In clinical and epidemiological researches, continuous predictors are often discretized into categorical variables for classification of patients. When the relationship between a continuous predictor and log relative hazards is U-shaped in survival data, there is a lack of a satisfying solution to find optimal cut-points to discretize the continuous predictor. In this study, we propose a novel approach named optimal equal-HR method to discretize a continuous variable that has a U-shaped relationship with log relative hazards in survival data. The main idea of the optimal equal-HR method is to find two optimal cut-points that have equal log relative hazard values and result in Cox models with minimum AIC value. An R package ‘CutpointsOEHR’ has been developed for easy implementation of the optimal equal-HR method. A Monte Carlo simulation study was carried out to investigate the performance of the optimal equal-HR method. In the simulation process, different censoring proportions, baseline hazard functions and asymmetry levels of U-shaped relationships were chosen. To compare the optimal equal-HR method with other common approaches, the predictive performance of Cox models with variables discretized by different cut-points was assessed. Simulation results showed that in asymmetric U-shape scenarios the optimal equal-HR method had better performance than the median split method, the upper and lower quantiles method, and the minimum p-value method regarding discrimination ability and overall performance of Cox models. The optimal equal-HR method was applied to a real dataset of small cell lung cancer. The real data example demonstrated that the optimal equal-HR method could provide clinical meaningful cut-points and had good predictive performance in Cox models. In general, the optimal equal-HR method is recommended to discretize a continuous predictor with right-censored outcomes if the predictor has an asymmetric U-shaped relationship with log relative hazards based on Cox regression models.

(1) Background: Growing evidence suggests that electroencephalography (EEG), recording the brain’s electrical activity, can be a promising diagnostic tool for Alzheimer’s disease (AD). The diagnostic biomarkers based on quantitative EEG (qEEG) have been extensively explored, but few of them helped clinicians in their everyday practice, and reliable qEEG markers are still lacking. The study aims to find robust EEG biomarkers and propose a systematic discrimination framework based on signal processing and computer-aided techniques to distinguish AD patients from normal elderly controls (NC). (2) Methods: In the proposed study, EEG signals were preprocessed firstly and Maximal overlap discrete wavelet transform (MODWT) was applied to the preprocessed signals. Variance, Pearson correlation coefficient, interquartile range, Hoeffding’s D measure, and Permutation entropy were extracted as the input of the candidate classifiers. The AD vs. NC discriminant performance of each model was evaluated and an automatic diagnostic framework was eventually developed. (3) Results: A classification procedure based on the extracted EEG features and linear discriminant analysis based classifier achieved the accuracy of 93.18 ± 3.65 (%), the AUC of 97.92 ± 1.66 (%), the F-measure of 94.06 ± 4.04 (%), separately. (4) Conclusions: The developed discrimination framework can identify AD from NC with high performance in a systematic routine.