Assumption-lean inference for generalised linear model parameters

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.

Automated summary

Inference for parameters in generalised linear models is usually based on specified assumptions, but often there is excess uncertainty due to the data-adaptive model selection process. We propose novel nonparametric definitions that capture the association and interaction between variables even when the models are misspecified.