Statistical Issues Regarding the First-order Linear Approximation in Nonlinear Mixed Effects Models

Abstract

Since nonlinear mixed effects model is statistically quite complicated, it is not possible to obtain the analytical forms of the marginal mean and its corresponding covariance matrix for observations. To circumvent this issue, a first-order Taylor series expansion is generally employed to approximate a nonlinear model with a linear form additive in inter-subject random effects. This linear approximation is based on the assumption that the parameter variation among subjects is negligible, which is quite hard to satisfy in actual clinical data analyses. Consequently, the linear approximation probably leads to inconsistent estimators. This paper describes the statistical issues regarding the first-order linear approximation in nonlinear mixed effects models.