Modélisation conjointe de données longitudinales non-linéaires et de données de survie : Application au cancer de la prostate métastatique

Treatment evaluation for metastatic Castration-Resistant Prostate Cancer (mCRPC) relies on time-to-death. Prostate-specific antigen (PSA), assumed to be linked to survival, is frequently measured. Joint modelling which consists in the simultaneous analyse of biomarker's evolution and survival is particularly adapted, but often limited to linear longitudinal process. The main objective of this PhD is to study joint modelling when biomarker kinetics is described by a nonlinear mixed-effects model (NLMEM). First, we established by simulations that the SAEM algorithm of Monolix provided unbiased parameter estimations of a nonlinear joint model, with satisfying type 1 error and power to detect a link between the two processes. Then, we developed a mechanistic joint model to characterize the relationship between PSA kinetics and survival in mCRPC patients treated by docetaxel. The structural model of the NLMEM was defined by a system of differential equations (ODEs) describing the mechanism of PSA production by docetaxel-sensitive and -resistant cells. Model selection and evaluation were detailed. The final joint model showed the predominant role of the non-observed resistant cells on survival. Lastly, we expanded tools developed in a linear context for individual dynamic prediction using nonlinear joint model. A Bayesian method provided the distribution of individual parameters. Predictive performances of the model were assessed using time-dependent discrimination and calibration metrics. These works open the way for the development of mechanistic joint models, which enable to account for the impact of several biomarkers on survival through ODEs, in order to improve therapeutic evaluation and prediction.L'évaluation de traitements pour le cancer de la prostate métastatique hormono-résistant (CPmHR) repose sur le temps de décès. L'antigène spécifique de la prostate (PSA), supposé lié à la survie, est régulièrement mesuré. La modélisation conjointe qui consiste en l'analyse simultanée de l'évolution du biomarqueur et de la survie est alors particulièrement adaptée, mais souvent limitée à un processus longitudinal linéaire. L'objectif principal de cette thèse est d'étudier la modélisation conjointe quand la cinétique du biomarqueur est décrite par un modèle non-linéaire à effets mixtes (MNLEM). Tout d'abord, nous avons montré par simulations que l'algorithme SAEM de Monolix estimait sans biais les paramètres d'un modèle conjoint non-linéaire, avec un risque de première espèce et une puissance à détecter un lien entre les deux processus satisfaisants. Puis, nous avons développé un modèle conjoint mécanistique pour caractériser le lien entre la cinétique du PSA et la survie chez des patients ayant un CPmHR et traités par docetaxel. Le modèle structurel du MNLEM a été défini par un système d'équations différentielles (ODEs) décrivant le mécanisme de production du PSA par des cellules sensibles au docetaxel et des cellules résistantes. La sélection et l'évaluation du modèle ont été détaillées. Le modèle conjoint final souligne le rôle prépondérant sur la survie des cellules résistantes, non-observées. Enfin, nous avons étendu des outils développés dans le contexte linéaire pour faire de la prédiction individuelle dynamique en utilisant un modèle conjoint non-linéaire. Une méthode bayésienne a été mise en place pour fournir la distribution des paramètres individuels. Les performances prédictives du modèle ont pu être évaluées à l'aide de métriques de discrimination et de calibration dépendant du temps. Ces travaux ouvrent la voie au développement de modèles conjoints mécanistiques, qui permettent de tenir compte de l'influence de plusieurs biomarqueurs sur la survie, au moyen d'ODEs, afin d'améliorer l'évaluation thérapeutique et la prédiction

Methodological review showed that time-to-event outcomes are often inadequately handled in cluster randomized trials

International audienceObjectives: To estimate the prevalence of time-to-event (TTE) outcomes in cluster randomized trials (CRTs) and to examine their statistical management. Study design and setting: We searched PubMed to identify primary reports of CRTs published in six major general medical journals (2013-2018). Nature of outcomes and, for TTE outcomes, statistical methods for sample size, analysis, and measures of intracluster correlation were extracted.Results: A TTE analysis was used in 17% of the CRTs (32/184) either as a primary or secondary outcome analysis, or in a sensitivity analysis. Among the five CRTs with a TTE primary outcome, two accounted for both intracluster correlation and the TTE nature of the outcome in sample size calculation; one reported a measure of intracluster correlation in the analysis. Among the 32 CRTs with a least one TTE analysis, 44% (14/32) accounted for clustering in all TTE analyses. We identified 12 additional CRTs in which there was at least one outcome not analyzed as TTE for which a TTE analysis might have been preferred.Conclusion: TTE outcomes are not uncommon in CRTs but appropriate statistical methods are infrequently used. Our results suggest that further methodological development and explicit recommendations for TTE outcomes in CRTs are needed

Nonlinear joint models for individual dynamic prediction of risk of death using Hamiltonian Monte Carlo: application to metastatic prostate cancer

International audienceAbstractBackgroundJoint models of longitudinal and time-to-event data are increasingly used to perform individual dynamic prediction of a risk of event. However the difficulty to perform inference in nonlinear models and to calculate the distribution of individual parameters has long limited this approach to linear mixed-effect models for the longitudinal part. Here we use a Bayesian algorithm and a nonlinear joint model to calculate individual dynamic predictions. We apply this approach to predict the risk of death in metastatic castration-resistant prostate cancer (mCRPC) patients with frequent Prostate-Specific Antigen (PSA) measurements.MethodsA joint model is built using a large population of 400 mCRPC patients where PSA kinetics is described by a biexponential function and the hazard function is a PSA-dependent function. Using Hamiltonian Monte Carlo algorithm implemented in Stan software and the estimated population parameters in this population as priors, the a posteriori distribution of the hazard function is computed for a new patient knowing his PSA measurements until a given landmark time. Time-dependent area under the ROC curve (AUC) and Brier score are derived to assess discrimination and calibration of the model predictions, first on 200 simulated patients and then on 196 real patients that are not included to build the model.ResultsSatisfying coverage probabilities of Monte Carlo prediction intervals are obtained for longitudinal and hazard functions. Individual dynamic predictions provide good predictive performances for landmark times larger than 12 months and horizon time of up to 18 months for both simulated and real data.ConclusionsAs nonlinear joint models can characterize the kinetics of biomarkers and their link with a time-to-event, this approach could be useful to improve patient’s follow-up and the early detection of most at risk patients

Longitudinal analysis of organ-specific tumor lesion sizes in metastatic colorectal cancer patients receiving first line standard chemotherapy in combination with anti-angiogenic treatment

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Using the SAEM algorithm for mechanistic joint models characterizing the relationship between nonlinear PSA kinetics and survival in prostate cancer patients

International audienceJoint modelling is increasingly popular for investigating the relationship between longitudinal and time-to-event data. However numerical complexity often restricts this approach to linear models for the longitudinal part. Here we use a novel development of the Stochastic-Approximation Expectation Maximization algorithm that allows joint models defined by nonlinear mixed-effect models. In the context of chemotherapy in metastatic prostate cancer, we show that a variety of patterns for the Prostate Specific Antigen (PSA) kinetics can be captured by using a mechanistic model defined by nonlinear ordinary differential equations. The use of a mechanistic model predicts that biological quantities that cannot be observed, such as treatment-sensitive and treatment-resistant cells, may have a larger impact than PSA value on survival. This suggests that mechanistic joint models could constitute a relevant approach to evaluate the efficacy of treatment and to improve the prediction of survival in patients

Nonlinear multilevel joint model for individual lesion kinetics and survival to characterize intra-individual heterogeneity in patients with advanced cancer

In advanced cancer patients, tumor burden assessment relies on the Sum of the Longest Diameters (SLD) of the target lesions, a marker that lumps all lesions together and ignores intra-patient heterogeneity. Here, we relied on a rich dataset of 342 metastatic bladder cancer patients treated with a novel immunotherapy agent to develop a Bayesian multilevel joint model that can quantify the heterogeneity in lesion dynamics and measure their impact on survival. Using a nonlinear model of tumor growth inhibition, we estimated that dynamics differed greatly among lesions, and inter-lesion variability accounted for about 35% of the total variance of both tumor shrinkage and treatment effect duration. Next, we investigated the impact of individual lesion dynamics on survival. Lesions located in the liver and in the bladder had twice as much impact on the instantaneous risk of death as compared to those located in the lung or the lymph nodes. Finally we evaluated the gain of individual lesion follow-up for dynamic predictions. Consistent with results at the population levels, the individual lesion model outperformed a model relying only on SLD, especially at early landmark times and in patients having liver or bladder target lesions. Our results show that the use of SLD leads to a loss of information and our model can be used to characterize tumor dynamics and survival of advanced cancer patients

Restricted mean survival time to estimate an intervention effect in a cluster randomized trial

International audienceFor time-to-event outcomes, the difference in restricted mean survival time is a measure of the intervention effect, an alternative to the hazard ratio, corresponding to the expected survival duration gain due to the intervention up to a predefined time t*. We extended two existing approaches of restricted mean survival time estimation for independent data to clustered data in the framework of cluster randomized trials: one based on the direct integration of Kaplan-Meier curves and the other based on pseudo-values regression. Then, we conducted a simulation study to assess and compare the statistical performance of the proposed methods, varying the number and size of clusters, the degree of clustering, and the magnitude of the intervention effect under proportional and non-proportional hazards assumption. We found that the extended methods well estimated the variance and controlled the type I error if there was a sufficient number of clusters (≥ 50) under both proportional and non-proportional hazards assumption. For cluster randomized trials with a limited number of clusters (< 50), a permutation test for pseudo-values regression was implemented and corrected the type I error. We also provided a procedure to estimate permutation-based confidence intervals which produced adequate coverage. All the extended methods performed similarly, but the pseudo-values regression offered the possibility to adjust for covariates. Finally, we illustrated each considered method with a cluster randomized trial evaluating the effectiveness of an asthma-control education program

Nonlinear multilevel joint model for individual lesion kinetics and survival to characterize intra-individual heterogeneity in patients with advanced cancer

In advanced cancer patients, tumor burden assessment relies on the Sum of the Longest Diameters (SLD) of the target lesions, a marker that lumps all lesions together and ignores intra-patient heterogeneity. Here, we relied on a rich dataset of 342 metastatic bladder cancer patients treated with a novel immunotherapy agent to develop a Bayesian multilevel joint model that can quantify the heterogeneity in lesion dynamics and measure their impact on survival. Using a nonlinear model of tumor growth inhibition, we estimated that dynamics differed greatly among lesions, and inter-lesion variability accounted for about 35% of the total variance of both tumor shrinkage and treatment effect duration. Next, we investigated the impact of individual lesion dynamics on survival. Lesions located in the liver and in the bladder had twice as much impact on the instantaneous risk of death as compared to those located in the lung or the lymph nodes. Finally we evaluated the gain of individual lesion follow-up for dynamic predictions. Consistent with results at the population levels, the individual lesion model outperformed a model relying only on SLD, especially at early landmark times and in patients having liver or bladder target lesions. Our results show that the use of SLD leads to a loss of information and our model can be used to characterize tumor dynamics and survival of advanced cancer patients

Childhood cancer survival in France, 2000–2008

International audienceThis paper reports the latest survival data for French childhood cancer patients at the national level. Data from the two French National Registries of Childhood Cancer (Haematopoietic Malignancies and Solid Tumours) were used to describe survival outcomes for 15,479 children diagnosed with cancer between 2000 and 2008 in mainland France. The overall survival was 91.7% at 1 year, 86.9% at 2 years and 81.6% at 5 years. Relative survival did not differ from overall survival even for infants. Survival was lower among infants for lymphoblastic leukaemia and astrocytoma, but higher for neuroblastoma. For all cancers considered together, 5-year survival increased from 79.5% in the first (2000-2002) diagnostic period to 83.2% in the last (2006-2008) period. The improvement was significant for leukaemia, both myeloid and lymphoid, central nervous system tumours (ependymoma) and neuroblastoma. The results remained valid in the multivariate analysis, and, for all cancers combined, the risk of death decreased by 20% between 2000-2002 and 2006-2008. The figures are consistent with various international estimates and are the result of progress in treatment regimens and collaborative clinical trials. The challenge for the French registries is now to study the long-term follow-up of survivors to estimate the incidence of long-term morbidities and adverse effects of treatments