Bind MC, Rubin DB __Stat Methods Med Res__

Consider a statistical analysis that draws causal inferences from an observational dataset, inferences that are presented as being valid in the standard frequentist senses; i.e. the analysis produces: (1) consistent point estimates, (2) valid p-values, valid in the sense of rejecting true null hypotheses at the nominal level or less often, and/or (3) confidence intervals, which are presented as having at least their nominal coverage for their estimands. For the hypothetical validity of these statements, the analysis must embed the observational study in a hypothetical randomized experiment that created the observed data, or a subset of that hypothetical randomized data set. This multistage effort with thought-provoking tasks involves: (1) a purely conceptual stage that precisely formulate the causal question in terms of a hypothetical randomized experiment where the exposure is assigned to units; (2) a design stage that approximates a randomized experiment before any outcome data are observed, (3) a statistical analysis stage comparing the outcomes of interest in the exposed and non-exposed units of the hypothetical randomized experiment, and (4) a summary stage providing conclusions about statistical evidence for the sizes of possible causal effects. Stages 2 and 3 may rely on modern computing to implement the effort, whereas Stage 1 demands careful scientific argumentation to make the embedding plausible to scientific readers of the proffered statistical analysis. Otherwise, the resulting analysis is vulnerable to criticism for being simply a presentation of scientifically meaningless arithmetic calculations. The conceptually most demanding tasks are often the most scientifically interesting to the dedicated researcher and readers of the resulting statistical analyses. This perspective is rarely implemented with any rigor, for example, completely eschewing the first stage. We illustrate our approach using an example examining the effect of parental smoking on children's lung function collected in families living in East Boston in the 1970s.

Zach Branson and Marie-AbĂ¨le Bind __Stat Methods Med Res__

We present a randomization-based inferential framework for experiments characterized by a strongly ignorable assignment mechanism where units have independent probabilities of receiving treatment. Previous works on randomization tests often assume these probabilities are equal within blocks of units. We consider the general case where they differ across units and show how to perform randomization tests and obtain point estimates and confidence intervals. Furthermore, we develop rejection-sampling and importance-sampling approaches for conducting randomization-based inference conditional on any statistic of interest, such as the number of treated units or forms of covariate balance. We establish that our randomization tests are valid tests, and through simulation we demonstrate how the rejection-sampling and importance-sampling approaches can yield powerful randomization tests and thus precise inference. Our work also has implications for observational studies, which commonly assume a strongly ignorable assignment mechanism. Most methodologies for observational studies make additional modeling or asymptotic assumptions, while our framework only assumes the strongly ignorable assignment mechanism, and thus can be considered a minimal-assumption approach.