  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.
