Estimation of the rate constants in a data-sparse environment: comparison of a mathematical method and least squares...

A new method is presented for estimating the rate constants for the one-compartment open model with first-order absorption in a data-sparse environment. It is based on the principles of matrix algebra and system theory and requires only three to four plasma samples drawn at equal time intervals (a minimum of at least one sample in the absorption phase and one sample in the elimination phase). The utility of the technique is illustrated by comparing the parameter estimates from the matrix method with the estimates from a nonlinear computer parameter estimation program. In the preliminary evaluation of the method with both perfect data and data with randomly distributed error, the parameter estimates from the matrix method proved to be as good as the computer estimation for data-sparse systems. In a more realistic comparison with published patient data, the matrix method resulted in 0 to 456% better estimates of kel and ka than the computer estimation. Since the matrix method is mathematically simple and requires only three to four blood samples, it should prove very useful in data-sparse systems (e.g., clinical or small animal situations) where a minimum amount of blood samples can be drawn.