Anna Choi and Weng Kee Wong’s Contribution to the Discussion of ‘Assumption-Lean Inference for Generalised Linear Model Parameters’ by Vansteelandt and Dukes

原文摘要

We congratulate the authors for major advances in the methodology of estimands, in particular assumption-lean reference for the estimands in possibly misspecified generalised linear models. Whereas the simulation studies in Section 6 indeed support the ‘assumption-lean’ claim and the authors’ software in Practice of Epidemiology187 (pp. 1079–1084, 2018) facilitates such inference, the empirical example in Section 7 seems problematic to illustrate applications of the methodology. The example focuses on ‘data obtained from birth certificates from 2500 children born in King County, Washington in 2001’ in the First Steps program that was ‘set up in 1989’ in King County. These are longitudinal data, and the program is still ongoing. The methodology for longitudinal studies developed by Laird and Ware (1982) and applied to the Six Cities Study (Ryan, 2015, section 3) using generalised linear mixed models seems more appropriate for the re-analysis of the longitudinal data from the First Steps program of King County. Although Laird and Ware's methodology does not involve causal inference, Laird mentions how such inference can be added to the analysis in Ryan (2015, section 9 on statistical genetics). Chen et al. (2018, sections 3.6.3, 4.5, 5.4, 6.3, 6.4, 6.5, 7.4, 7.5) describe how causal inference/conclusions can be derived via multi-criteria statistical decision theory, exposure-adjusted incidence rates and multiple testing with familywise error or false discovery rate control for clinical trials data, control for confounding using inverse probability weighting, propensity scores, instrumental variables and research designs for unmeasured confounders, structural causal models and symbolic causal calculus for post-marketing safety data, empirical Bayes and Bayesian approaches to signal detection from adverse event databases. In addition, Sections 2.1.3 and 2.1.4 of that book describe recent advances in statistical learning methods which involve nonlinear basis functions such as neural networks and classification/regression trees and in validation of the prediction/regression model, in contrast to the linear (or partial linear) basis functions used in the present paper and complementary to the sample splitting asymptotic theory in its Theorem 2.

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