Addendum
Appendix - Population analysis of the renal substrates s-pindolol and fluconazole.
The renal substrates s-pindolol and fluconazole were analysed using a nonlinear mixed effects modelling framework within the NONMEM software (ver 7.2.0). The methodology was the same for both substrates and a generic approach is described here. For both substrates both plasma concentrations and urine amounts and volumes were available. Since the purpose of this analysis was to get estimates of clearance for each individual then quantification of the influence of covariates was not considered in this work. The assay details and limits of quantification are provided in the thesis. No concentrations were censored based on the limit of quantification.
Model building
Model building was conducted in NONMEM using the FOCE option with INTERACTION. One, two and three compartment models were considered and the best model selected based on statistical criteria (see Model Selection). The models were parameterised in terms of clearances (CL, Q1, Q2) and volumes (V1, V2, V3), where CL is clearance, Q1 is the first intercompartmental clearance (etc), V1 is the volume of distribution of the central compartment, V2 the volume of distribution of the 2nd peripheral compartment (etc). The absorption of the substrate from the gut was assumed to follow a first-order process, zero order and lag-time models were also considered and choice based on fit of the model to the data. The residual error was modelled as additive, proportional or a combined error model. The combined error structure was given as
,
where is a p x 1 vector of parameter values for the ith individual, is the dose for the ith subject, the time of the jth observation for the ith subject. The residual error is shown here for the combined model with a structure:
,
and a 2 x 2 vector of residual variances.
Between-subject variances were considered for estimation for all fixed effects parameters (e.g. CL, V1, V2 ...). The model for the between-subject variance was given,
and .
In this work only the diagonal elements of the BSV matrix () were considered for estimation.
Model selection
Model selection was based on a likelihood ratio test determined by a decrease in the objective function value (OFV) provided by NONMEM. For comparison of nested models, the OFV is approximately, asymptotically 2 distributed with degrees of freedom equal to the number of parameters difference between successive models. A difference of 3.84 units for 1 degree of freedom is at the critical value where P=0.05. Since covariates were not considered in this analysis then forward selection and backward elimination procedures were not considered. Model selection was also based on stability and plausible parameter estimates. Stability was determined as convergence to the same solution for dispersed initial parameter values. Plausible parameter estimates was based on positive values of clearance and volume parameters with at least 1 volume parameter value exceeding plasma volume.
Model evaluation
The model was evaluated based on goodness of fit criteria which included residual and weighted residual plots. Since the model was not intended to be used for predictive purposes then more sophisticated model evaluation techniques such as visual or numerical predictive checks were not considered.