Deep Partially Linear Transformation Model for Right-Censored Survival Data (2412.07611v2)

Abstract: Although the Cox proportional hazards model is well established and extensively used in the analysis of survival data, the proportional hazards (PH) assumption may not always hold in practical scenarios. The semiparametric transformation model extends the conventional Cox model and also includes many other survival models as special cases. This paper introduces a deep partially linear transformation model (DPLTM) as a general and flexible framework for estimation, inference and prediction. The proposed method is capable of avoiding the curse of dimensionality while still retaining the interpretability of some covariates of interest. We derive the overall convergence rate of the maximum likelihood estimators, the minimax lower bound of the nonparametric deep neural network (DNN) estimator, the asymptotic normality and the semiparametric efficiency of the parametric estimator. Comprehensive simulation studies demonstrate the impressive performance of the proposed estimation procedure in terms of both estimation accuracy and prediction power, which is further validated by an application to a real-world dataset.

• The paper introduces the Deep Partially Linear Transformation Model (DPLTM), combining linear models and deep neural networks to analyze right-censored survival data with both linear and nonlinear effects.
• Theoretical analysis establishes the convergence rates of the model's estimators, demonstrating performance benefits and semiparametric efficiency.
• Empirical studies using simulations and real-world data show DPLTM outperforms traditional models in estimating complex relationships and improving prediction accuracy.

Analysis of the Deep Partially Linear Transformation Model for Right-Censored Survival Data

The paper "Deep Partially Linear Transformation Model for Right-Censored Survival Data" offers a comprehensive exploration into the intersection of deep learning and semiparametric statistical methodologies while addressing the limitations of the Cox proportional hazards model. The Cox model, due to its assumption of proportional hazards, often falls short when applied to complex survival data. To circumvent these shortcomings, this paper introduces the Deep Partially Linear Transformation Model (DPLTM), which serves as a versatile tool accommodating both linear and nonlinear covariate effects in survival analysis.

Key Contributions

The authors propose a robust model that enhances the interpretability of linear covariates while leveraging the nonparametric power of deep neural networks to handle high-dimensional datasets. This hybrid approach effectively alleviates the curse of dimensionality, which is a notable challenge in traditional survival models. The following aspects of the research stand out:

• Model Framework: The DPLTM applies a deep ReLU network to model nonlinear covariate effects, maintaining linear models for covariates of primary interest. This configuration allows for enhanced interpretability without sacrificing the model's flexibility in capturing complex data patterns.
• Theoretical Foundations: The convergence rates of the model's estimators are rigorously derived, revealing impressive performance benefits over nonparametric methods such as kernels or splines. The paper establishes the minimax lower bound for the nonparametric estimator and demonstrates semiparametric efficiency for the parametric estimator, ensuring strong theoretical underpinnings for the proposed methodology.
• Empirical Validation: A series of simulation studies and an application to real-world data from the SEER database validate the model's efficacy. In simulation experiments, DPLTM consistently outperforms traditional linear and additive models, showcasing its capability to accurately estimate complex nonlinear relationships and improve prediction accuracy.

Implications and Future Work

The implications of adopting DPLTM are considerable, particularly in the field of public health and biomedical research, where datasets with intricate relationships are common. By facilitating more accurate predictions and maintaining critical interpretability, this model enhances decision-making processes in clinical settings. Furthermore, the flexibility of the DPLTM framework allows for potential extensions to other survival models and data scenarios, such as cure models or interval-censored data.

Looking forward, the paper suggests exploring the integration of DPLTM with more advanced neural network architectures, such as convolutional or transformer networks, which could further enhance the model's applicability in contexts involving unstructured data like genomics or medical imaging. This pathway opens up numerous avenues for future research in combining deep learning techniques with survival analysis, potentially leading to more personalized and precise treatments in healthcare.

Conclusion

The integration of deep neural networks within partially linear transformation models represents a sophisticated advancement in survival analysis. The DPLTM offers a method that not only addresses the limitations of traditional models but also harnesses the computational power of deep learning to capture complexities within the data. As a result, this research provides a substantial contribution to the field, equipping researchers with a potent tool for analyzing right-censored survival data.