Power considerations when a continuous outcome variable is dichotomized

An investigator can compare two groups with respect to a continuous outcome variable, Y, by comparing the means of Y or by collapsing that variable into categories. For example, antihypertensive treatments can be compared on the basis of blood pressure measurements, or on the basis of the proportions of patients with blood pressure in prespecified ranges. This report is concerned with the loss of power when inherently continuous variables are dichotomized. The report will focus on the power loss when a normally distributed variable with a known, common variance in each of two groups is dichotomized. Power is shown to depend on the relationship between the means of the two groups and the cutoff point, and it varies from negligible to substantial. The results will be applied to data from the Lovastatin Restenosis Trial. Initially the trial considered a dichotomous outcome (proportion of patients with elevated percent diameter stenosis), but the endpoint was later changed to the mean percent diameter stenosis. The modification in the design of the trial was well justified because the power loss was considerable when comparing proportions.