Development of a novel population pharmacokinetic model
When the predictive performance of the published model was inadequate, an alternative population PK model was constructed. During construction, the number of compartments was evaluated. In this study, the initial visit with PK profiling was considered as the first occasion. Subsequent occasions were defined as a visit with a PK assessment. PK parameters were expressed by CL, Q, and V; inter-individual (IIV) and inter-occasional variability (IOV) of these parameters was estimated. Residual error is described with a combined additive and proportional model. We evaluated candidate models by examination of PK parameter estimates, their respective residual standard errors (RSE), objective function value (OFV), GOF plots and visual predictive checks (VPC).
Stepwise covariate modelling (SCM) was used to perform covariate analysis applying the generalized additive models (GAM) approach27,28. This approach allows to test if potential patient characteristics are able to explain IIV and IOV in PK parameters. We applied a forward inclusion and backward elimination process. Age, height, body weight, LBW, FFM, BMI and centre of inclusion were available and explored as covariates. Allometric scaling was applied with fixed exponents of 0.75 for CL and 1.00 for V29,30. As height was not available in two patients, their height was fitted by a linear regression model based on available height and age of other patients, and used to calculate LBW and BMI. We explored the impact of the centre on FIX predictions as haemophilia treatment centres used different laboratory specifications according to local protocol. This was tested by incorporating a residual error per centre.
In the SCM, covariates were screened for relevance by univariate analysis. Improvement of the model was deemed significant if addition of a covariate to the model decreased the OFV (ΔOFV) with 3.84 (p<0.05, Chi-square distribution, 1 df ). When two parameters were added simultaneously, e.g. during expansion of a two-compartment model to a three-compartment model, a ΔOFV of -5.99 (p<0.05, Chi-square distribution, 2 df ) was warranted. Subsequently, all significant covariates were simultaneously added to the model, followed by backward elimination. Elimination of a covariate that resulted in an OFV increase of >6.64 (p<0.01, Chi-square distribution, 1 df ) was regarded as a significant improvement to the model.
The novel population PK model was internally validated with a visual predictive check (VPC) to compare the distribution of the observations with the distribution of the predictions. The robustness of the parameter estimates was assessed by bootstrap analysis. Bias of the novel population PK model were assessed throughout the PE (Eq. 4).