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).