Should responder analyses be conducted on continuous outcomes?

Continuous outcomes are often dichotomized to classify trial subjects as responders or nonresponders, with the difference in rates of response between treatment and control defined as the "responder effect." In this article, we caution that dichotomization of continuous interval outcomes may not be best practice. Defining clinical benefit or harm for continuous interval outcomes as the difference between the means of treatment and control, that is, the "continuous treatment effect," we examine the case where treatment and control outcomes are normally distributed and differ only in location. For this case, continuous treatment effects may be considered clinically relevant if they exceed a prespecified minimum clinically important difference. In contrast, using minimum clinically important differences as dichotomization thresholds will not ensure clinically relevant responder effects. For example, in some situations, increasing the threshold may actually relax the criterion for effectiveness by increasing the calculated responder effect. Using responder effects to quantitatively assess benefit or risk of investigational drugs for continuous interval outcomes presents interpretational challenges. In particular, when the dichotomization threshold is halfway between the treatment and control outcome means, the responder effect is at a maximum with a magnitude monotonically related to the number of standard deviations between the mean outcomes of treatment and control. Large responder effect benefits may therefore reflect clinically unimportant continuous treatment effects amplified by small standard deviations, and small responder effect risks may reflect either clinically important continuous treatment effects minimized by large standard deviations, or selection of a dichotomization threshold not providing maximum responder effect.