoint since the causal necessity and suciency cannot be dened by dichotomizing it. Schwartz et al. (2011) set the stage for analyzing principal strata eects with continuous intermediate”
Transparent Parametrizations of Models for Potential Outcomes (2012, background): “…treatments and intermediate variables (Frangakis et al., 2004); clustered treatments (e.g., Frangakis et al., 2002); surrogate endpoints (Li et al., 2010); continuous intermediate variables, including partial compliance (e.g., Jin and Rubin, 2008; Schwartz et al., 2010); just to name a few.”
Augmented designs to assess principal strata direct effects (2011, background): “…is not impossible with continuous mediating variables, although continuous intermediate outcomes induce an infinite number of possible principal strata, in theory, leading to substantial complications in both inference and interpretation (e.g. Jin and Rubin (2008) and Schwartz et al. (2010)).”
Principal stratification analysis using principal scores (2016, background): “We need more structural assumptions on the causal problems (Jin and Rubin, 2008; Schwartz et al., 2011) and more sophisticated statistical inferential tools.”