The impact of misspecification of residual error or correlation structure on the type I error rate for covariate inclusion

Abstract

It has been shown that when using the FOCE method in NONMEM, the likelihood ratio test (LRT) can be sensitive to the use of an inappropriate estimation method in that ignoring an existing eta-epsilon interaction leads to actual significance levels for type I errors being higher than the nominal levels. The objective of this study was to assess through simulations the LRT sensitivity to various types of residual error model misspecifications in both continuous and categorical data. The study contained two parts, simulations based on continuous and categorical data. Data sets containing 250 individuals with up to 24 observations per individual were simulated multiple times (1000) with different types of residual error models for the continuous data and different strength of correlation between observations for the categorical data. The data sets were analyzed using either the correct or a simpler (incorrect) model with or without addition of a covariate. The type I error rate of inclusion of the non-informative covariate on the 5% level was calculated as the number of runs where the drop in the objective function value (OFV) was larger than 3.84 when the covariate relationship was included in the model using the correct or the incorrect model. The difference in OFV between the model with the correct and the incorrect structure was also calculated as a measure of the residual error model misspecification. For continuous data the FOCE method was used in most cases (with interaction when appropriate). The Laplacian estimation method was used for one of the continuous models and for categorical data. The results showed that the residual error model misspecifications when the erroneous model was used were pronounced, as indicated by the OFV being substantially higher than for the corresponding correct models. The significance levels of the LRT with the incorrect model were appropriate in all cases but ignoring (serial) correlations between observations (continuous and categorical data) as well as when the eta-epsilon interaction was ignored (which has previously been shown, continuous data). When ignoring correlation, the type I error rates were shown to be sensitive to the correlation strength, the number of observations per individual and the magnitude of the inter-individual variability on clearance. We conclude that the LRT appears robust towards all tested cases, but ignoring (serial) correlations between observations and eta-epsilon interaction.