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The Effect of Collinearity on the Selection of Covariates in Population Pharmacokinetic Analysis

Jakob Ribbing and E. Niclas Jonsson

Uppsala University, Sweden

Identifying covariate relations is usually an important part of the development of population pharmacokinetics/pharmacodynamics (PK/PD) models. This is commonly a time consuming task, especially if there is a large number of possible covariate relationships to investigate. However, with many potential covariates it is often the case that some, or many of them, are correlated, i.e. more than one covariate carry the same type of information.

The aim of this simulation study was to investigate the impact of correlated covariates on the power to identify the true covariate as well as on the bias in the estimated covariate coefficient. The investigation was carried out over a range of data set sizes, correlations and covariate strengths.

Data sets with 20 to 1000 subjects were investigated. For each data set size, 10,000 covariate datasets with five covariates each were created by sampling from a multivariate standard normal distribution. The true covariate was set up to have a strong, medium, weak and no correlation to the other four covariates, respectively. The latter four were constrained to have no correlation to each other.

Data sets, in which each individual had three observations, were simulated using a one compartment, i.v. bolus model. The covariate influenced clearance according to one of several magnitudes (including no influence). Models with each of the simulated covariates influencing clearance and the model without any covariate were fitted to the data and the power to select the true covariate was recorded. The estimated coefficient for all covariates was also retained for further analysis.

The results show that the power to select the true covariate decrease as a function of the correlation to the competing covariate, with only a minor influence of the data set size and covariate strength. The relative bias in the coefficients decreased with increasing data set size and covariate strength while it increased with increasing correlation to competing covariates.