To quantify the association between tumor dynamics and overall survival across cancers: a Bayesian meta-analysis
Assil Merlaud (1, 2, 3), Marion Kerioui (1, 4), Jérémie Guedj (1), Davide Ronchi (5), René Bruno (2, 6), Alyse Lin (7), Phyllis Chan (7), Benjamin Wu (7), Jin Y. Jin (7), Pascal Chanu (2, 8), Julie Bertrand (1)
(1) Université Paris Cité, IAME, Inserm, F-75018, Paris, France, (2) Institut Roche, Boulogne-Billancourt, France, (3) Clinical Pharmacology, Genentech-Roche, Paris, France (4) MRC Biostatistics Unit, Institute of Public Health, Cambridge, UK, (5) Department of Electrical, Computer and Biomedical Engineering, University of Pavia, Pavia, Italy, (6) Clinical Pharmacology, Genentech-Roche, Marseille, France, (7) Clinical Pharmacology, Genentech Inc. South San Francisco, USA, (8) Clinical Pharmacology, Genentech-Roche, Lyon, France
Context: In oncology clinical trials, the primary clinical endpoint is often overall survival (OS), which requires long study duration. Tumor size measurements, summarized as the Sum of Longest Diameters (SLD) of target lesions according to RECIST1, are often collected over time as a marker of disease progression and treatment response. Indeed, the on-treatment growth constant of the SLD or kg in the model by Stein et al 2 has been shown to be a good predictor of OS across tumor types treated by chemotherapy or immunotherapy using a two-stage approach 3,4 . Joint models are known to better capture the association between a biomarker and the event of interest, by simultaneously accounting for both outcomes5. Thus, we propose to assess whether the strength of the association between kg and OS is similar across cancer types using a joint model approach, in a desire to bridge predictive capabilities among clinical trials.
Objectives: This study aims to develop a meta-analysis of nonlinear joint models6,7 of SLD trajectories and survival in the atezolizumab (ATZ) based treatment arm of 10 clinical trials. The primary goal is to assess the associations between kg and OS across five cancer types and then to quantify the variability of these associations.
Methods: The impact of treatment was investigated in non-small cell lung cancer (NSCLC), small cell lung cancer (SCLC), metastatic urothelial carcinoma (mUC), renal cell carcinoma (RCC) and triple negative breast cancer (TNBC).
A Stein model 8 was fitted to describe the SLD dynamics and we assumed an impact of the logarithm of the kg on the survival accelerated failure time9 OS sub-model. The parameters were estimated for each clinical trials separately in a Bayesian framework using Stan10. Posterior predictive checks (PPCs)11 were used to assess the goodness of fit. As joint model and Bayesian sampling algorithms are known to be computationally expensive, within chain parallelization was implemented to minimize the inference cost. Finally, the inter-study variability was estimated using a random-effect meta-analysis on the estimates of the joint model parameters focusing on the kg-OS association parameters.
Results: The analysis included 21 679 tumor measurements and survival data from 3305 patients of phase II/III studies. Vectorization and within-chain parallelization enabled to reduce the run times by 3 and 9, respectively on a data set of 425 patients and 3780 samples. The PPCs indicated good performance of the joint-models across the 10 studies.
As expected, kg under treatment varied considerably across studies. For RCC patients treated by ATZ and bevacizumab, the estimate was 0.00029 days?¹, resulting in a tumor volume doubling time of 6.5 years. In contrast, for SCLC treated with ATZ, carboplatin, and etoposide, the estimate was ten-fold higher: 0.0019 days-1, translating to a median doubling time of 1 year.
The association parameter between the kg and the lognormal survival function selected to fit the OS is referred as the kg accelerated factor (AF). For each individual study, an increase of kg was found to significantly reduce the OS time. However, non-negligible variability was identified across studies, with a doubling of the kg leading to a decrease of 36% in OS time for SCLC patients treated with ATZ in combination with carboplatin, and etoposide versus a decrease of 20% for RCC patients treated by ATZ and bevacizumab.
Actually a between-study standard deviation of 0.10 was estimated using the meta-analysis. Also using the pooled estimate of the kg AF enabled to obtain a large 95% prediction interval of this kg AF of [0.31; 0.81], meaning that for a new study one would predict a decrease of survival times between 54% and 13% for a doubling of kg.
Conclusion: This work reinforces the idea that kg can help describe OS, regardless of the study, cancer and treatment type. However, the magnitude of the kg-OS association varied across studies and cancer types. It was previously shown that the association between SLD dynamics and OS varied across organs for mUC patients12. Modelling the dynamics of each lesion within a patient instead of the SLD should enable to capture the kg-OS association at the organ level13, which we expect to show a reduced heterogeneity across cancer types.
References:
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