Cardiovascular disease (CVD) remains a leading global health burden, with carotid intima-media thickness (cIMT) recognized as a sensitive, non-invasive biomarker for early atherosclerosis and future cardiovascular risk. Although ultrasound imaging is the standard method for measuring cIMT, its accessibility may be limited in large-scale populations with intensive screening demands or in low-resource settings, posing a significant challenge for stroke survivors who have a high need for CVD assessment. While existing cIMT prediction models based solely on tabular data have been proposed to bypass the need for strong reliance on image-derived features, they typically frame the task as a binary classification problem, indicating only the presence or absence of vascular risk, thereby failing to effectively capture its actual severity. In contrast, this work proposes a prognostic learning model to effectively estimate cIMT, enabling precise quantification of atherosclerosis severity without relying on imaging data. By constructing a patient similarity graph relying on demographic and clinical-derived features to (i) bypass the need for revealing the actual clinical measurements, promoting privacy, and (ii) to explicitly account for patient's interdependencies, this work introduces a graph-guided self-supervised learning (Self-SL) framework to learn informative representations for the cIMT prediction task. These learned representations encode key local and global graph information that can readily assist the downstream task requiring only a minimal amount of labeled data. Applied to the UK Biobank cohort, the model outperforms conventional learning models, achieving up to 93.22% average MSE reduction, underscoring graph similarity strength in capturing latent clinical patterns.