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.

翻译：平均处理效应（ATE）是因果推断文献中常被估计的参数，但它仅针对二元暴露定义。因此，尽管一些研究者提出了担忧，许多旨在估计连续暴露因果效应的研究仍通过将连续值二分为两个类别来创建新的二元暴露变量。本文通过证明二分化ATE与两种特定修正处理策略下平均结果差异的等价性，肯定了二分化作为回答连续暴露因果问题的统计学有效方法。这些策略施加了与二分化暴露变量相对应的截断值，并假设相对自选择得以保持。相对自选择是指个体具有某一连续暴露变量值的概率密度与另一值的概率密度之比。这些策略假设，对于截断后具有非零概率密度的暴露变量的任意两个值，该比率将保持不变。通过这种等价性，我们阐明了二分化背后的假设，并讨论了如何正确解释由此产生的估计量。此外，我们引入了一个可在二分化后计算的新目标参数，该参数将观测世界作为基准。我们认为，该参数比传统的二分化ATE参数更能解决相关的因果问题。我们通过一项模拟研究来说明这些假设在数据分析中的影响，并展示如何正确实现所讨论参数的估计量。最后，我们将该方法应用于评估加利福尼亚州一项旨在限制油气井暴露对出生结局影响的法律的效果，以进一步阐明其潜在假设。