Testing and Confidence Intervals for High Dimensional Proportional Hazards Model
This work addresses statistical inference challenges in high-dimensional survival analysis, providing robust methods for researchers and practitioners in fields like biostatistics and epidemiology, though it is incremental as it builds on existing decorrelation principles.
The paper tackles the problem of hypothesis testing and confidence interval construction for low-dimensional components in high-dimensional proportional hazards models, proposing a decorrelation-based approach that achieves asymptotic normality and semiparametric optimality without requiring model selection consistency, with numerical results supporting the theory.
This paper proposes a decorrelation-based approach to test hypotheses and construct confidence intervals for the low dimensional component of high dimensional proportional hazards models. Motivated by the geometric projection principle, we propose new decorrelated score, Wald and partial likelihood ratio statistics. Without assuming model selection consistency, we prove the asymptotic normality of these test statistics, establish their semiparametric optimality. We also develop new procedures for constructing pointwise confidence intervals for the baseline hazard function and baseline survival function. Thorough numerical results are provided to back up our theory.