To the predict hazard ratio, the architecture of DeepSurv network [1] that performs the neural network with the negative log-partial likelihood function of Cox model is applied. The Cox model is a hazard function h(t), and can be interpreted as the risk of death at time t as follows:

where, t represents the survival time, h(t) is the hazard function, (β1, β2, …,βn) are coefficients measuring the impact of covariates, and ho(t) is the baseline hazard function. Generally, to estimate the regression coefficients, Cox partial likelihood is optimized. The Cox partial likelihood Lβ is given by:

where Ti, Ei are event time and event indicator for each observation, respectively and xi is a vector of clinical covariates for patient i. R(Ti) is the set of patients for which no event has occurred at time t. In contrast to the conventional regression method, the hazard ratio network estimates the hazard ratio value by setting the negative log partial likelihood of (7) as loss function [1].

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