Penalized Deep Partially Linear Cox Models with Application to CT Scans of Lung Cancer Patients
This work addresses survival analysis for lung cancer patients using CT scans, offering a method to handle high-dimensional data, but it is incremental as it builds on existing partially linear Cox models with deep learning enhancements.
The authors tackled the challenge of fitting partially linear Cox models for survival analysis when parametric components exceed sample size and nonparametric modeling faces dimensionality issues, by proposing a Penalized Deep Partially Linear Cox Model that selects features with SCAD penalty and uses a deep neural network, achieving proven convergence and asymptotic properties with performance validated in simulations and applied to lung cancer CT scan data.
Lung cancer is a leading cause of cancer mortality globally, highlighting the importance of understanding its mortality risks to design effective patient-centered therapies. The National Lung Screening Trial (NLST) employed computed tomography texture analysis, which provides objective measurements of texture patterns on CT scans, to quantify the mortality risks of lung cancer patients. Partially linear Cox models have gained popularity for survival analysis by dissecting the hazard function into parametric and nonparametric components, allowing for the effective incorporation of both well-established risk factors (such as age and clinical variables) and emerging risk factors (e.g., image features) within a unified framework. However, when the dimension of parametric components exceeds the sample size, the task of model fitting becomes formidable, while nonparametric modeling grapples with the curse of dimensionality. We propose a novel Penalized Deep Partially Linear Cox Model (Penalized DPLC), which incorporates the SCAD penalty to select important texture features and employs a deep neural network to estimate the nonparametric component of the model. We prove the convergence and asymptotic properties of the estimator and compare it to other methods through extensive simulation studies, evaluating its performance in risk prediction and feature selection. The proposed method is applied to the NLST study dataset to uncover the effects of key clinical and imaging risk factors on patients' survival. Our findings provide valuable insights into the relationship between these factors and survival outcomes.