Stratified neural networks in a time-to-event setting

Abstract

Deep neural networks are frequently employed to predict survival conditional on omics-type biomarkers, e.g., by employing the partial likelihood of Cox proportional hazards model as loss function. Due to the generally limited number of observations in clinical studies, combining different data sets has been proposed to improve learning of network parameters. However, if baseline hazards differ between the studies, the assumptions of Cox proportional hazards model are violated. Based on high dimensional transcriptome profiles from different tumor entities, we demonstrate how using a stratified partial likelihood as loss function allows for accounting for the different baseline hazards in a deep learning framework. Additionally, we compare the partial likelihood with the ranking loss, which is frequently employed as loss function in machine learning approaches due to its seemingly simplicity. Using RNA-seq data from the Cancer Genome Atlas (TCGA) we show that use of stratified loss functions leads to an overall better discriminatory power and lower prediction error compared to their non-stratified counterparts. We investigate which genes are identified to have the greatest marginal impact on prediction of survival when using different loss functions. We find that while similar genes are identified, in particular known prognostic genes receive higher importance from stratified loss functions. Taken together, pooling data from different sources for improved parameter learning of deep neural networks benefits largely from employing stratified loss functions that consider potentially varying baseline hazards. For easy application, we provide PyTorch code for stratified loss functions and an explanatory Jupyter notebook in a GitHub repository.

Breast Cancer Surgery 10-Year Survival Prediction by Machine Learning: A Large Prospective Cohort Study

“…Our survival analysis results can be considered to be relatively reliable because the predictions were based on prospective, longitudinal, and long-term (10-year) data obtained from multiple medical institutions. Compared to the prediction models discussed in previous works, in which predictions were based on a dataset for a single medical center [ 4 , 5 , 6 ], the use of data from several institutions in our study provides a relatively more accurate and reliable estimate of survival after breast cancer surgery. Additionally, the data used in this study were registry data compiled from data for several institutions.…”

“…Additionally, the data used in this study were registry data compiled from data for several institutions. In comparison with the use of data for a single institution, the use of registry data in this study improved accuracy in depicting breast cancer surgery treatment for a large population [ 4 , 5 , 6 , 18 ]. Another advantage of using registry data was that the potential effects of a bias resulting from the referral of patients or the bias resulting from the practices of a single high-volume surgeon or a single high-volume institution were minimized [ 18 ].…”

“…In contrast with other machine learning tools proposed for prognostic use in oncology, this study performed model training using data for all patients treated at oncology or hematology/oncology clinics. That is, all patients were included regardless of whether they had received cancer-directed therapy [ 5 , 7 , 8 ]. Another strength of this study is that the forecasting models and machine learning algorithms in this study included a higher number of predictors compared to those reported in the literature, and data for all of the included predictors were typically available in real time and in structured formats from medical recorder databases [ 6 , 7 , 8 ].…”

“…Researchers have developed various models for predicting breast cancer surgery outcomes, but proposed models for predicting survival 10 years after breast cancer surgery consistently reveal three major weaknesses. First, the accuracy of recently proposed models for predicting breast cancer surgery survival is consistently inferior to that of conventional models [ 3 , 4 ]; second, health insurance claims data is the most commonly used input data for the proposed forecasting models is, which have limited real-time availability in the typical clinical scenario [ 5 , 6 ]; and third, most proposed models do not consider factors that have well established associations with breast cancer survival, e.g., demographic and clinical characteristics, care quality, and QOL before surgery [ 7 , 8 ]. Statistical machine learning and deep learning algorithms have been found to have diverse applications in the medical field [ 4 , 5 , 6 , 7 , 8 , 9 ].…”

“…First, the accuracy of recently proposed models for predicting breast cancer surgery survival is consistently inferior to that of conventional models [ 3 , 4 ]; second, health insurance claims data is the most commonly used input data for the proposed forecasting models is, which have limited real-time availability in the typical clinical scenario [ 5 , 6 ]; and third, most proposed models do not consider factors that have well established associations with breast cancer survival, e.g., demographic and clinical characteristics, care quality, and QOL before surgery [ 7 , 8 ]. Statistical machine learning and deep learning algorithms have been found to have diverse applications in the medical field [ 4 , 5 , 6 , 7 , 8 , 9 ]. For example, these methods can be used to account for specific clinical and genetic characteristics of the individual patient with a given disease, by improving the accuracy of identifying and ranking risk factors for death from the disease.…”