Conditional weighted residuals (CWRES): a model diagnostic for the FOCE method

Abstract

Purpose: Population model analyses have shifted from using the first order (FO) to the first-order with conditional estimation (FOCE) approximation to the true model. However, the weighted residuals (WRES), a common diagnostic tool used to test for model misspecification, are calculated using the FO approximation. Utilizing WRES with the FOCE method may lead to misguided model development/evaluation. We present a new diagnostic tool, the conditional weighted residuals (CWRES), which are calculated based on the FOCE approximation.

Materials and methods: CWRES 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.

Results: Using real and simulated data the CWRES distributions behave as theoretically expected under the correct model. In contrast, in certain circumstances, the WRES have distributions that greatly deviate from the expected, falsely indicating model misspecification. CWRES/WRES comparisons can also indicate if the FOCE estimation method will improve the results of an FO model fit to data.

Conclusions: 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.