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

For 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 is calculated using the sum of the longest diameters (SLD) of the target lesions, a measure that lumps all lesions together and ignores intra-patient heterogeneity. Here, we used 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 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 21% and 28% of the total variance in tumor shrinkage and treatment effect duration, respectively. 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 compared to those located in the lung or the lymph nodes. Finally, we evaluated the utility of individual lesion follow-up for dynamic predictions. Consistent with results at the population level, the individual lesion model outperformed a model relying only on SLD, especially at early landmark times and in patients with liver or bladder target lesions. Our results show that an individual lesion model can characterize the heterogeneity in tumor dynamics and its impact on survival in advanced cancer patients.

Assessing the Increased Variability in Individual Lesion Kinetics During Immunotherapy: Does It Exist, and Does It Matter?

PURPOSE: Several studies have raised the hypothesis that immunotherapy may exacerbate the variability in individual lesions, increasing the risk of observing divergent kinetic profiles within the same patient. This questions the use of the sum of the longest diameter to follow the response to immunotherapy. Here, we aimed to study this hypothesis by developing a model that estimates the different sources of variability in lesion kinetics, and we used this model to evaluate the impact of this variability on survival. METHODS: We relied on a semimechanistic model to follow the nonlinear kinetics of lesions and their impact on the risk of death, adjusted on organ location. The model incorporated two levels of random effects to characterize both between- and within-patient variability in response to treatment. The model was estimated on 900 patients from a phase III randomized trial evaluating programmed death-ligand 1 checkpoint inhibitor atezolizumab versus chemotherapy in patients with second-line metastatic urothelial carcinoma (IMvigor211). RESULTS: The within-patient variability in the four parameters that characterize individual lesion kinetics represented between 12% and 78% of the total variability during chemotherapy. Similar results were obtained during atezolizumab, except for the durability of the treatment effects, for which the within-patient variability was markedly larger than during chemotherapy (40% v 12%, respectively). Accordingly, the occurrence of divergent profile consistently increased over time in patients treated with atezolizumab and was equal to about 20% after 1 year of treatment. Finally, we show that accounting for the within-patient variability provided a better prediction of most at-risk patients than a model relying solely on the sum of the longest diameter. CONCLUSION: Within-patient variability provides valuable information for the assessment of treatment efficacy and the detection of at-risk patients.

Modelling the association between biomarkers and clinical outcome: An introduction to nonlinear joint models.

Nonlinear joint models are a powerful tool to precisely analyse the association between a nonlinear biomarker and a time-to-event process, such as death. Here, we review the main methodological techniques required to build these models and to make inferences and predictions. We describe the main clinical applications and discuss the future developments of such models.

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

OBJECTIVES: 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.

Bayesian inference using Hamiltonian Monte-Carlo algorithm for nonlinear joint modeling in the context of cancer immunotherapy.

Treatment evaluation in advanced cancer mainly relies on overall survival and tumor size dynamics. Both markers and their association can be simultaneously analyzed by using joint models, and these approaches are supported by many softwares or packages. However, these approaches are essentially limited to linear models for the longitudinal part, which limit their biological interpretation. More biological models of tumor dynamics can be obtained by using nonlinear models, but they are limited by the fact that parameter identifiability require rich dataset. In that context Bayesian approaches are particularly suited to incorporate the biological knowledge and increase the information available, but they are limited by the high computing cost of Monte-Carlo by Markov Chains algorithms. Here, we aimed to assess the performances of the Hamiltonian Monte-Carlo (HMC) algorithm implemented in Stan for inference in a nonlinear joint model. The method was validated on simulated data where HMC provided proper posterior distributions and credibility intervals in a reasonable computational time. Then the association between tumor size dynamics and survival was assessed in patients with advanced or metastatic bladder cancer treated with atezolizumab, an immunotherapy agent. HMC confirmed limited sensitivity to prior distributions. A cross-validation approach was developed and identified the current slope of tumor size dynamics as the most relevant driver of survival. In summary, HMC is an efficient approach to perform nonlinear joint models in a Bayesian framework, and opens the way for the use of nonlinear models to characterize both the rapid dynamics and the intersubject variability observed during cancer immunotherapy treatment.

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

The purpose of this work is to assess the heterogeneity across organs of response to treatment in metastatic colorectal patient based on longitudinal individual target lesion diameters (ILD) in comparison to sum of tumor lesion diameters (SLD). Data were from the McCAVE trial, in which 189 previously untreated patients with metastatic colorectal carcinoma (mCRC) received either bevacizumab (control, C) or vanucizumab (experimental, E), on top of standard chemotherapy. Bayesian hierarchical longitudinal non-linear mixed effect models were fitted to the data using Hamilton Monte Carlo algorithm to characterize the time dynamics of the tumor burden, and to obtain estimates of the tumor shrinkage and regrowth rates. The ILD model brought more nuanced results than to the SLD model. Besides substantial differences in tumor size at baseline (with lesions located in liver more than twice as large as the ones in lungs), it revealed a more durable response in lesions located in lymph nodes and 'other organs' compared to liver and lungs. Specifically, in lymph nodes and 'other organs', the projected time to nadir was doubled in group E (2.12 and 2.44 years respectively) compared to group C (1.07 and 1.20 years respectively). This long period of tumor shrinkage associated with a slightly larger change from baseline at nadir (- 51.4% in lymph nodes and - 62.6% in 'other organs' in the group E, compared to - 46.2% and - 46.9% in group C) resulted in a clinically meaningful difference in the tumor dynamics of patients in group E compared to the group C. The proportion of variance explained by the inter-lesion variability for each model parameter was large (ranging between 10 and 56%), reflecting the heterogeneity in tumor dynamics across organs. These findings suggest that there is value in understanding both within- and between-patient variability in tumor size's time dynamics using an appropriate modeling framework, as this information may help in pairing the right treatment with individual patient profile.

Association Between Tumor Size Kinetics and Survival in Patients With Urothelial Carcinoma Treated With Atezolizumab: Implication for Patient Follow-Up.

We characterized the association between tumor size kinetics and survival in patients with advanced urothelial carcinoma treated with atezolizumab (anti-programmed death-ligand 1, Tecentriq) using a joint model. The model, developed on data from 309 patients of a phase II clinical trial, identified the time-to-tumor growth and the instantaneous changes in tumor size as the best on-treatment predictors of survival. On the validation dataset containing data from 457 patients from a phase III study, the model predicted individual survival probability using 3-month or 6-month tumor size follow-up data with an area under the receptor-occupancy curve between 0.75 and 0.84, as compared with values comprised between 0.62 and 0.75 when the model included only information available at treatment initiation. Including tumor size kinetics in a relevant statistical framework improves the prediction of survival probability during immunotherapy treatment and may be useful to identify most-at-risk patients in "real-time."

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

BACKGROUND: Joint 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. METHODS: A 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. RESULTS: Satisfying 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. CONCLUSIONS: As 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.

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

Joint modeling 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 Mixed-effect Models for Prostate-specific Antigen Kinetics and Link with Survival in the Context of Metastatic Prostate Cancer: A Comparison by Simulation of Two-stage and Joint Approaches.

In metastatic castration-resistant prostate cancer (mCRPC) clinical trials, the assessment of treatment efficacy essentially relies on the time to death and the kinetics of prostate-specific antigen (PSA). Joint modeling has been increasingly used to characterize the relationship between a time to event and a biomarker kinetics, but numerical difficulties often limit this approach to linear models. Here, we evaluated by simulation the capability of a new feature of the Stochastic Approximation Expectation-Maximization algorithm in Monolix to estimate the parameters of a joint model where PSA kinetics was defined by a mechanistic nonlinear mixed-effect model. The design of the study and the parameter values were inspired from one arm of a clinical trial. Increasingly high levels of association between PSA and survival were considered, and results were compared with those found using two simplified alternatives to joint model, a two-stage and a joint sequential model. We found that joint model allowed for a precise estimation of all longitudinal and survival parameters. In particular, the effect of PSA kinetics on survival could be precisely estimated, regardless of the strength of the association. In contrast, both simplified approaches led to bias on longitudinal parameters, and two-stage model systematically underestimated the effect of PSA kinetics on survival. In summary, we showed that joint model can be used to characterize the relationship between a nonlinear kinetics and survival. This opens the way for the use of more complex and physiological models to improve treatment evaluation and prediction in oncology.

Childhood cancer survival in France, 2000-2008.

This 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.