Generating survival time using distribution function network

Conventional methods produce survival time using hazard ratios and specific distribution functions. Rather than generating the survival time using a particular distribution function, a method which generates the survival time through integration of a proposed distribution function network and the pre-trained hazard ratio network was proposed. To train the distribution function network, a loss function is designed to calculate the mean difference between the observation and the value obtained from the survival time generation function [6]. The proposed loss function is a variant of MSE (Mean squared error), which is the simplest and most used loss function. In addition, MSE has the advantage of being easy to understand and implement through common methods. Generally, the survival time is generated as follows:

where u is the random variable with the specific mean parameter. eβx represents the hazard ratio and T is the survival time. By inserting (7) into MSE, the proposed loss function is formulated. The final loss function (Loss) is given by:

where ypredofi represents the output of the distribution function network, y_death time of i is the true value of individual i, and hθ^x represents the hazard ratio from hazard ratio network.

After completing the training, the survival generation function is calculated using the predicted hazard ratio and distribution estimate. The survival generation function is defined as

where y^survival_time is the estimated survival time.