Survival time prediction by integrating cox proportional hazards network and distribution function network

Abstract

Abstract Background The Cox proportional hazards model is commonly used to predict hazard ratio, which is the risk or probability of occurrence of an event of interest. However, the Cox proportional hazard model cannot directly generate an individual survival time. To do this, the survival analysis in the Cox model converts the hazard ratio to survival times through distributions such as the exponential, Weibull, Gompertz or log-normal distributions. In other words, to generate the survival time, the Cox model has to select a specific distribution over time. Results This study presents a method to predict the survival time by integrating hazard network and a distribution function network. The Cox proportional hazards network is adapted in DeepSurv for the prediction of the hazard ratio and a distribution function network applied to generate the survival time. To evaluate the performance of the proposed method, a new evaluation metric that calculates the intersection over union between the predicted curve and ground truth was proposed. To further understand significant prognostic factors, we use the 1D gradient-weighted class activation mapping method to highlight the network activations as a heat map visualization over an input data. The performance of the proposed method was experimentally verified and the results compared to other existing methods. Conclusions Our results confirmed that the combination of the two networks, Cox proportional hazards network and distribution function network, can effectively generate accurate survival time.

Keywords

• Prognosis
• Survival time prediction
• Deep learning
• Distribution function network
• Cox proportional hazards network