Ilya Shpitser’s Contribution to the Discussion of ‘Assumption-Lean Inference for Generalised Linear Model Parameters’ by Vansteelandt and Dukes

原文摘要

A hallmark of principled causal inference is being careful and explicit about assumptions underlying data analysis. In their timely paper, the authors, Professor Stijn Vansteelandt and Oliver Dukes, adopt this view to provide a general roadmap for cautious statistical inference about target parameters. The authors distinguish between assumptions made for substantive reasons and those made for convenience. An important feature of their approach is that an estimand with respect to an unrestricted model (hereafter, the ‘non-parametric estimand’) must be specified prior to imposing any model restrictions. The authors illustrate their roadmap by defining and estimating main effect and interaction parameters in regression models. These estimands are defined without reference to any model restrictions, but at the same time specialise to known special cases if restrictions hold, for example if the partially linear regression model is true. The proposal recapitulates developments in mediation analysis, where direct and indirect effect parameters were initially defined as simple functions of regression coefficients in linear causal models, with the definition eventually generalising to a fully non-parametric one based on nested potential outcomes (Pearl, 2001; Robins & Greenland, 1992) or separable effects based on treatment components (Robins & Richardson, 2010). In causal inference, an estimand in an unrestricted model is often implied by the combination of the causal model, substantive considerations, and identification theory yielding an identified functional for the target causal parameter. The difficulty with the authors’ proposal is that the considerations one should appeal to when defining the non-parametric estimand are unclear. The authors propose a number of desiderata such an estimand must satisfy, but (a) these are perhaps arguable, and (b) given a particular specialised parameter defined in a parametric or semi-parametric model, for instance a regression coefficient, it seems there will be many non-parametric estimands that reduce to the specialised parameter under restricted models, and otherwise satisfy the authors’ desiderata. Different estimands will yield substantively different conclusions, and it is not clear how to choose among them. It would not be surprising if pragmatic considerations (e.g. ease of inference, availability of software) guided such a choice in practice. Indeed, it appears that the authors themselves were guided by pragmatic considerations when choosing among multiple possibilities for the non-parametric interaction parameter. This would seem to be contrary to the spirit of the authors’ proposal. As a causal inference researcher myself, I applaud the call to clarity about assumptions and estimands made by the authors. However, absent clear substantive guidance or an analogue of identification theory in causal inference, making the crucial choice of one non-parametric estimand out of many appears to be a ‘black art’.

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