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Next we detail how both the WRES and the CWRES are calculated.
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In this same situation we demonstrate that use of the CWRES would not result in such an error. In the following sections we first present a motivating example demonstrating the possibility of misguided model development using the WRES as a diagnostic while performing FOCE analysis. The CWRES have the advantage of being directly related to a term in the objective function used in the FOCE method of model fitting, thus giving more detailed information about the fit of a model to data using this method. In this work we present a new diagnostic tool, the conditional weighted residuals (CWRES), which are calculated in a similar manner to the WRES but based on the FOCE approximation. Use of the WRES as a diagnostic when performing modeling using the FOCE methods leads to the possibility of misguided model development and diagnosis, or, at the very least, less informed model development.
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This is the case even if the model development process has taken place using the FOCE methods. The WRES, however, are always calculated based on the FO approximation to the model. Of the 131 papers found in the above Pub-Med search, 50% specifically mentioned examining the WRES during model diagnosis, of those, 80% provided a plot of the WRES in their publication. The WRES have also become a common model diagnostic in the literature. Presently, use of the WRES is suggested by the United States’ Food and Drug Administration (FDA) as an appropriate diagnostic for evaluating model misspecification ( 11). The NONMEM user’s guide ( 10) suggests use of the weighted residuals (WRES), the weighted difference between the model prediction and the data, as one model diagnostic. Once a model has been fit to pharmacometric data it is crucial to evaluate the goodness of that fit. A search on pub-med for all articles that used NONMEM for pharmacometric analysis in 2005 (search terms: NONMEM, population pharmacokinetics and population pharmacodynamics) revealed 131 studies, of which 15% used the FO method, 21% used the FOCE method, 28% used the FOCEI method, 16% used a combination of these methods and 20% did not discuss the estimation method employed. As a result, the NONMEM community has shifted from the FO method to the FOCE and FOCEI methods. The FOCE methods allow for hypothesis testing during model building ( 7) and generally produce less biased model parameter estimates ( 8, 9). Since then, improved methods of approximating the model have been developed including the first-order with conditional estimation (FOCE) method and the FOCE method with interaction (FOCEI).
#Difference between fo same as foce nonmem series
When NONMEM was first introduced the only parameter estimation method available was the first-order (FO) method, based on the first-order Taylor series approximation to the population PK/PD model. In order to estimate the parameters of these pharmacometric models various computer programs have been developed ( 3– 6), of which the most popular is NONMEM (Globomax, USA). Utilization of population pharmacokinetic (PK) and pharmacodynamic (PD) models to describe clinical data is becoming increasingly important in drug development ( 1, 2). Utilization of CWRES could improve model development and evaluation and give a more accurate picture of if and when a model is misspecified when using the FO or FOCE methods. CWRES/WRES comparisons can also indicate if the FOCE estimation method will improve the results of an FO model fit to data. In contrast, in certain circumstances, the WRES have distributions that greatly deviate from the expected, falsely indicating model misspecification. Using real and simulated data the CWRES distributions behave as theoretically expected under the correct model. Materials and MethodsĬWRES are calculated as the FOCE approximated difference between an individual’s data and the model prediction of that data divided by the root of the covariance of the data given the model. We present a new diagnostic tool, the conditional weighted residuals (CWRES), which are calculated based on the FOCE approximation. Utilizing WRES with the FOCE method may lead to misguided model development/evaluation. However, the weighted residuals (WRES), a common diagnostic tool used to test for model misspecification, are calculated using the FO approximation. Population model analyses have shifted from using the first order (FO) to the first-order with conditional estimation (FOCE) approximation to the true model.