Approximate Small-Sample Tests of Fixed Effects in Nonlinear Mixed Models

Nonlinear mixed effect models have been studied extensively over several decades, particularly in pharmacokinetic and pharmacodynamic applications. Here, we focus on investigating the performance of commonly applied tests of linear hypotheses about the fixed effect parameters under different approximations to the likelihood function and to the estimated covariance matrix of the estimators. Included are the first-order approximation (FIRO), first-order conditional approximation (FOCE), and Gaussian quadrature approximation (AGQ) estimation methods. There is no straightforward way to mimic the approximations and adjustments taken in linear mixed models, such as the Kackar–Harville–Jeske–Kenward–Roger approach. By simulations, we illustrate the accuracy of p-values for the tests considered here. The observed results indicate that FOCE and AGQ estimation methods outperform FIRO. The test with an adjustment coefficient that takes into consideration the number of sampling units and the number of fixed effect parameters (Gallant-type) seems to perform closest to desirable even for small-sample sizes.