An accurate model of patient survival time can help in the treatment and care of cancer patients. The common practice of providing survival time estimates based only on population averages for the site and stage of cancer ignores many important individual differences among patients. In this paper, we propose a local regression method for learning patient-specific survival time distribution based on patient attributes such as blood tests and clinical assessments. When tested on a cohort of more than 2000 cancer patients, our method gives survival time predictions that are much more accurate than popular survival analysis models such as the Cox and Aalen regression models. Our results also show that using patient-specific attributes can reduce the prediction error on survival time by as much as 20% when compared to using cancer site and stage only.