Stroke is the third leading cause of death and the principal cause of serious long-term disability in the United States. Accurate prediction of stroke is highly valuable for early intervention and treatment. In this study, we compare the Cox proportional hazards model with a machine learning approach for stroke prediction on the Cardiovascular Health Study (CHS) dataset. Specifically, we consider the common problems of data imputation, feature selection, and prediction in medical datasets. We propose a novel automatic feature selection algorithm that selects robust features based on our proposed heuristic: conservative mean. Combined with Support Vector Machines (SVMs), our proposed feature selection algorithm achieves a greater area under the ROC curve (AUC) as compared to the Cox proportional hazards model and L1 regularized Cox model. Furthermore, we present a margin-based censored regression algorithm that combines the concept of margin-based classifiers with censored regression to achieve a better concordance index than the Cox model. Overall, our approach outperforms the current state-of-the-art in both metrics of AUC and concordance index. In addition, our work has also identified potential risk factors that have not been discovered by traditional approaches. Our method can be applied to clinical prediction of other diseases, where missing data are common and risk factors are not well understood.