Implications of Including and Excluding Correlation of Random Effects in Hierarchical Mixed Effects Pharmacokinetic Models
Nicholas H.G. Holford 1, Jogarao V.S. Gobburu,2 Diane R. Mould 3
1 Dept of Pharmacology & Clinical Pharmacology, University of Auckland, Private Bag 92019, Auckland, New Zealand, 2 Pharmacometrics, Division of Pharmaceutical Evaluation-1, Office of Clinical Pharmacology and Biopharmaceutics, Center for Drug Evaluation and Research, Food and Drug Administration, Rockville, MD 20852. 3 Projections Research Inc., Phoenixville, PA 19460
Population modeling is increasingly being employed to make important decisions during drug development. Fundamentally, pharmacokinetic and pharmacodynamic parameters (e.g.: clearance, volume of distribution, maximal effect) are mutually independent. On the other hand, a common (initially unidentified) covariate could explain between subject variability in more than one parameter. Estimation of random correlation between parameters is controversial. To our knowledge, no systematic investigation of the influence of random correlation of parameter estimation has been reported. The present analysis was conducted to explore the consequences of including or excluding correlation terms in a population pharmacokinetic model. 1000 sparse (120 subjects, 4 observations/ subject) and dense data sets (30 subjects, 6 observations/subject) were simulated for an aminoglycoside drug given intravenously with or without correlation between clearance and volume of distribution. True and false models were fitted to the simulated data and bias and imprecision of the parameters were calculated. The bias and imprecision of true and alternate model parameters were within 20%. There is a high probability (>80%) of correctly identifying the true model using the log-likelihood ratio test. Inclusion or exclusion of correlation of random effects using the log likelihood ratio test as the model selection criteria is reliable. False inclusion or exclusion of correlation of random effects is generally forgiving with respect to model selection and bias and imprecision of the parameter estimates but clearance estimates are not equivalent if correlation is ignored.