Linear Cox Proportional Hazards Models Research Articles

Sparsesurv: a Python package for fitting sparse survival models via knowledge distillation.

Sparse survival models are statistical models that select a subset of predictor variables while modeling the time until an event occurs, which can subsequently help interpretability and transportability. The subset of important features is often obtained with regularized models, such as the Cox Proportional Hazards model with Lasso regularization, which limit the number of non-zero coefficients. However, such models can be sensitive to the choice of regularization hyperparameter. In this work, we develop a software package and demonstrate how knowledge distillation, a powerful technique in machine learning that aims to transfer knowledge from a complex teacher model to a simpler student model, can be leveraged to learn sparse survival models while mitigating this challenge. For this purpose, we present sparsesurv, a Python package that contains a set of teacher-student model pairs, including the semi-parametric accelerated failure time and the extended hazards models as teachers, which currently do not have Python implementations. It also contains in-house survival function estimators, removing the need for external packages. Sparsesurv is validated against R-based Elastic Net regularized linear Cox proportional hazards models as implemented in the commonly used glmnet package. Our results reveal that knowledge distillation-based approaches achieve competitive discriminative performance relative to glmnet across the regularization path while making the choice of the regularization hyperparameter significantly easier. All of these features, combined with a sklearn-like API, make sparsesurv an easy-to-use Python package that enables survival analysis for high-dimensional datasets through fitting sparse survival models via knowledge distillation. sparsesurv is freely available under a BSD 3 license on GitHub (https://github.com/BoevaLab/sparsesurv) and The Python Package Index (PyPi) (https://pypi.org/project/sparsesurv/).

Interpretable prognostic modeling of endometrial cancer

Endometrial carcinoma (EC) is one of the most common gynecological cancers in the world. In this work we apply Cox proportional hazards (CPH) and optimal survival tree (OST) algorithms to the retrospective prognostic modeling of disease-specific survival in 842 EC patients. We demonstrate that linear CPH models are preferred for the EC risk assessment based on clinical features alone, while interpretable, non-linear OST models are favored when patient profiles can be supplemented with additional biomarker data. We show how visually interpretable tree models can help generate and explore novel research hypotheses by studying the OST decision path structure, in which L1 cell adhesion molecule expression and estrogen receptor status are correctly indicated as important risk factors in the p53 abnormal EC subgroup. To aid further clinical adoption of advanced machine learning techniques, we stress the importance of quantifying model discrimination and calibration performance in the development of explainable clinical prediction models.

Cross-Phase Adversarial Domain Adaptation for Deep Disease-free Survival Prediction with Gastric Cancer CT Images.

Predicting gastric cancer disease-free survival (DFS) and identifying patients probably with high risk are imperative for more appropriate clinical treatment plans. Compared with CT-based radiomics researches adopting linear Cox proportional hazards models, deep neural networks can perform nonlinear transformations and investigate complex associations of image features with prognosis. Exploring shared information between post-contrast CT (with better visual enhancement) and pre-contrast CT (with few side effects and contraindications) is another challenge. In this work, a cross-phase adversarial domain adaptation (CPADA) framework is proposed to adapt a deep DFS prediction network (DDFS-Net) from arterial phase to pre-contrast phase. The DDFS-Net is designed for feature learning and trained by optimizing the average negative log function of Cox partial likelihood. The CPADA maps the feature space of pre-contrast phase (target) to arterial phase (source) in an adversarial manner by measuring Wasserstein distance. The proposed methods are evaluated on a dataset of 249 gastric cancer patients by concordance index, receiver operating characteristic curves, and Kaplan-Meier survival curves. The results demonstrate that our DDFS-Net outperforms linear survival analysis methods, and the CPADA works better than supervised learning and direct transfer schemes.Clinical Relevance-This work enables preoperative DFS prediction and risk stratification in gastric cancer. It is feasible and effective to infer a patient's risk of failure given a pre-contrast CT image by DDFS-Net adapted by CPADA.

Quasi-linear Cox proportional hazards model with cross- L1 penalty

BackgroundTo accurately predict the response to treatment, we need a stable and effective risk score that can be calculated from patient characteristics. When we evaluate such risks from time-to-event data with right-censoring, Cox’s proportional hazards model is the most popular for estimating the linear risk score. However, the intrinsic heterogeneity of patients may prevent us from obtaining a valid score. It is therefore insufficient to consider the regression problem with a single linear predictor.Methodswe propose the model with a quasi-linear predictor that combines several linear predictors. This provides a natural extension of Cox model that leads to a mixture hazards model. We investigate the property of the maximum likelihood estimator for the proposed model. Moreover, we propose two strategies for getting the interpretable estimates. The first is to restrict the model structure in advance, based on unsupervised learning or prior information, and the second is to obtain as parsimonious an expression as possible in the parameter estimation strategy with cross- L1 penalty. The performance of the proposed method are evaluated by simulation and application studies.ResultsWe showed that the maximum likelihood estimator has consistency and asymptotic normality, and the cross- L1-regularized estimator has root-n consistency. Simulation studies show these properties empirically, and application studies show that the proposed model improves predictive ability relative to Cox model.ConclusionsIt is essential to capture the intrinsic heterogeneity of patients for getting more stable and effective risk score. The proposed hazard model can capture such heterogeneity and achieve better performance than the ordinary linear Cox proportional hazards model.

DeepSurv: personalized treatment recommender system using a Cox proportional hazards deep neural network

BackgroundMedical practitioners use survival models to explore and understand the relationships between patients’ covariates (e.g. clinical and genetic features) and the effectiveness of various treatment options. Standard survival models like the linear Cox proportional hazards model require extensive feature engineering or prior medical knowledge to model treatment interaction at an individual level. While nonlinear survival methods, such as neural networks and survival forests, can inherently model these high-level interaction terms, they have yet to be shown as effective treatment recommender systems.MethodsWe introduce DeepSurv, a Cox proportional hazards deep neural network and state-of-the-art survival method for modeling interactions between a patient’s covariates and treatment effectiveness in order to provide personalized treatment recommendations.ResultsWe perform a number of experiments training DeepSurv on simulated and real survival data. We demonstrate that DeepSurv performs as well as or better than other state-of-the-art survival models and validate that DeepSurv successfully models increasingly complex relationships between a patient’s covariates and their risk of failure. We then show how DeepSurv models the relationship between a patient’s features and effectiveness of different treatment options to show how DeepSurv can be used to provide individual treatment recommendations. Finally, we train DeepSurv on real clinical studies to demonstrate how it’s personalized treatment recommendations would increase the survival time of a set of patients.ConclusionsThe predictive and modeling capabilities of DeepSurv will enable medical researchers to use deep neural networks as a tool in their exploration, understanding, and prediction of the effects of a patient’s characteristics on their risk of failure.

Following the Organ Supply

Disparity in access to liver transplantation (LT) in the United States persists despite directives from the federal government to reduce geographic variation. We assessed the impact of socioeconomic status (SES) and traveling to alternative donation service areas (DSAs) on patient survival. A prospective cohort study integrating transplant registry and U.S. Census data was analyzed using multivariate linear Cox proportional hazards models. A separate matched-pairs analysis was used to assess the benefit of traveling on patient survival and transplantation rate. High SES is associated with increased access to LT (adjusted hazard ratio [aHR], 1.05; 95% confidence interval [95% CI], 1.01-1.08) and reduced mortality after waitlisting (aHR [95% CI], 0.88 [0.85-0.93]). Increased access is mediated, in part, through inter-DSA travel. Travel was associated with high SES, white race, blood group O, private insurance, and residence in regions 1, 5, and 11. Transplant candidates in the highest SES quartile were approximately 70% more likely to travel (aHR [95% CI], 1.67 [1.43-1.97]) than those in the lowest SES quartile. Compared with matched control patients, travelers were 74% more likely to be transplanted (aHR [95% CI], 1.74 [1.56-1.94]) and 20% less likely to die after listing (aHR [95% CI], 0.79 [0.69-0.92]). High SES and inter-DSA travel are strongly associated with increased LT access and reduced mortality. Travelers are more likely to be sociodemographically advantaged and privately insured and to live in regions with reduced access to deceased-donor organs.

CDO1 Promoter Methylation is a Biomarker for Outcome Prediction of Anthracycline Treated, Estrogen Receptor-Positive, Lymph Node-Positive Breast Cancer Patients

BackgroundVarious biomarkers for prediction of distant metastasis in lymph-node negative breast cancer have been described; however, predictive biomarkers for patients with lymph-node positive (LNP) disease in the context of distinct systemic therapies are still very much needed. DNA methylation is aberrant in breast cancer and is likely to play a major role in disease progression. In this study, the DNA methylation status of 202 candidate loci was screened to identify those loci that may predict outcome in LNP/estrogen receptor-positive (ER+) breast cancer patients with adjuvant anthracycline-based chemotherapy.MethodsQuantitative bisulfite sequencing was used to analyze DNA methylation biomarker candidates in a retrospective cohort of 162 LNP/ER+ breast cancer patients, who received adjuvant anthracycline-based chemotherapy. First, twelve breast cancer specimens were analyzed for all 202 candidate loci to exclude genes that showed no differential methylation. To identify genes that predict distant metastasis, the remaining loci were analyzed in 84 selected cases, including the 12 initial ones. Significant loci were analyzed in the remaining 78 independent cases. Metastasis-free survival analysis was conducted by using Cox regression, time-dependent ROC analysis, and the Kaplan-Meier method. Pairwise multivariate regression analysis was performed by linear Cox Proportional Hazard models, testing the association between methylation scores and clinical parameters with respect to metastasis-free survival.ResultsOf the 202 loci analysed, 37 showed some indication of differential DNA methylation among the initial 12 patient samples tested. Of those, 6 loci were associated with outcome in the initial cohort (n = 84, log rank test, p < 0.05).Promoter DNA methylation of cysteine dioxygenase 1 (CDO1) was confirmed in univariate and in pairwise multivariate analysis adjusting for age at surgery, pathological T stage, progesterone receptor status, grade, and endocrine therapy as a strong and independent biomarker for outcome prediction in the independent validation set (log rank test p-value = 0.0010).ConclusionsCDO1 methylation was shown to be a strong predictor for distant metastasis in retrospective cohorts of LNP/ER+ breast cancer patients, who had received adjuvant anthracycline-based chemotherapy.