Visual predictive check of longitudinal models and dropout
Authors: Hu Chuanpu , Roy Amit , Kondic Anna 
Published: February 2025

Objectives:Visual predictive check (VPC) is commonly used to evaluate pharmacometrics models [1,2]. However, certain misconceptions exist, and their performance may be hampered if patients with worse outcomes drop out earlier, as often occurs in clinical trials, especially in oncology [3,4]. While methods accounting for dropouts have appeared in literature [5,6], they vary in assumptions, flexibility, and performance, and the differences between them are not widely understood. This presentation aims to:• Elucidate which methods can be used to handle VPC with dropout • Provide a more informative VPC approach using confidence intervalsMethods:Two main dropout-VPC approaches, both parametric, were classified as the full and the conditional approaches in a theoretical framework to clarify their differences. In addition, a non-parametric approach using Cox proportional hazard was proposed with the conditional approach. Confidence intervals were included in VPC assessments. The practical performances of these approaches were illustrated with an application to the tumor growth dynamics (TGD) modeling of data from two cancer clinical trials of nivolumab and Docetaxel where patients were followed until disease progression. The dataset consisted of 855 patients, with 3504 tumor size measurements. VPCs using simulated dataset based on the study design were also conducted to further illustrate model performance.Results:A modified Wang model was developed for TGD data. A Weibull model was also developed to facilitate the parametric dropout-VPC methods. Confidence intervals were shown to add information. VPC results based on the real as well as simulated data showed that the more familiar full approach did not provide meaningful improvement for TGD model evaluation over the naive approach of not adjusting for dropout, and could be outperformed by the conditional approach using either the Weibull model or the Cox proportional hazard model. Conclusion: Including confidence intervals in VPC should improve interpretation, the conditional approach was shown to be more generally applicable when dropout occurs, and the nonparametric approach could provide additional robustness.Citations: [1] Post TM et al. (2008). Extensions to the visual predictive check to facilitate model performance evaluation. J Pharmacokinet Pharmacodyn 35 (2):185-202. [2] Bergstrand M et al. (2011). Prediction-Corrected Visual Predictive Checks for Diagnosing Nonlinear Mixed-Effects Models. The AAPS Journal 13 (2):143-151. [3] Hu C and Sale M (2003) A joint model for nonlinear longitudinal data with informative dropout. J Pharmacokinet Pharmacodyn 30 (1):83-103.[4] Ruiz-Garcia A et al. (2023). A comprehensive regulatory and industry review of modeling and simulation practices in oncology clinical drug development. J Pharmacokinet Pharmacodyn 50 (3):147-172.[5] Mandema JW and Stanski DR (1996) opulation pharmacodynamic model for ketorolac analgesia. Clin Pharmacol Ther 60 (6):619-635.[6] Hu C et al. (2011). Informative dropout modeling of longitudinal ordered categorical data and model validation: application to exposure-response modeling of physician's global assessment score for ustekinumab in patients with psoriasis. J Pharmacokinet Pharmacodyn 38 (2):237-260.