ETAs in the original model are replaced with new added THETAs to obtain the standard errors of these added THETA estimates. Parameters θ, Ω and Σ are fixed at the values obtained from the estimation step for all the subjects. The new command for estimating the SE of EBE of η is '-se_of_eta.' To do this, PsN Internally generates modified NONMEM® control stream and dataset for each subject.
One added feature of the PsN 2.2.6 with respect to the previous versions is the computation of standard errors of EBE of η.
#Psn nonmem software#
PsN is a free software for pre- and post-processing of NONMEM® runs and outputs, developed by the Pharmacometrics Research Group at Uppsala University and available at. In NONMEM® VI, EBE can be used as support points to calculate the joint density for NONPAR (nonparametric) estimation option. Since EBEs are used in the objective function calculation in FOCE or Laplacian method, both methods rely on accurate EBEs. The empirical distribution of EBE can be used to test the normal distribution assumption on Ω, or the validity of the mixture model, or the necessity of using some other kind of nonparametric distribution. However, such a method is not recommended when there is difference between the empirical distribution of η̂ and the estimated Ω, i.e., when the shrinkage is greater than about 20%. Apparent relationship between EBE and covariate indicates the necessity of further refining the structural model, for example, including that covariate in the structural model. If relationships between covariates and EBEs do not exist, EBE theoretically should have no trend with the covariates. EBE can be used for screening covariates for the structural model development. Individual PK/PD parameters and accordingly individual drug concentrations or effects are described using EBE. INTERACTION option does not affect the output for the additive residual error model, but produces different estimates which are regarded as more accurate for other residual error models (proportional error, combined additive and proportional error, power function error, etc.). The INTERACTION estimation option considers interaction of η and ε, and uses η̂ instead of 0 for η during the calculation of variance of Y.
The computation time increases in the order of FO, FOCE, and Laplacian. The difference of FOCE objective function with respect to the Laplacian objective function is the use of the first order partial derivatives for the linear approximation whereas the Laplacian method uses up to the second order partial derivatives. In the FOCE or Laplacian method, computation of the individual η estimates (η̂) is necessary during the minimization process. Individual η estimates (η̂) are not calculated during the minimization process for the FO method, however they can be estimated with the final θ, Ω, and Σ with the POSTHOC option. FOCE method stands for "First Order Conditional Estimation," for which individual η (η̂) is estimated during the minimization process.
Laplacian method (L) uses "Laplacian" integral approximation of the objective function using up to the second order partial derivatives. FO method employs "First Order" linear approximation of F with respect to η. The available estimation methods from NONMEM® VI and their characteristics are as follows. There are several numerical methods to estimate the aforementioned PK/PD parameters.
The estimates of each subject's η (η̂) has several namesrealized η, post hoc η, empirical Bayes estimate (EBE) of η, or maximum a posteriori (MAP) estimate of η. The random variable η cannot be directly observed but can be estimated using subject level observations (Y, i.e., dependent variable) and the final estimates of θ, Ω, and Σ.