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.

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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.

The impact of variants of concern (VoC) on SARS-CoV-2 viral dynamics remains poorly understood and essentially relies on observational studies subject to various sorts of biases. In contrast, experimental models of infection constitute a powerful model to perform controlled comparisons of the viral dynamics observed with VoC and better quantify how VoC escape from the immune response. Here we used molecular and infectious viral load of 78 cynomolgus macaques to characterize in detail the effects of VoC on viral dynamics. We first developed a mathematical model that recapitulate the observed dynamics, and we found that the best model describing the data assumed a rapid antigen-dependent stimulation of the immune response leading to a rapid reduction of viral infectivity. When compared with the historical variant, all VoC except beta were associated with an escape from this immune response, and this effect was particularly sensitive for delta and omicron variant (p<10-6 for both). Interestingly, delta variant was associated with a 1.8-fold increased viral production rate (p=0.046), while conversely omicron variant was associated with a 14-fold reduction in viral production rate (p<10-6). During a natural infection, our models predict that delta variant is associated with a higher peak viral RNA than omicron variant (7.6 log10 copies/mL 95% CI 6.8 – 8 for delta; 5.6 log10 copies/mL 95% CI 4.8 – 6.3 for omicron) while having similar peak infectious titers (3.7 log10 PFU/mL 95% CI 2.4 – 4.6 for delta; 2.8 log10 PFU/mL 95% CI 1.9 – 3.8 for omicron). These results provide a detailed picture of the effects of VoC on total and infectious viral load and may help understand some differences observed in the patterns of viral transmission of these viruses.

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.