Individual Observation-Shrinkage Scaling of Residuals in a Generalized Least Square Type of Estimation in NONMEM
Vijay D Ivaturi , Andrew C Hooker , Mats O Karlsson
Department of Pharmaceutical Biosciences, Uppsala University, Uppsala, Sweden
Objectives: A generalized least square (GLS) type of approach is often used in regression analysis where the predictions from a first model fit are used to weigh the residuals in a subsequent fit, thus making the estimation of the residual variance component independent of the structural model predictions. This approach is useful when the underlying data distribution is not known or deviates heavily from normality, and thus relies only on the relation between the mean and the variance function (1). The objective of this work is to introduce the concept of an individual data point shrinkage (ISHR) scaled GLS approach (GLS-ISHR) and evaluate this method with respect to different estimation algorithms (FO, FOCE/FOCE-I) , bias of parameter estimates and robustness to residual error model misspecification.
Methods: 100 replicates of sparse (n=2), moderate (n=5) and rich designs (n=11) with 100 individuals each were simulated for estimation from a one-compartment first-order absorption and elimination model with proportional RE (30% CV) and exponential parameter variability (50% CV). This is an extension of a previous work which used GLS where residual weighting from previous model prediction was done by scaling with population shrinkage (GLS-PSHR) (2). Within NONMEM, GLS estimation algorithms were reproduced by fitting sequential models. The IPREDs and PREDs obtained from a first model fit are used to model the residual error in a second step. GLS-ISHR was fit with a mixture (MIX) of IPRED and PRED weighted by average individual data point shrinkage across 30 replicates computed as Σ(1-SD(IWRES))ij/30 , where IWRES= (DVij-IPREDij)/σij; GLS-ISHR = PREDorig·iwres_shrinkageorig + (1-iwres_shrinkageorig)*IPREDorig. Parameter estimate bias and robustness to model misspecification were computed for the GLS-ISHR approach, the GLS-PSHR approach and two other GLS methods (GLS-PRED, GLS-IPRED) and was compared to the regular FO/ FOCE/FOCEI estimation algorithms.
Results: In general there was an improvement of parameter precision and bias using the GLS-ISHR approach compared to FO and FOCE, but was not always the case when compared to FOCE-I. Population shrinkage obtained from the model fit was lowered using the GLS-ISHR approach compared to FO, FOCE and FOCE-I. Robustness to model specification was both design and magnitude of misspecification dependent. The greater the deviation of the underlying data from normality, the better GLS-ISHR performed compared to the FOCE(I) methods.
Conclusions: GLS-ISHR improved on all other GLS methods previously reported and was sufficiently robust to residual error model misspecification. Further work on testing GLS methods on real datasets will serve to confirm the robustness of this method.
Acknowledgement: This work was part of the DDMoRe project.
References:
[1] Carroll, R. J. and Ruppert, D. (1988). Transformations and Weighting in Regression. London: Chapman and Hall.
[2] Hooker A., Langdon G., Karlsson M. (2007), AAPS. Evaluation of Generalized Least Squares Type Estimation For Population Pharmacometric Models