The effect of collinearity on parameter estimates in nonlinear mixed effect models

Purpose. To demonstrate how correlations among predictor variables in a population pharmacokinetic model affect the ability to discern which covariates should enter into the structural pharmacokinetic model. Methods. Monte Carlo simulation was used to generate multiple-dose concentration-time data similar to that seen in a Phase III clinical trial. The drugs' pharmacokinetics were dependent on two covariates. Five data sets were simulated with increasing correlation between the two covariates. All data sets were analyzed using NONMEM both with and without inclusion of the covariates in the structural pharmacokinetic model. Summary measures far ill-conditioning and sensitivity analysis were used to examine how increasing correlation among covariates affects the accuracy and precision of the parameter estimates. Results. When covariates were included in the structural pharmacokinetic model and the correlation between covariates increased, the standard error of the parameter estimates increased and the value of parameter estimates themselves became increasingly biased. When the correlation between predictor variables was 0.75, the standard errors of the parameter estimates were too large to declare statistical significance. Conclusions. Correlations among predictor variables greater than 0.5 when entered into the model simultaneously should be a warning to researchers because the (1) the accuracy of the parameter estimates themselves may be biased and (2) the precision of the estimates may be inflated due to ill-conditioning.