Statistical methods of determining a cut off value between normal and disease groups

Abstract

The classical method to determine the cut off value between normal and disease group is to calculate two standard deviations of the difference between mean values of two groups under the independence assumption. However, this independence assumption does not hold in general, and in our study in particular, when two biomarker proteins of breast cancer are measured several times for a few years. In this paper we propose a method to determine the cut off value for this case by implementing the inherent nature of the study using linear mixed effect model. We use a linear mixed effect model to take it into consideration that the subject is of a random effect. Furthermore, we can also estimate the growth curve of the biomarker values as time elapses. For a fixed type I error rate we calculate the conditional probability that the test is positive given that the subject does have the disease and then compare the sensitivity of our method with that of classical method using a leave-one-out cross validation. We observe that our method is more efficient than the classical method.