Bayesian sample size estimation for logistic regression

The paper1 is devoted to the logistic regression analysis [1], applied to classification problems in biomedicine. A group of patients is investigated as a sample set; each patient is described with a set of features, named as biomarkers and is classified into two classes. Since the patient measurement is expensive the problem is to reduce number of measured features in order to increase sample size. The responsive variable is assumed to follow a Bernoulli distribution. Also, parameters of the regression function are evaluated [2]. With given set of features, the model is excessively complex. The problem is to select a set of features of smaller size, that will classify patients effectively. In logistic regression features are usually selected by stepwise regression [3]. In the computational experiment, exhaustive search is implemented. This makes the experts sure that all possible combinations of the features were considered. The authors use the area under ROC curve [4] as the optimum criterion in the feature selection procedure. The problem of classification is associated with minimum sample size determination. In the paper, the following methods are discussed: