Nonparametric estimation of conditional survival function with time-varying covariates using DeepONet.

Area of Science:

• Biostatistics
• Machine Learning
• Survival Analysis

Background:

• Traditional survival models often impose restrictive assumptions like proportional hazards.
• These assumptions limit the accurate modeling of time-varying covariates' complex effects.

Purpose of the Study:

• To develop a nonparametric method for conditional survival function estimation.
• To leverage deep learning for capturing arbitrary, potentially long-term covariate effects.

Main Methods:

• Utilized Deep Operator Networks (DeepONet), a deep learning architecture for operator learning.
• Modeled the conditional hazard function as a nonlinear operator of covariate histories.
• Employed a nonparametric full likelihood loss function for censored survival data.

Main Results:

• DeepONet demonstrated strong performance in simulation studies.
• The Cox model produced biased results when instantaneous effect assumptions were violated.
• The proposed method achieved a lower integrated Brier score on ADNI data compared to the Cox model.

Conclusions:

• The DeepONet approach offers a flexible alternative to traditional survival models.
• This method effectively handles complex, non-instantaneous covariate effects in survival analysis.
• The approach shows promise for analyzing complex biomedical data, such as Alzheimer's disease progression.