Comparison of State-of-the-Art Neural Network Survival Models with the Pooled Cohort Equations for Cardiovascular Disease Risk Prediction.

BACKGROUND: The Pooled Cohort Equations (PCEs) are race- and sex-specific Cox proportional hazards (PH)-based models used for 10-year atherosclerotic cardiovascular disease (ASCVD) risk prediction with acceptable discrimination. In recent years, neural network models have gained increasing popularity with their success in image recognition and text classification. Various survival neural network models have been proposed by combining survival analysis and neural network architecture to take advantage of the strengths from both. However, the performance of these survival neural network models compared to each other and to PCEs in ASCVD prediction is unknown. METHODS: In this study, we used 6 cohorts from the Lifetime Risk Pooling Project (with 5 cohorts as training/internal validation and one cohort as external validation) and compared the performance of the PCEs in 10-year ASCVD risk prediction with an all two-way interactions Cox PH model (Cox PH-TWI) and three state-of-the-art neural network survival models including Nnet-survival, Deepsurv, and Cox-nnet. For all the models, we used the same 7 covariates as used in the PCEs. We fitted each of the aforementioned models in white females, white males, black females, and black males, respectively. We evaluated models' internal and external discrimination power and calibration. RESULTS: The training/internal validation sample comprised 23216 individuals. The average age at baseline was 57.8 years old (SD = 9.6); 16% developed ASCVD during average follow-up of 10.50 (SD = 3.02) years. Based on 10 × 10 cross-validation, the method that had the highest C-statistics was Deepsurv (0.7371) for white males, Deepsurv and Cox PH-TWI (0.7972) for white females, PCE (0.6981) for black males, and Deepsurv (0.7886) for black females. In the external validation dataset, Deepsurv (0.7032), Cox-nnet (0.7282), PCE (0.6811), and Deepsurv (0.7316) had the highest C-statistics for white male, white female, black male, and black female population, respectively. Calibration plots showed that in 10 × 10 validation, all models had good calibration in all race and sex groups. In external validation, all models overestimated the risk for 10-year ASCVD. CONCLUSIONS: We demonstrated the use of the state-of-the-art neural network survival models in ASCVD risk prediction. Neural network survival models had similar if not superior discrimination and calibration compared to PCEs.

Precision medicine: Subgroup identification in longitudinal trajectories.

In clinical studies, the treatment effect may be heterogeneous among patients. It is of interest to identify subpopulations which benefit most from the treatment, regardless of the treatment's overall performance. In this study, we are interested in subgroup identification in longitudinal studies when nonlinear trajectory patterns are present. Under such a situation, evaluation of the treatment effect entails comparing longitudinal trajectories while subgroup identification requires a further evaluation of differential treatment effects among subgroups induced by moderators. To this end, we propose a tree-structured subgroup identification method, termed "interaction tree for longitudinal trajectories", which combines mixed effects models with regression splines to model the nonlinear progression patterns among repeated measures. Extensive simulation studies are conducted to evaluate its performance and an application to an alcohol addiction pharmacogenetic trial is presented.