Covariate analysis has become a customary and expected part of population pharmacokinetic (PK) and pharmacokinetic/ pharmacodynamic (PK/PD) modeling.1 The covariate submodel describes, explains, and predicts the impact of patient characteristics on drug exposure and effects. Various criteria have been discussed for assessing the utility of a covariate. These criteria include reduction in interindividual variability (IIV)2 and measures of the clinical importance.3 When we fit the covariate submodel, we are regressing the typical value of a parameter (for example, typical value of clearance [TVCL]) on a potential covariate (Zi). Consider, for example, the following covariate submodel. The probability of demonstrating that: is dependent on the following formula. Where θc is the true slope, ω is the IIV (expressed as a standard deviation), and is the corrected sum of squares for the covariate (a measure of the diversity of the covariate in the dataset). Hence, the basic statistical properties of the covariate submodel alone indicate that the probability of detecting a covariate relationship is dependent on the true value of the slope and CSS.4 The probability, given the data observed, of concluding that θc ≠ 0 (when, in fact, θc = 0) is the statistical significance (p-value). The relationship between creatinine clearance (CrCL) and drug clearance (CL) can be used as an instructive example for investigating how the statistical properties of the covariate submodel come into play in the context of a population PK model. Because there are well-defined categories of renal impairment,5 a clinical significance ratio (CSR) can be constructed as a gauge on the clinical importance of the covariate effect. For our purposes, CSR was defined as the ratio of the population estimated typical value of CL in moderate renal dysfunction compared to normal renal function:
Where: CrCL = 45 mL/min represents moderate renal dysfunction and CrCL = 115 mL/min represents normal renal function. A CSR value of 1 would then indicate no difference in the TVCL with moderate renal dysfunction and with normal renal function. Figure 1 shows the covariate scenarios used in our simulation study. In the base model (where θc is assumed equal to 0), the estimated IIV encompasses all variability in TVCL; in the covariate model, θc explains some of the variability in TVCL and the estimated IIV should be reduced in comparison, where the greater the absolute value of the slope, the greater the reduction in IIV. The examples displayed here are for a clinical significance ratio of 0.9.
American Conference on Pharmacometrics (ACoP), Fort Lauderdale, Florida, May 2013
By S. Willavize and Jill Fiedler-Kelly