A clinician desires to use a risk-stratification method that achieves confident risk-stratification - the risk estimates of the different patients reflect the true risks with a high probability. This allows him/her to use these risks to make accurate predictions about prognosis and decisions about screening, treatments for the current patient. We develop Risk-stratify - a two phase algorithm that is designed to achieve confident risk-stratification. In the first phase, we grow a tree to partition the covariate space. Each node in the tree is split using statistical tests that determine if the risks of the child nodes are different or not. The choice of the statistical tests depends on whether the data is censored (Log-rank test) or not (U-test). The set of the leaves of the tree form a partition. The risk distribution of patients that belong to a leaf is different from the sibling leaf but not the rest of the leaves. Therefore, some of the leaves that have similar underlying risks are incorrectly specified to have different risks. In the second phase, we develop a novel recursive graph decomposition approach to address this problem. We merge the leaves of the tree that have similar risks to form new leaves that form the final output. We apply Risk-stratify on a cohort of patients (with no history of cardiovascular disease) from UK Biobank and assess their risk for cardiovascular disease. Risk-stratify significantly improves risk-stratification, i.e., a lower fraction of the groups have over/under estimated risks (measured in terms of false discovery rate; 33% reduction) in comparison to state-of-the-art methods for cardiovascular prediction (Random forests, Cox model, etc.). We find that the Cox model significantly over estimates the risk of 21,621 patients out of 216,211 patients. Risk-stratify can accurately categorize 2,987 of these 21,621 patients as low-risk individuals.