The average treatment effect (ATE) is a common parameter estimated in causal inference literature, but it is only defined for binary treatments. Thus, despite concerns raised by some researchers, many studies seeking to estimate the causal effect of a continuous treatment create a new binary treatment 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 treatments 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 treatment 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 treatment variable versus another. The policies assume that, for any two values of the treatment 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 status-quo world. We argue that this parameter addresses more relevant causal questions than the traditional binarized ATE parameter. Finally, 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.

翻译：平均处理效应（ATE）是因果推断文献中常见的参数，但仅针对二值处理变量定义。因此，尽管部分研究者提出担忧，许多旨在估计连续处理变量因果效应的研究仍通过将连续值划分为两个类别来创建新的二值处理变量。本文通过证明二值化ATE与两种特定修正处理策略下平均结果差异的等价性，确认二值化是回答连续处理变量因果问题的有效统计方法。这些策略设定与二值化处理变量对应的截断值，并假设个体相对自选择效应保持不变。相对自选择效应是指个体暴露于连续处理变量某一值相较于另一值的概率密度比值。策略假设，对于截断后具有非零概率密度的任意两个处理变量值，该比值保持不变。通过这一等价性，我们澄清了二值化背后的假设，并讨论了如何正确解读所得估计量。此外，我们引入了一个考虑现状世界的新目标参数，该参数可在二值化后计算。我们认为该参数比传统二值化ATE参数能回答更相关的因果问题。最后，我们通过模拟研究说明这些假设在数据分析中的实际含义，并演示如何正确实现所讨论参数的估计量。