Torben Martinussen’s contribution to the Discussion of ‘Parameterizing and simulating from causal models’ by Evans and Didelez

原文摘要

I congratulate the authors on an interesting and useful contribution to the literature on causal inference. The authors propose a nice way of generating data so that a given causal structure of interest is preserved. This is a handy tool to have when for instance one needs to generate data to investigate small sample performance of a new inference procedure. I find it less attractive to use the suggested procedure for estimation purposes as is also alluded to in the paper and is used in the worked data application. This is the classical statistical approach, which is in opposition to the ‘roadmap’ approach advocated by van der Laan among others (see for instance van der Laan & Rose, 2011). Instead of relying on a statistical model (parametric or semi-parametric), one only restricts the data-generating probability measure P if there is some prior knowledge about P such as certain independences if for instance we are dealing with a randomized study. Without such prior knowledge, then no specific structure is imposed on P. The next step is to define a target estimand that should be motivated from the scientific interest of the given study. This estimand does not refer to any specific statistical model so it is not a specific regression coefficient in a given model, say. In the worked application, the focus is on the estimand Following the roadmap, the next step is to find the corresponding efficient influence function, which in this case is where f is used generically for density functions. This leads to the one-step estimator (or one can also use the targeted maximum likelihood estimation, see van der Laan & Rose, 2011) where subscript n refers to quantities estimated from the data for instance using machine learning methods (Chernozhukov et al., 2018).

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