An essential component of insulin therapy for type 1 diabetes involves the prediction of blood glucose levels as function of exogenous perturbations such as insulin dose and meal intake. Fluctuations in blood glucose are generated by a complex biophysical system and have demonstrated substantial variation at different times of a day within a subject and between subjects. In this paper, we present a new data-driven dynamic model with time-varying coefficients that are used to explicitly quantify the time-varying patient-specific effects of insulin dose and meal intake on blood glucose fluctuations. Using the 3-variate time series of blood glucose level, insulin dose and meal intake of an individual type 1 diabetic subject, we apply an extended Kalman Filter technique to estimate time-varying coefficients of the patient-specific model. We evaluate our empirical model using a FDA-approved simulator with 30 patients. The model developed in this paper can be used in model-based control such as adaptive control and model predictive control of blood glucose by means of an artificial pancreas.