Discussion of PENCOMP

We would like to congratulate Zhou, Elliott, and Little (henceforth referred to as ZEL) on an interesting article in an important area of research. ZEL propose a new approach for causal inference using a full probability model that extends their earlier work for multiple imputation of missing data (Zhang and Little 2009). In addition, they extend their approach to more complex causal inference settings with time varying treatments and confounders. The proposed approach has numerous attractive features including it being relatively simple to implement, and that under “standard” assumptions it has the double robustness property like many semiparametric, moment-based estimators (Bang and Robins 2005). Given that the approach uses a full probability model (not just moments), attractive features of Bayesian inference for quantifying uncertainty about uncheckable assumptions (like no unmeasured confounding) can be part of the inference (Roy, Lum, and Daniels 2017; Kim et al. 2017). On the other hand the proposed approach has some limitations. First, it is “hard coded” to average causal effects and would require different models for other causal effects (e.g., quantile causal effects); of course, semiparametric approaches share the same limitation. However, it is not clear how straightforward it would be to extend the proposed approach to other causal effects. In Section 3.2, we discuss approaches that allow estimation of any causal effects. Second, it would seem unlikely that either the propensity score or outcome regression model would be correct within the simple models considered in the manuscript, especially when considering multiple time points in the longitudinal setting when consistency relies on correctly specifying multiple models at once. Further, “searching” for more complex models (i.e., interactions, nonlinearities) can be challenging. In Section 3.1, we will discuss “default” approaches that would result in considerably more flexible (and realistic) models. The rest of this discussion, where we will address three main issues, is organized as follows. In Section 2, we discuss the practical utility of the double robustness property in longitudinal settings. In Section 3, we discuss generalizing ZEL with more flexible regression models and an alternative using Bayesian nonparametric (BNP) methods for the regression of the outcome on confounders (i.e., not the propensity score). In Section 4, we discuss the issue of overlap/positivity violations in