VALIDATION

2.4.1 Posterior predictive check

A posterior predictive check method [77] was chosen as an initial validation procedure. With this approach the compatibility of the data and model is assessed by comparing simulated concentrations with observed concentrations. Simulated concentrations were estimated via the simulation function in NONMEM. A dataset with significant covariates, doses and time measurements, but without the observed concentrations, was created. The estimation command in NONMEM was replaced by a simulation command ($SIMULATION), and the thetas, omegas and sigmas were fixed to the estimates from the final model. 100 simulations were performed.

For each subject in each simulation, Cmax, Ctrough and AUC0-12 were calculated and compared with Cmax, Ctrough and AUC0-12 from the observed data. The mean values of the observed data were compared to 95% confidence interval (CI) limits from the simulated data. Paired statistic tests using SPSS were performed to determine whether the observed and simulated mean values were significant different.

2.4.2 Jackknife estimation

A Jackknife run was performed in order to find the confidence interval (CI) of the pharmacokinetic parameters. Each patient was in order excluded form the data set, which then gave 17 Jackknife datasets. These Jackknife datasets were examined in NONMEM using the final pharmacokinetic population model, producing a new set of estimates for the pharmacokinetic parameters. The pharmacokinetic estimates from the Jackknife datasets were tested for normality in SPSS, and a 95% CI were then calculated.

A Jackknife run will also identify individuals that have large influence on the estimation of the values of the parameters.

MATERIALS AND METHODS

2.4.3 Data splitting

A data-splitting method was applied to confirm the robustness of the final model, and to determine the contribution of data from individuals in a subset group [78]. The full data set were divided into 10 subsets randomly. Each subset contained data from approximately 90%

of the patients, and were examined in NONMEM using the final model. The 10 subset groups are presented in table 3.

Table 3: Subset groups.

Group Patient(s) excluded

1 8

2 30

3 36

4 11 19

5 7 9

6 10 12

7 14 31

8 35 37

9 18 33

10 32 34

The parameter estimates determined from the subset analyses were compared in terms of the SD’s of the parameters in the full dataset.

The OFV was also calculated by another NONMEM run for the full data set, but with the parameter estimates fixed at the estimates from the subset analyses. The OFVs obtained in this step were compared with the OFV from the full data set. 95% CI for the absolute difference in OFV is achieved if the absolute difference of these values from that of the final model is ≤ 3.84.

MATERIALS AND METHODS

2.4.3.1 Predictive performance

The NONMEM estimates from each of the 10 subsets were used to predict CsA concentrations in the remaining 10% of the patients’ data. 10 control files with initial estimates of theta, omega and sigma replaced by the estimates from the 10 subsets were created. The individual concentrations were estimated using the “posthoc” subroutine and with the $ESTIMATION command set to MAXEVAL = 0, which means that the estimation step will be omitted. A dataset with significant covariates and doses was created. The predictive performance was tested without any concentration measurements provided in the dataset, with one concentration at time 0 and 2 hours post-dose provided, with two concentrations at time 0 and 2 hours post-dose and time 1 and 2 hours post-dose provided and three blood samples at time 0, 1 and 2 hours post-dose and 0, 1 and 3 hours post-dose provided. The choices of time measurements was based on empiricism and the fact that AUC0-4 is a good predictor for clinical outcome [55].

Estimated AUC0-12 at the different time measurements given were compared with observed AUC0-12,calculated using the linear-trapezoidal method. To evaluate predictive performance, the mean percentage prediction error (%MPE) and the mean precentage absolute prediction error (%MAPE) were calculated.

%

Bias is estimated by mean prediction error (MPE) and the precision of the predictions is estimated by the mean absolute prediction error (MAPE).

MATERIALS AND METHODS

2.4.4 External validation with Bayesian procedure

The Bayesian approach was applied to an external group of 10 kidney transplant patients.

These new patients participated in a different study were the pharmacokinetics in elderly were examined [79]. The main characteristics of the patients in the external group are presented in table 4.

Table 4: Patient demographics in the external group.

A MAP (maximum a posteriori) Bayesian estimator using the same time measurements as in the predictive check of the data splitting analyses were tested. The final pharmacokinetic population model was used to obtain Bayesian individual estimates of the pharmacokinetic parameters in the external validation set. Bayesian estimation was performed using the

“posthoc” subroutine and with the $ESTIMATION command set to MAXEVAL = 0.

Predictive performance was evaluated in same procedure as explained in section 2.4.3.1.

Patient ID

CsA morning -dose (mg)

Sex (F/M)

Age (yrs)

A 225 M 28

B 200 M 67

C 275 M 29

D 175 F 55

E 150 M 78

F 225 M 63

G 175 M 64

H 125 F 73

I 300 M 48

J 125 M 75

Mean 198 58

SD 59 18

SD:standard deviation, F:femal, M:man

MATERIALS AND METHODS

2.5 NON-POPULATION ANALYSES

A non-compartmental analysis of the dataset was first performed. This was done by manual calculation in Excel. In addition a pharmacokinetic modeling analysis of the dataset using WinNonlin was performed. WinNonlin is a tool for nonlinear modeling. A 2-compartment model with first order absorption and a lag-time was chosen from the library in WinNonlin to fit the data.

This was done in order to test for significant different estimates of CL and Vd between non-compartment analysis, simple pharmacokinetic modeling and pharmacokinetic population modeling.

2.6 STATISTICS

When testing different models in NONMEM, the models were considered statistic different if p < 0.05 (corresponding to OFV ≥ 3.84).

Statistic analyses were performed using SPSS for Windows (version 12). Normality was first assessed to determine which statistic analysis to apply. In the predictive check analysis, student’s t-test was used to assess differences between observed and simulated values for AUC0-12 and Cmax (normally distributed), and Wilcoxen matched pairs signed ranks test was used to assess differences between observed and simulated values for Cmin (not normally distributed) [80]. When testing for significant differences in the estimation of CL/F and Vd/F between non-compartment calculations, WinNonlin and NONMEM, one-way repeated measures ANOVA test was used to asses differences in the estimation of CL/F (normally distributed), and Friedman Test was used to asses differences in the estimation of Vd/F (not normally distributed) [80].

RESULTS

3 RESULTS

3.1 DIFFERENT COMPARTMENT MODELS WITH DIFFERENT ABSORPTION