A note on fitting one-compartment models: non-linear least squares versus linear least squares using transformed data

Drug concentrations in one-compartment systems are frequently modeled using a single exponential function. Two methods of estimation are commonly used for determining the parameters of such a model. In the first method, non-linear least-squares regression is used to calculate the parameters. In the second method, the data are first transformed by a logarithmic function, and then the log-concentration data are fit using linear least-squares regression. The assumptions for fitting these models are discussed with special emphasis on which data points are most influential in determining parameter values. The similarities between fitting a linear regression model to the log-concentration data and fitting a weighted regression model to the original data are noted. An example is presented that illustrates the differences in fitting a model to the log-transformed data versus fitting unweighted and weighted models to the original-scale data.