Residual variability was assessed by testing proportional, additive and combined error models to describe differences between individual predictions and observations (Eq. 4). Where θ is the typical estimate for the proportional or additive error, IPRED is the individual predicted concentration and Y is the modelled value of the observed variable.
Equation 4\(Y=\ \text{IPRED}\ (1+\theta_{\text{prop}})+\ \theta_{\text{add}}\)
For ivacaftor-M1 and M6 separate proportional error models for plasma and DBS samples were implemented.
In order to define the weight of the prior value of the PK parameters, predefined residual standard error (RSE) values were used. Three types of prior weight were predefined and based on numbers described in literature: informative (10% RSE), moderately informative (30% RSE) and weakly informative/vague (105). (6) The first step was to assign informative priors on all parameters, except for CL, IIV and the residual error. No priors were assigned to CL, as data were thought to be rich enough to estimate this parameter without a prior. Also, as described above IIV was only applied on CL and no priors were used to estimate the IIV on other PK parameters. As well as the residual error, which was also estimated without priors on basis of the available data.
The next step was to change one parameter at the time to a vague prior, and assess whether this parameter could be estimated on basis of the available data – with weakly prior information. If estimation was not possible, the following step was to change this parameter to a moderate informative prior. If estimation was still not possible, the parameter was set to the informative prior again. These steps were repeated for all parameters in order to obtain a stable structural model, which was defined by being able to estimate the model parameters with a value within an expected range with a maximum RSE of 30%.
Following the development of the structural model, a covariate analysis was conducted to determine whether covariates could explain IIV. A covariate search can only be applied on parameters without a prior, in this case CL. (6) The covariates assessed included age, adherence and CF mutation. Stepwise forward inclusion was used in the covariate analysis. A reduction in objective function value (OFV) ≥3.81 (P=0.05) was considered statistically significant. Dichotomous and continuous covariates were included in the model (Eq. 5 and 6). In this context, θi represents the individual model predicted PK parameter for an individual with covariate value covi. θpop is the population estimate for that parameter, covm is the median covariate value and θcov denotes the covariate effect.
Equation 5\(\theta_{i}=\ \theta_{\text{pop}}*\ {\theta_{\text{cov}}}^{\text{cov}_{i}}\)
Equation 6\(\theta_{i}=\ \theta_{\text{pop}}*{(\frac{\text{cov}_{i}}{\text{cov}_{m}})}^{\theta_{\text{cov}}}\)