A two-phase linear regression model for biologic half-life data

In estimating the biologic half-life of an infused drug or biologic agent, one very frequently used model is the biexponential, which reflects a two-compartment physiologic model. The difficulty in using this model is that it is nonlinear in the parameters and requires relatively sophisticated analysis. Furthermore, an interval estimate is not usually reported. We propose the use of a two-phase linear regression approach, which is tantamount to breaking down the model into two straight lines based on the selection of the logarithm of concentration as the ordinate and time as the abscissa. We show how to determine the joint or changeover point for the two lines using a simple iterative procedure, how to select between a one-phase and a two-phase model, and how to provide a simple confidence interval estimate for half-life when it exists. An example using data from a study of Factor VIII pharmacokinetics is given.