Case Study: Estimation of Drug Effectiveness-Inverse Interpolation of Noisy Data by Nonlinear Least-Squares

Abstract

This paper describes a method of using in vitro measurements of drug effectiveness to predict drug performance in vivo. The inhibitions obtained for different drug concentrations in vitro were fitted using a family of non-linear functions, the best of the family being found using a least-squares criterion. In this way, the drug concentration in vitro which would give the same inhibition as observed in vivo was estimated.

The choice of the mathematical model for the general inhibition function, the number of parameters and the asymptotic conditions are considered. The program, which is written in standard Fortran77, forms a package suitable for other applications involving more than one independent parameter. Here the package is used to give the “best” approximation to the underlying shape of the data and thus allows predictions at intermediate values either of inhibition or concentration. In particular, it allows the prediction of the drug concentration at which the inhibition of protein formation rises to the 50% level. The results of applying this nonlinear least-squares method to the problem are sufficient to indicate that it gives satisfactory values in the sense that they agree with the in vivo results of drug administration.

A diagram illustrating the method and a table of typical results are included.