Lasso-Regularized Pseudo-Observation Regression for High-Dimensional Survival Data: Theory, Methodology, and Applications

Abstract: High-dimensional survival data present two simultaneous challenges: the number of covariates may be large relative to the sample size, and the outcome of interest may be unobserved because of censoring. Pseudo-observations provide estimated responses that enable direct regression modeling of survival quantities of interest. However, the theoretical properties of sparse high-dimensional estimators, such as the Lasso, in pseudo-observation regression remain underexplored. We study Lasso regression with pseudo-observations under sparsity and convex loss functions. Under suitable regularity and curvature conditions, we derive finite-sample oracle inequalities, convergence rates, and sufficient conditions for consistency. The resulting rates have the same leading order as those for standard high-dimensional Lasso. We also extend the framework to Group Lasso for superdataset landmarking, obtaining corresponding guarantees while accounting for dependence across repeated landmark records and pseudo-observations. We evaluate regularized survival prediction methods through Monte Carlo simulations and an application to the NKI breast cancer dataset. The simulations compare Cox-Lasso, pseudo-observation Lasso, and outcome-weighted Lasso under sliding and superdataset landmarking. Cox-Lasso generally achieves lower prediction errors under sliding landmarking, while methods perform more similarly under superdataset landmarking. IPCW-based pseudo-observation and outcome-weighted methods generally achieve better variable-selection performance under superdataset landmarking. In the real-data application to five-year survival prediction, no single method performs best across prediction accuracy, discrimination, and calibration.