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In this commentary, we revisit Sir Austin Bradford Hill's seminal Alfred Watson Memorial Lecture in 1962 through the eyes of two practicing biostatisticians of the current era. We summarize some eternal takeaway messages from Hill's lecture regarding observations and experiments translated through the modern lexicon of causal inference. Finally, we pose a series of questions that we would have liked to pose to Sir Austin Bradford Hill if he were to deliver the lecture in 2020. [ABSTRACT FROM AUTHOR]

Avin et al (2005) showed that, in the presence of exposure-induced mediator-outcome confounding, decomposing the total causal effect (TCE) using standard conditional exchangeability assumptions is not possible even under a nonparametric structural equation model with all confounders observed. Subsequent research has investigated the assumptions required for such a decomposition to be identifiable and estimable from observed data. One approach was proposed by VanderWeele et al (2014). They decomposed the TCE under three different scenarios: (1) treating the mediator and the exposure-induced confounder as joint mediators; (2) generating path-specific effects albeit without distinguishing between multiple distinct paths through the exposure-induced confounder; and (3) using so-called randomised interventional analogues where sampling values from the distribution of the mediator within the levels of the exposure effectively marginalises over the exposure-induced confounder. In this paper, we extend their approach to the case where there are multiple mediators that do not influence each other directly but which are all influenced by an exposure-induced mediator-outcome confounder. We provide a motivating example and results from a simulation study based on from our work in dental epidemiology featuring the 1982 Pelotas Birth Cohort in Brazil. [ABSTRACT FROM AUTHOR]

In most nonrandomized observational studies, differences between treatment groups may arise not only due to the treatment but also because of the effect of confounders. Therefore, causal inference regarding the treatment effect is not as straightforward as in a randomized trial. To adjust for confounding due to measured covariates, a variety of methods based on the potential outcomes framework are used to estimate average treatment effects. One of the key assumptions is treatment positivity, which states that the probability of treatment is bounded away from zero and one for any possible combination of the confounders. Methods for performing causal inference when this assumption is violated are relatively limited. In this article, we discuss a new balance‐related condition involving the convex hulls of treatment groups, which I term relaxed covariate overlap. An advantage of this concept is that it can be linked to a concept from machine learning, termed the margin. Introduction of relaxed covariate overlap leads to an approach in which one can perform causal inference in a three‐step manner. The methodology is illustrated with two examples. [ABSTRACT FROM AUTHOR]

A recent topic of much interest in causal inference is model selection. In this article, we describe a framework in which to consider penalized regression approaches to variable selection for causal effects. The framework leads to a simple 'impute, then select' class of procedures that is agnostic to the type of imputation algorithm as well as penalized regression used. It also clarifies how model selection involves a multivariate regression model for causal inference problems and that these methods can be applied for identifying subgroups in which treatment effects are homogeneous. Analogies and links with the literature on machine learning methods, missing data, and imputation are drawn. A difference least absolute shrinkage and selection operator algorithm is defined, along with its multiple imputation analogs. The procedures are illustrated using a well-known right-heart catheterization dataset. Copyright © 2015 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]