Estimating dichotomised outcomes in two groups with unequal variances: a distributional approach

Dichotomisation in medical research is sometimes necessary for decision-making or communication purposes. This practice has been criticised in the case of continuous data, and it has been said that means should be compared instead. However when the two groups have unequal variances, comparing means might not show the whole picture as a particular group with a risk defined by a threshold in an outcome may have been affected differently by an intervention than when there is a simple shift of distribution. A statistically sound method using a distributional approach for the dichotomisation of normally distributed outcomes has been described under the assumption of equal variances. This assumption is not sustainable in some situations, and in this work, we develop the method further to cover the case of unequal variances. Through examples from the literature and our own data, we illustrate the effect of unequal variance on dichotomised estimates and present a validation of the method through simulations.