Approximate testing in two-stage nonlinear mixed models.

We investigate here small sample properties of approximate F-tests about fixed effects parameters in nonlinear mixed models. For estimation of population fixed effects parameters as well as variance components, we apply the two-stage approach. This method is useful and popular when the number of observations per sampling unit is large enough. The approximate F-test is constructed based on large sample approximation to the distribution of nonlinear least squares estimates of subject-specific parameters. We recommend a modified test statistic that takes into consideration approximation to the large sample Fisher information matrix (See [1]). Our main focus is on comparing finite sample properties of broadly used approximate tests (Wald test and likelihood ratio test) and the modified F-test under the null hypothesis, especially accuracy of p-values (See [2]). For that purpose two extensive simulation studies are conducted based on pharmacokinetic models (See [3, 4]).