Dichotomizing Continuous Data Which Retains Statistical Precision Using a Bayesian Distributional Approach That Reflects the True Uncertainty

Although dichotomization is widely criticized by statisticians, it is sometimes useful and necessary in medical research for decision-making or communication purposes. In order to address the issue of dichotomization, a previous literature developed an asymptotic distributional approach from a frequentist perspective assuming that the data are normally distributed and the variances in two groups are equivalent. This approach was further extended to the case of unequal variances. The previous works improve the dichotomization in many ways but assumes that the variance of data is known which does not reflect the realistic situation where both mean and variance are unknown. In this paper, we develop a Bayesian distributional methodology that inherits the advantages of previous attempts but considers all levels of uncertainty. For comparison purposes, we also reframe the original asymptotic approach from a Bayesian perspective. We show through simulation studies that the Bayesian asymptotic method overestimates or underestimates the true variation under certain situations. An example of pain data is also provided to illustrate the performance of the proposed approach. The effects of unequal variances on the asymptotic method are demonstrated in the example as well.