On responder analyses when a continuous variable is dichotomized and measurement error is present

In clinical studies results are often reported as proportions of responders, i.e. the proportion of subjects who fulfill a certain response criterion is reported, although the underlying variable of interest is continuous. In this paper, we consider the situation where a subject is defined as a responder if the (error-free) continuous measurements post-treatment are below a certain fraction of (error-free) continuous measurements obtained pre-treatment. Focus is on the one-sample case, but an extension to the two-sample case is also presented. The bias of different estimates for the proportion of responders is derived and compared. In addition, an asymptotically unbiased ML-type estimate for the proportion of responders is presented. The results are illustrated using data obtained in a clinical study investigating pre-menstrual dysphoric disorder (PMDD).