Bridging binarization: causal inference with dichotomized continuous exposures.

The average treatment effect (ATE) is a common parameter estimated in causal inference literature, but it is only defined for binary exposures. Thus, despite concerns raised by some researchers, many studies seeking to estimate the causal effect of a continuous exposure create a new binary exposure variable by dichotomizing the continuous values into two categories. In this paper, we affirm binarization as a statistically valid method for answering causal questions about continuous exposures by showing the equivalence between the binarized ATE and the difference in the average outcomes of two specific modified treatment policies. These policies impose cut-offs corresponding to the binarized exposure variable and assume preservation of relative self-selection. Relative self-selection is the ratio of the probability density of an individual having an exposure equal to one value of the continuous exposure variable versus another. The policies assume that, for any two values of the exposure variable with non-zero probability density after the cut-off, this ratio will remain unchanged. Through this equivalence, we clarify the assumptions underlying binarization and discuss how to properly interpret the resulting estimator. Additionally, we introduce a new target parameter that can be computed after binarization that considers the observed world as a benchmark. We argue that this parameter addresses more relevant causal questions than the traditional binarized ATE parameter. We present a simulation study to illustrate the implications of these assumptions when analyzing data and to demonstrate how to correctly implement estimators of the parameters discussed. Finally, we present an application of this method to evaluate the effect of a law in the state of California which seeks to limit exposures to oil and gas wells on birth outcomes to further illustrate the underlying assumptions.