Chapter 29 Weighting Data

return to the Course index
previous | next

Extended Least Squares (ELS)

Another approach to choosing the most appropriate weighting scheme is to fit parameters of the variance model during the optimization process. The form of the variance versus data equation needs to be determined. Once the form and parameters involved are determined the optimization process can determine the variance and model parameters given good initial estimates and enough good data. There are some differences. Since there are more parameters more data are necessary. Different algorithms are necessary for the optimization. A different objective function, the function minimized during the optimization, is needed and different optimization algorithms are necessary. The programs Phoenix™ and ADAPT include these algorithms.

Equation 29.7.1 Objective Function for Extended Least Squares Optimization

Note the inclusion of the lnV term in Equation 29.7.1. This will prevent the optimization algorithm from driving the value of V high and thus the weight low to minimize the objective function (WSS) without regard for the model parameter values. vp is variance parameter value.

The equation for V, the variance of each data point, may take a number of forms. Some of these are shown in Equation 29.7.2.

Equation 29.7.2 Example Variance Equations

References

Peck, C.C., Sheiner, L.B. and Nichols, A.I. 1984 "The Problem of Choosing Weights in Nonlinear Regression Analysis of Pharmacokinetic Data", Drug Metabolism Reviews, 15, pp 133-148
Peck, C.C., Beal, S.L., Sheiner, L.B. and Nichols, A.I. 1984 "Extended Least Squares Nonlinear Regression: A Possible Solution to the 'Choice of Weights' Problem in Analysis of Individual Pharmacokinetic Data", J. Pharmcokin. Biopharm., 12, pp 545-558

This page was last modified: Sunday, 28th Jul 2024 at 5:09 pm

Privacy Statement - 25 May 2018

iBook and pdf versions of this material and other PK material is available