SurvLoss: A New Survival Loss Function for Neural Networks to Process Censored Data

Abstract

This paper presents SurvLoss, a novel asymmetric partial loss and error calculation function for survival analysis and regression, enabling the inclusion of censored samples. An observation in a dataset for which the complete information regarding an event of interest is not available is called censored. Censored samples are ubiquitous in the industry and play a crucial role in Prognostics and Health Management (PHM) by providing a realistic representation of data, improving the accuracy of analyses, and supporting better decision-making in various industries and the healthcare sector. The proposed approach can effectively equip the conventional regression loss functions such as Mean Absolute Error (MAE), Mean Squared Error (MSE), or Root Mean Squared Error (RMSE) with the ability to process censored samples. This can impact the field hugely by providing a more accessible usage of neural network models in survival analysis. The proposed survival loss incorporates censored samples by penalizing predictions outside the censoring region and skipping them otherwise. Then, it uses weighted averaging to aggregate the loss from censored samples with the loss from event samples. Unlike many other methods in the field, the proposed model distinguishes itself by avoiding superficial assumptions and exclusively relies on the available information, considering the entirety of the data.

We compared the proposed loss function with its baseline on two publicly available datasets. The first dataset, called C-MAPSS, is from NASA Turbofan Jet Engines simulation, and the second is a recently published real-world dataset from SCANIA trucks. The goal of both datasets is to predict the remaining useful life (RUL) of the machines.
The experimental results show that optimization algorithms for training deep neural networks like Adam can effectively utilize the proposed loss function to calculate gradients, update the model's weights, and reduce training and test errors. Moreover, the proposed model outperformed the baseline by taking advantage of the censored samples. The proposed loss function paves the way for the employment of advanced architectures of neural networks with bigger training sizes in survival analysis.