Mats J Stensrud and Aaron L. Sarvet’s Contribution to the Discussion of ‘Assumption-Lean Inference for Generalised Linear Model Parameters’ by Vansteelandt and Dukes

原文摘要

We congratulate Vansteelandt and Dukes (V & D) with their innovative and interesting article. Here we further explore the interpretation of V & D’s main effects estimand. An algorithm for causal inference. There has been tremendous progress in causal inference by approaching causal queries in the following way (Hernan & Robins, 2020; Richardson & Robins, 2013; Robins, 1986): Choose a causal target: an estimand that corresponds to a scientific question of interest (usually a causal parameter). Specify a set of (reasonable) assumptions to define a model, and deduce a functional that equals the causal target at every law in the model. If the functional is fully comprised of observed data parameters, then we have full identification. If the functional is partially comprised of observed data parameters, then we have partial identification. Implement an estimator of the observed components of the identification functional. An analysis that results in partial identification, that is, it goes through 2.b, might be considered the classical ‘assumption-lean’ approach. The assumptions and the causal target are fixed. The investigators leverage their (limited) assumptions to derive bounds, that is ‘worst-cases’, for the value of the causal target. V & D do not follow this algorithm. Their algorithm fixes a functional of observed data—what they call an ‘estimand’. Then they consider an assumption (a parametric modelling assumption) that may or may not hold, and they derive what we might call a lower bound on the interpretation of their ‘estimand’. For example, V & D's Expression (5) corresponds to an average treatment effect under usual identification assumptions and a strong parametric assumption. In the absence of the strong parametric assumption, it corresponds to a variance weighted treatment effect (Robins et al., 2008). But, those who make decisions based on data cannot avoid discrete commitments about assumptions in their analyses. V & D’s algorithm does provide novel information (in the form of a worst-case interpretation) when the investigator is not willing to commit to the (parametric) model assumption. However, in this case decision-makers must be aware of the implications of the worst-case interpretation and how it differs from a causal target that more naturally corresponds to their scientific question of interest. Failure to do so could lead to wrong conclusions, as illustrated in the following example. Thus VD(p, q) > 0 when |q − 0.5| < |p − 0.5|, and VD(p, q) < 0 when |q − 0.5| > |p − 0.5|. This example illustrates a more general point. V & D’s main effects estimand does not necessarily correspond to an ATE, even when the ATE is 0 and even when there is no unmeasured confounding. In more complex settings, with higher dimensional treatments and non-linear link functions, these issues can still exist.

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