Assumption-lean inference for generalised linear model parameters

• 成果类型: Article
• 署名作者: Vansteelandt, Stijn; Dukes, Oliver
• 署名单位: Ghent University; University of London; London School of Hygiene & Tropical Medicine
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• DOI: 10.1111/rssb.12504
• 发表日期: 2022
• 页码: 657-685
• 关键词: semiparametric regression; Causal Inference; odds ratio; estimator

摘要

Inference for the parameters indexing generalised linear models is routinely based on the assumption that the model is correct and a priori specified. This is unsatisfactory because the chosen model is usually the result of a data-adaptive model selection process, which may induce excess uncertainty that is not usually acknowledged. Moreover, the assumptions encoded in the chosen model rarely represent some a priori known, ground truth, making standard inferences prone to bias, but also failing to give a pure reflection of the information that is contained in the data. Inspired by developments on assumption-free inference for so-called projection parameters, we here propose novel nonparametric definitions of main effect estimands and effect modification estimands. These reduce to standard main effect and effect modification parameters in generalised linear models when these models are correctly specified, but have the advantage that they continue to capture respectively the (conditional) association between two variables, or the degree to which two variables interact in their association with outcome, even when these models are misspecified. We achieve an assumption-lean inference for these estimands on the basis of their efficient influence function under the nonparametric model while invoking flexible data-adaptive (e.g. machine learning) procedures.