<p>Our study focuses on the case-cohort study design as a cost-effective alternative to large prospective cohort studies, effectively addressing challenges such as expensive covariate measurements and rare events. Specically, we target the additive hazards model and propose three estimation methods to handle case-cohort data. Our aim is to utilize the bootstrap method for estimating the variances of the proposed estimators using case-cohort data. We employ a novel nonparametric bootstrap method with an equivalent sampling scheme, simplifying the resampling process to a single-stage, enhancing practicality. Through simulation studies, we compare variance estimates obtained by the bootstrap method with asymptotic theoretical estimates. The bootstrap method demonstrates strong performance. Furthermore, we provide a real-life example to illustrate the application of our proposed method.</p>