Binary regression with continuous outcomes

Clinical research often involves continuous outcome measures, such as blood cholesterol, that are amenable to statistical techniques of analysis based on the mean, such as the t-test or multiple linear regression. Clinical interest, however, frequently focuses on the proportion of subjects who fall below or above a clinically relevant cut-off value, as a measure of the risk of disease. The customary approach to analyse such data is to dichotomize the continuous outcome measure and use statistical techniques based on binary data and the binomial distribution. In this paper, we use a parametric approach and the framework of generalized linear models to fit various regression models, including the logistic, on the basis of the original continuous outcome. We consider the Gaussian and the three-parameter log-normal distributions for the continuous outcome, assessing both precision and bias under various conditions. In simulation analyses, we find that we are unable to fit some of the samples with the 'dichotomous' approach, but we can with the 'continuous' approach, and that the latter yields estimates between 25 and 85 per cent more efficient than the former. We illustrate the method, programmed using GLIM macros, with data from clinical studies of the risk of hypoxaemia during open thoracic surgery and the risk of nocturnal hypoglycaemia among diabetic children.