Dichotomizing Continuous Outcome Variables: Dependence of the Magnitude of Association and Statistical Power on the Cutpoint

Dichotomizing a continuous outcome variable casts that variable in traditional epidemiologic terms (that is, disease, no disease). One consequence is overall reduced statistical power. A more fundamental concern is that the magnitude of various measures of association (for example, prevalence ratio, odds ratio) and statistical power depend on the cutpoint used to dichotomize the variable. The phenomenon is illustrated with a hypothetical situation assuming a two-level predictor variable and a normally distributed outcome variable. As the cutpoint is increased from lower to higher values, the prevalence ratio increases steadily, the odds ratio is described by a U-shaped curve, and statistical power is described by an inverted U-shaped curve. Furthermore, the extent of these effects depends on the difference between the means of the continuous outcome variable for the two levels of the predictor variable. An empirical example is given using data on education and blood pressure (dichotomized to create a high blood pressure vs low blood pressure variable). Except at each end of the distribution, the results follow the hypothetical example. The observation has implications for public health and medical treatment; different cutpoints should be examined to determine the optimal cutpoint in terms of policy and/or treatment decisions. The observation described here also has implications for statistical interpretation; statements about the magnitude of association or statistical significance have limited meaning unless both the cutpoint and the distribution of the outcome variable are specified.