Arkady Bolotin Fuzzy Logic Approach to Robust Regression Models of Uncertain Medical Categories
3528 - 3533
2008
2
10
International Journal of Computer, Electrical, Automation, Control and Information Engineering http://waset.org/publications/11889
http://waset.org/publications/22
World Academy of Science, Engineering and Technology
Dichotomization of the outcome by a single cutoff point is an important part of various medical studies. Usually the relationship between the resulted dichotomized dependent variable and explanatory variables is analyzed with linear regression, probit regression or logistic regression. However, in many reallife situations, a certain cutoff point dividing the outcome into two groups 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 show that neither the beta in the linear regression model, nor its significance level is robust to the small variations in the dichotomization cutoff point. As an alternative robust approach to the problem of uncertain medical categories, we propose to use the linear regression model with the fuzzy membership function as a dependent variable. This fuzzy membership function denotes to what degree the value of the underlying (continuous) outcome falls below or above the dichotomization cutoff point. In the paper, we demonstrate that the linear regression model of the fuzzy dependent variable can be insensitive against the uncertainty in the cutoff point location. In the paper we present the modeling results from the real study of low hemoglobin levels in infants. We systematically test the robustness of the binomial regression model and the linear regression model with the fuzzy dependent variable by changing the boundary for the category Anemia and show that the behavior of the latter model persists over a quite wide interval.
International Science Index 22, 2008