The likelihood ratio test appears robust to most residual error model misspecifications
Silber, Hanna E., Maria C. Kjellsson and Mats O. Karlsson
Department of Pharmaceutical Biosciences, Uppsala University, Sweden
Background: It has been shown that when using the FOCE method in NONMEM, the likelihood ratio test (LRT) can be sensitive to misspecification of the residual error model in that ignoring an existing η-ε interaction leads to actual significance levels for type I errors being higher than the nominal levels [1].
Objective: To assess LRT sensitivity to residual error misspecifications.
Methods: Data sets containing 250 individuals with six or twelve observations per individual were simulated multiple times (n=1000) according to a steady state infusion with different residual error model structures; (1) autocorrelation, (2) inter-individual variability in the residual error magnitude, (3) replication (L2) error, (4) time-varying residual error magnitude, (5) heavy-tailed residual error distribution, (6) inter-occasion variability, and (7) an η-ε interaction. The data sets were analyzed using a reduced model with an additive residual error on log-transformed data with or without a covariate relationship on clearance. The type I error rate of inclusion of a 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. The type I error rate was also calculated using the correct error model. The difference in OFV between the model with the correct and the reduced error structure was also calculated. The study was performed using the FOCE method in NONMEM.
Results: The misspecifications when the reduced models were used were pronounced, as indicated by the OFV being on average 206 – 2269 higher than for the corresponding correct error models. The significance levels of the LRT with the reduced model were still appropriate and similar to those when the correct error models were used, in all cases between 4.1 and 5.8%. The only exception was, as expected based on findings in [1], the reduced model ignoring an existing η-ε interaction, where the type I error rate was 31.1%.
Conclusion: The LRT appears robust towards all tested residual error misspecifications but ignoring the h-e interaction.
Reference:
1. Wahlby et al. Assessment of type I error rates for the statistical sub-model in NONMEM. J Pharmacokinet Pharmacodyn, 2002. 29:251-69.