It is common in analyses designed to estimate the causal effect of a continuous exposure/treatment to dichotomize the variable of interest. By dichotomizing the variable and assessing the causal effect of the newly fabricated variable practitioners are implicitly making assumptions. However, in most analyses these assumptions are ignored. In this article we formally address what assumptions are made in dichotomizing variables to assess causal effects. We introduce two assumptions, either of which must be met, in order for the estimates of the causal effects to be unbiased estimates of the parameters of interest. We title those assumptions the Mechanism Equivalence and Effect Equivalence assumptions. Furthermore, we quantify the bias induced when these assumptions are violated. Lastly, we present an analysis of a Malaria study that exemplifies the danger of naively dichotomizing a continuous variable to assess a causal effect.
Stitelman, Ori M.; Hubbard, Alan E.; and Jewell, Nicholas P., "The Impact Of Coarsening The Explanatory Variable Of Interest In Making Causal Inferences: Implicit Assumptions Behind Dichotomizing Variables" (April 2010). U.C. Berkeley Division of Biostatistics Working Paper Series. Working Paper 264.