Conditional inference for ultrahigh-dimensional additive hazards model

In the realm of high-throughput genomic data, modeling with ultrahigh-dimensional covariates and censored survival outcomes is of great importance. We conduct conditional inference for the ultrahigh-dimensional additive hazards model, allowing both the covariates of interest and nuisance covariates to be ultrahigh-dimensional. The presence of right censorship with survival outcomes adds an extra layer of complexity to the original data structure, posing significant challenges for the ultrahigh-dimensional additive hazards model. To address this, we introduce an innovative test statistic based on the quadratic norm of the score function. Moreover, when there is a high correlation between the covariates of interest and nuisance covariates, we propose a decorrelated score function-based test statistic to enhance statistical power. Additionally, we establish the limiting distributions of the test statistics under both the null and local alternative hypotheses, further enhancing the computational appeal of our approach. The proposed statistics are thoroughly evaluated through extensive simulation studies and applied to two real data examples.