Monitoring the Patient: Four Different Bayesian Methods to Make Individual Patient Drug Models

Four different methods which use Bayes’ theorem are described. The first is the conventional maximum a posteriori probability (MAP) approach using parametric models. Next is a Bayesian approach for nonparametric (NP) models. Then a new hybrid approach using a combination of these two methods is presented, which begins with a MAP approach to the data but adds more NP support points in the area of the MAP estimate to form an augmented population model. Then, the NP Bayesian approach using the augmented population model is discussed. This not only increases the precision of estimation using the NP approach, but also permits it to be done far outside the stated boundaries of the original NP population model. The hybrid approach can be used for patients with a severe drug interaction, or patients of another type, such as children, when only a population model for adults is available. The hybrid approach thus allows bridging from one population to another. We can use a model for adults to care for children initially, and when enough data is present, make a model for children. Then the entire process can be used to care for newborns, and then to make a proper NP population model for them. Finally, a sequential NP Bayesian approach is described, which permits the model parameters to be updated whenever a new dose is given or serum concentration (or other) data point is encountered. This interacting multiple model (IMM) approach, derived from the aerospace community, tracks drug behavior best of all current thresholds in acutely changing intensive care unit patients, and permits more precise control of their unstable models in their rapidly changing clinical situations.