The relationship between SARS-CoV-2 viral load and infectiousness is poorly known. Using data from a cohort of cases and high-risk contacts, we reconstructed viral load at the time of contact and inferred the probability of infection. The effect of viral load was larger in household contacts than in non-household contacts, with a transmission probability as large as 48% when the viral load was greater than 1010 copies per mL. The transmission probability peaked at symptom onset, with a mean probability of transmission of 29%, with large individual variations. The model also projects the effects of variants on disease transmission. Based on the current knowledge that viral load is increased by two- to eightfold with variants of concern and assuming no changes in the pattern of contacts across variants, the model predicts that larger viral load levels could lead to a relative increase in the probability of transmission of 24% to 58% in household contacts, and of 15% to 39% in non-household contacts.
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.”
The relationship between SARS-CoV-2 viral load and infectiousness is not known. Using data from a prospective cohort of index cases and high-risk contact, we reconstructed by modelling the viral load at the time of contact and the probability of infection. The effect of viral load was particularly large in household contacts, with a transmission probability that increased to as much as 37% when the viral load was greater than 10 log 10 copies per mL. The transmission probability peaked at symptom onset in most individuals, with a median probability of transmission of 15%, that hindered large individual variations (IQR: [8, 37]). The model also projects the effects of variants on disease transmission. Based on the current knowledge that viral load is increased by 2 to 4-fold on average, we estimate that infection with B1.1.7 virus could lead to an increase in the probability of transmission by 8 to 17%.
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.
Background: Tumor dynamics typically rely on the sum of the longest diameters (SLD) of target lesions, and ignore heterogeneity in individual lesion dynamics located in different organs. Patients and methods: Here we evaluated the benefit of analyzing lesion dynamics in different organs to predict survival in 900 patients with metastatic urothelial carcinoma treated with atezolizumab or chemotherapy (IMvigor211 trial). Results: Lesion dynamics varied largely across organs, with lymph nodes and lung lesions showing on average a better response to both treatments than those located in the liver and locoregionally. A benefit of atezolizumab was observed on lung and liver lesion dynamics that was attributed to a longer duration of treatment effect as compared to chemotherapy (P value ¼ 0.043 and 0.001, respectively). The impact of lesion dynamics on survival, assessed by a joint model, varied greatly across organs, irrespective of treatment. Liver and locoregional lesion dynamics had a large impact on survival, with an increase of 10 mm of the lesion size increasing the instantaneous risk of death by 12% and 10%, respectively. In comparison, lymph nodes and lung lesions had a lower impact, with a 10-mm increase in the lesion size increasing the instantaneous risk of death by 7% and 5%, respectively. Using our model, we could anticipate the benefit of atezolizumab over chemotherapy as early as 6 months before the end of the study, which is 3 months earlier than a similar model only relying on SLD.
Conclusion:We showed the interest of organ-level tumor follow-up to better understand and anticipate the treatment effect on survival.
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.
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.
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