Anna Mishina 1, Kirill Peskov 1,2,3, Kirill Zhudenkov 1,2
1 M&S Decisions (Dubai, United Arab Emirates), 2 Research Center of Model-Informed Drug Development, Sechenov First Moscow State Medical University (Moscow, Russia), 3 Marchuk Institute of Numerical Mathematics of the Russian Academy of Sciences (INM RAS) (Moscow, Russia)
Introduction:
Joint modeling methodology that integrates longitudinal biomarkers and time-to-event outcomes has become an essential component of pharmacometric analyses in oncology[1]. Numerous applications have demonstrated their value for quantifying biomarker–survival relationship and supporting dynamic predictions, and several integrative and tutorial-style publications have formalized the joint modeling workflow, providing practical guidance for model development and validation[2,3].
Despite this methodological progress, the available diagnostic techniques are not always sufficient and representative to support model selection. While existing dynamic discrimination performance metrics, such as ROC AUC and Brier Score (BS) assess a model’s ability to distinguish between patients who experience the event and those who do not, they do not evaluate how accurately the model describes the shape of the survival function. Therefore, in this work we introduce simulation-based diagnostics that targets precise survival description.
Methods:
This study analyzed data from 381 patients with advanced non-small cell lung cancer treated with Erlotinib (NCT00364351), sourced from Project DataSphere data repository[4]. Overall survival (OS) was modeled within a joint modeling framework, with tumor size (SLD), and selected laboratory biomarkers were evaluated as prognostic predictors. Model development and simulations were performed using MonolixSuite 2023R1.
Candidate baseline covariates were screened using stepwise Cox regression. Optimal longitudinal submodels for each biomarker were built and selected based on parameter identifiability (RSE < 51%) and minimal Akaike Information Criteria5. Joint models with different biomarker combinations were then constructed and evaluated using standard goodness-of-fit plots and time-dependent ROC AUC and BS for the OS endpoint.
The tested diagnostic methods incorporate two simulation-based diagnostics for the survival submodel: (i) EBE-based survival simulations and (ii) simulations conditioned on observed longitudinal data. Individual parameters were defined either by empirical Bayes estimates or by 500 samples from the individual conditional distribution. Survival curves were simulated, event times were generated via inverse transform sampling[6] with administrative censoring (matching enrollment and study duration characteristics), and replicated clinical trials were constructed to produce Kaplan–Meier-based diagnostics for model comparison.
Results:
Among univariate joint models with identifiable parameters, those incorporating hematological biomarkers demonstrated the highest prognostic performance. The joint model with neutrophil-to-lymphocyte ratio (NLR) as dynamic predictor demonstrated ROC AUC = 0.89 and BS = 0.14 at 12 months. In contrast, the model based solely on SLD showed inferior discrimination (AUC = 0.82, BS = 0.17), while models with alkaline phosphatase (ALP) or lactate dehydrogenase (LDH) performed the poorest performance (AUC ≤ 0.75, BS = 0.20). The NLR model was therefore selected as the backbone for multivariate extensions including SLD, ALP, and LDH. Adding SLD to the NLR model (NLR+SLD) visibly improved discrimination over the univariate NLR model. However, further inclusion of ALP and LDH, either in three- or four-variate combinations, resulted in no improvement in discrimination performance.
Evaluation of survival description performance using simulations conditioned on observed longitudinal data showed that the experimental Kaplan–Meier (KM) curve lay entirely within the 95% prediction intervals (PI) for all tested models and closely followed the simulated median trends. Notably, the width of the 95% PI decreased with increasing model complexity: the summary PI area over 23 months (S) was 1.91 for the univariate NLR model, 1.73 for the bivariate NLR+SLD model, and 1.66 for the four-variate model (NLR+SLD+ALP+LDH). Thus, uncertainty in population survival predictions driven by individual parameter uncertainty was the lowest for the most sophisticated model.
Important insight was that EBE-based survival simulations were systematically biased relative to the observed KM profile. Because EBEs are fixed point estimates, this approach does not propagate heterogeneity in parameter uncertainty across individuals (especially, in case of high shrinkage). In oncology datasets, patients with poorer prognosis may discontinue early and contribute fewer longitudinal measurements, resulting in broader conditional parameter distributions. Ignoring this feature leads to distorted population-level predictions.
Conclusion:
In this work we introduced diagnostics based on survival simulations conditioned on observed longitudinal data. Accounting for conditional uncertainty proved essential for unbiased population survival assessment and for distinguishing between models beyond basic discrimination metrics.
References:
1. Liu H, Ibrahim EIK, Centanni M, Sarr C, Venkatakrishnan K, Friberg LE. Integrated modeling of biomarkers, survival and safety in clinical oncology drug development. Adv Drug Deliv Rev. 2025;216:115476. doi:10.1016/j.addr.2024.115476
2. Rizopoulos D. Joint Models for Longitudinal and Time-to-Event Data.
3. Zhudenkov K, Gavrilov S, Sofronova A, et al. A workflow for the joint modeling of longitudinal and event data in the development of therapeutics: Tools, statistical methods, and diagnostics. CPT Pharmacomet Syst Pharmacol. 2022;11(4):425-437. doi:10.1002/psp4.12763
4. https://data.projectdatasphere.org/projectdatasphere/html/home
5. Mishina A, Zhudenkov K, Helmlinger G, Peskov K. A Systematic Comparative Analysis of Tumor Size Models Based on Erlotinib Clinical Data in Advanced NSCLC. CPT Pharmacomet Syst Pharmacol. 2025;14(12):1970-1981. doi:10.1002/psp4.70095
6. Kosinsky U, Azarov I, Chu L, Helmlinger G, Peskov K, Aksenov S. Comparison of different approaches to modeling early tumor size dynamics for accurate prediction of survival in non-small cell lung cancer (NSCLC) clinical trials. ACoP 2018, October 8-11, 2018.
Reference: PAGE 34 (2026) Abstr 12314 [www.page-meeting.org/?abstract=12314]
Poster: Drug/Disease Modelling - Oncology