A novel approach to determine two optimal cut-points of a continuous predictor with a U-shaped relationship to hazard ratio in survival data: simulation and application

By Yimin Chen, Jialing Huang, Xianying He, Yong-Xiang Gao, G. Mahara, Zhuochen Lin, Jinxin Zhang. 2019

33 citations recorded by the source corpus.

BackgroundIn 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.MethodsThe 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.ResultsSimulation 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.ConclusionsIn 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.

Subfields: Statistics and Probability

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Citations in the corpus

AutoScore: A Machine Learning–Based Automatic Clinical Score Generator and Its Application to Mortality Prediction Using Electronic Health Records (2020, background): “Several studies [34,35] have reported U-shaped nonlinearity between continuous variables and health-related outcomes.”