All models are wrong”, is wrong: Estimates of associations in a model-free world

The logistic regression model has become a panacea for estimating associations in the context of high-dimensional (e.g., many) confounders. It is commonly known that associations estimated in a misspecified model, are biased, and one would be hard pressed to argue that there is any theoretical justification, for instance, in assuming a simple additive logistic regression model (one that includes only main effects and no interactions or more complicated functional forms, e.g., polynomials). Thus, the implicit assumption of using such models has been articulated as such (Box, 1979): “all models are wrong, but some are useful”. However, recent advances in model selection, and in defining estimates that do not rely on a parametric model, are challenging this approach/philosophy. Typically, the real statistical model, as defined by what constraints one really know about the mechanism generating the data, is a so-called semi-parametric model (that is, there are nearly no constraints one can impose from previous knowledge). Fortunately, there is theory and available software for how to estimate a regression in the absence of a known model. In addition, research in causal inference provides interesting and relevant parameters, which do not rely on specifying a parametric model and typically, they have more meaningful public health interpretation than say an adjusted odds ratio. These parameters can include things like the average treatment (or exposure) effect, or they can examine so-called causal additive interaction. In this talk, we discuss these developments that utilize on so-called ensemble learning (SuperLearner), and defining parameters in a non-parametric structural equation model (NPSEM). The result is a methodology that remove the “art” out of model selection, and provide parameter estimates targeted to the scientific/public health question. We illustrate the methodology in a data analysis estimating the impacts of alcohol outlet density on alcohol related harm.