Torben Martinussen’s contribution to the Discussion of ‘Parameterizing and simulating from causal models’ by Evans and Didelez
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马丁努森对《因果模型的参数化与模拟》的讨论
- 研究问题
- 这篇讨论关注：保留指定因果结构的数据生成方法用于模拟和用于估计时，应如何与科学问题驱动的目标参数推断相衔接？
- 方法与思路
- 讨论作者建议先依据已有知识限制数据分布，再定义科学目标参数，随后使用有效影响函数构造一步估计或目标最大似然估计。
- 材料陈述的贡献
- 该讨论肯定保持因果结构的模拟用途，同时对其估计用途提出保留，并以目标参数与有效影响函数的路线提出替代思路。
- 阅读关注点
- 应结合原讨论和被讨论主文，核对目标参数、有效影响函数及估计式，并区分评论者的建议与主论文实际提出的结果。
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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).