Robustness of the regression models for uncertain categories

Dichotomization of the outcome by a single cut-off point is an important part of medical studies. Usually the relationship between the resulted dichotomized dependent variable and explanatory variables is analyzed with linear regression, probit or logistic regression. However, in many real-life situations, a certain cut-off point is unknown and can be specified only approximately, i.e. surrounded by some (small) uncertainty. It means that in order to have any practical meaning the regression model must be robust to this uncertainty. In this paper, we test the robustness of the linear regression model and get that neither the beta in the model, nor its significance level is robust to the small variations in the dichotomization cut-off point. As an alternative robust approach to the problem of uncertain categories, we propose to make use of the linear regression model with the fuzzy membership function as a dependent variable. In the paper, we test the robustness of the linear regression model of such fuzzy dependent variable and get that this model can be insensitive against the uncertainty in the cut-off point location. To demonstrate theoretical conclusions, in the paper we present the modelling results from the real study of low haemoglobin levels in infants.