Dichotomising continuous data while retaining statistical power using a distributional approach

Dichotomisation of continuous data is known to be hugely problematic because information is lost, power is reduced and relationships may be obscured or changed. However, not only are differences in means difficult for clinicians to interpret, but thresholds also occur in many areas of medical practice and cannot be ignored. In recognition of both the problems of dichotomisation and the ways in which it may be useful clinically, we have used a distributional approach to derive a difference in proportions with a 95% CI that retains the precision and the power of the CI for the equivalent difference in means. In this way, we propose a dual approach that analyses continuous data using both means and proportions to replace dichotomisation alone and that may be useful in certain situations. We illustrate this work with examples and simulations that show good performance of the parametric approach under standard distributional assumptions from our own research and from the literature.