Joint modeling of overall survival and tumor size dynamics in non-small cell lung cancer: Clinical trial simulations and validation of predictions at study and subject levels
Dmitry Onishchenko (1), James Dunyak (2), Gabriel Helmlinger (2), Eric Masson (2), Helen Tomkinson (3), Kirill Peskov (1), Nidal Al-Huniti (2)
(1) M&S Decisions, Moscow, Russia, (2) Quantitative Clinical Pharmacology, AstraZeneca, Waltham, USA, (3) Quantitative Clinical Pharmacology, AstraZeneca, Cambridge, UK
Objectives: Projecting survival estimates from early- to late-phase studies is a critical step in anti-cancer drug development. Surrogate endpoints such as progression-free survival (PFS) and overall response rate (ORR) are commonly used to assess efficacy in Phase 2 trials, while their association with overall survival (OS) in Phase 3 trials is known to be weak. An earlier FDA analysis modeled non-small cell lung cancer (NSCLC) tumor dynamics and OS in a 2-step approach , yet without considering dependencies between the two variables. Joint modeling  is a technique which allows to simultaneously fit a longitudinal variable (e.g., tumor size dynamics) and a time-to-event variable (e.g., OS). It enables one to convert full information from individual tumor size assessments into personalized predictions of survival, thereby avoiding dichotomization of patient response measures. To assess its predictive power, a joint model must be validated both at population and patient levels.
Methods: Clinical data from the Iressa IPASS Phase 3 study of gefitinib in NSCLC  were used to fit a joint model of tumor size dynamics and OS. Model validation was performed on a follow-up study data (IFUM, Phase 4 ). We simulated clinical trials using the model and compared mean simulated survival vs. observed data. A delayed effect of tumor dynamics on survival was also incorporated in the model. Model covariates were selected by performing various types of posterior predictive checks, including survival prediction for censored patients. The survival estimation method was implemented in R packages JM and JMbayes .
Results: The fitted model accurately estimated patient survival in the follow-up study using early data cut-off for tumor assessments. Individual odds of experiencing an event were evaluated in real time along with study-level survival estimates. Treatment, EGFR mutation status, and ECOG performance status were evaluated as covariates for the survival function. Associations between tumor dynamics (size and time derivative) and time to death were statistically significant (P-values <0.05).
Conclusions: Joint modeling of tumor size dynamics and survival allows for effective simulation of clinical trials, personalized predictions and robust validation of predictive survival models. It is applicable to different types of endpoints, including PFS and OS, and may thus provide a generalizable tool for prospective forecasting of survival in various study populations.
 Wang et al, Clin Pharmacol Ther. 2009 86(2):167-74.
 Ibrahim et al, J Clin Oncol. 2010 28(16):2796-801
 Mok et al, N Engl J Med. 2009 361(10):947-57 (NCT00322452)
 Douillard et al, Br J Cancer 2014 110:55-62 (NCT01203917)
 Rizopoulos, J Stat Softw. 2010 35(9):1-33