Jointly modeling hypoglycemic event times and longitudinal glucose measurement with Brownian motion

Diabetes patients need to carefully monitor their blood sugar level. Hypoglycemia is considered as adverse event. It is very important to identify the risk factor of hypoglycemic event during the glucose management for diabetes patients. We proposed a first hitting time model of the Brownian motion to model the hypoglycemic event. The event occurs when a underlying process hit a lower boundary, i.e., the clinical standard of the hypoglycemic event. The process could be the movement of the blood sugar level.