Evaluation of Type I Error Rates When Modeling Ordered Categorical Data in NONMEM

The development of non-linear mixed pharmacokinetic/pharmacodynamic models for continuous variables is usually guided by graphical assessment of goodness of fit and statistical significance criteria. The latter is usually the likelihood ratio test (LR). When the variable to be modeled is categorical, on the other hand, the available graphical methods are less informative and/or more complicated to use and the modeler needs to rely more heavily on statistical significance assessment in the model development. The aim of this study was to evaluate the type I error rates, obtained from using the LR test, for inclusion of a false parameter in a non-linear mixed effects model for ordered categorical data when modeling with NONMEM. Data with four ordinal categories were simulated from a logistic model. Two nested multinomial models were fitted to the data, the model used for simulation and a model containing one additional parameter. The difference in fit (objective function value) between models was calculated. Three types of models were explored; (i) a model without interindividual variability (IIV) where the addition of a parameter describing IIV was assessed, (ii) a model with IIV where the addition of a drug effect parameter (either categorical or continuous drug exposure measure) was evaluated, and (iii) a model including IIV and drug effect where the inclusion of a random effects parameter on the drug effect was assessed. Alterations were made to the simulation conditions, for example, varying the number of individuals and the size and distribution of the IIV, to explore potential influences on the type I error rate. The estimated type I error rate for inclusion of a false random effect parameter in model (i) and (iii) were, as expected, lower than the nominal. When the additional parameter was a fixed effects parameter describing drug effect (model(II)) the estimated type I error rates were in agreement with the nominal. None of the different simulation conditions tried changed this pattern. Thus, the LR test seems appropriate for judging the statistical significance of fixed effects parameters when modeling categorical data with NONMEM.