Summary: Based on a real dataset, we compare two kinds of neural networks (BP neural network and Bayesian regularized BP neural network) and logistic regression in medical statistics. By using SPSS 21.0 and Matlab, after variable screening, train the three models and compare their prediction accuracies. Besides, the authors draw their ROC curves and compare their areas under the curve (AUC) among the three models. All of the three models reach the prediction accuracy over 89%. Bayesian regularized BP neural network has a best result with the highest prediction accuracy and the largest AUC. Unlike the researches before, in our study, BP neural Network does not have a better performance than logistic regression. The small sample size may result in the BP neural network without a good training. However, it may also highlight an advantage of Bayesian regularized BP neural network, which still gets a good output under the situation of a small sample.