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Even after resection of early-stage non-small-cell lung cancer (NSCLC), patients have a high risk of developing recurrence and second primary lung cancer. We aimed to assess efficacy of a follow-up approach including clinic visits, chest x-rays, chest CT scans, and fibre-optic bronchoscopy versus clinical visits and chest x-rays after surgery for resectable NSCLC. In this multicentre, open-label, randomised, phase 3 trial (IFCT-0302), patients aged 18 years or older and after complete resection of pathological stage I–IIIA NSCLC according to the sixth edition of the TNM classification were enrolled within 8 weeks of resection from 122 hospitals and tertiary centres in France. Patients were randomly assigned (1:1) to CT-based follow-up (clinic visits, chest x-rays, thoraco-abdominal CT scans, and fibre-optic bronchoscopy for non-adenocarcinoma histology) or minimal follow-up (visits and chest x-rays) after surgery for NSCLC, by means of a computer-generated sequence using the minimisation method. Procedures were repeated every 6 months for the first 2 years and yearly until 5 years. The primary endpoint was overall survival analysed in the intention-to-treat population. Secondary endpoints, also analysed in the intention-to-treat population, included disease-free survival. This trial is registered with ClinicalTrials.gov, NCT00198341, and is active, but not enrolling. Between Jan 3, 2005, and Nov 30, 2012, 1775 patients were enrolled and randomly assigned to a follow-up group (888 patients to the minimal follow-up group; 887 patients to the CT-based follow-up group). Median overall survival was not significantly different between follow-up groups (8·5 years [95% CI 7·4–9·6] in the minimal follow-up group vs 10·3 years [8·1–not reached] in the CT-based follow-up group; adjusted hazard ratio [HR] 0·95, 95% CI 0·83–1·10; log-rank p=0·49). Disease-free survival was not significantly different between follow-up groups (median not reached [95% CI not estimable–not estimable] in the minimal follow-up group vs 4·9 [4·3–not reached] in the CT-based follow-up group; adjusted HR 1·14, 95% CI 0·99–1·30; log-rank p=0·063). Recurrence was detected in 246 (27·7%) of 888 patients in the minimal follow-up group and in 289 (32·6%) patients of 887 in the CT-based follow-up group. Second primary lung cancer was diagnosed in 27 (3·0%) patients in the minimal follow-up group and 40 patients (4·5%) in the CT-based follow-up group. No serious adverse events related to the trial procedures were reported. The addition of thoracic CT scans during follow-up, which included clinic visits and chest x-rays after surgery, did not result in longer survival among patients with NSCLC. However, it did enable the detection of more cases of early recurrence and second primary lung cancer, which are more amenable to curative-intent treatment, supporting the use of CT-based follow-up, especially in countries where lung cancer screening is already implemented, alongside with other supportive measures. French Health Ministry, French National Cancer Institute, Weisbrem-Benenson Foundation, La Ligue Nationale Contre Le Cancer, and Lilly Oncology. For the French translation of the abstract see Supplementary Materials section.

We present a unifying, tractable approach for studying the spread of viruses causing complex diseases requiring to be modeled using a large number of types (e.g., infective stage, clinical state, risk factor class). We show that recording each infected individual’s infection age, i.e., the time elapsed since infection, has three benefits. First, regardless of the number of types, the age distribution of the population can be described by means of a first-order, one-dimensional partial differential equation (PDE) known as the McKendrick-von Foerster equation. The frequency of type i is simply obtained by integrating the probability of being in state i at a given age against the age distribution. This representation induces a simple methodology based on the additional assumption of Poisson sampling to infer and forecast the epidemic. We illustrate this technique using French data from the COVID-19 epidemic. Second, our approach generalizes and simplifies standard compartmental models using high-dimensional systems of ordinary differential equations (ODEs) to account for disease complexity. We show that such models can always be rewritten in our framework, thus, providing a low-dimensional yet equivalent representation of these complex models. Third, beyond the simplicity of the approach, we show that our population model naturally appears as a universal scaling limit of a large class of fully stochastic individual-based epidemic models, where the initial condition of the PDE emerges as the limiting age structure of an exponentially growing population starting from a single individual.

We study a polygenic trait under stabilizing selection at statistical equilibrium, where genetic effect, mutation rate and mutational bias are heterogeneous across loci. The model assumes L biallelic sites subject to reversible mutations, each allele described by its frequency in the population. Using a diffusion approximation, a mean-field approximation and neglecting linkage disequilibrium, we predict consistent phenomena across several regimes of selection: (1) a small deviation Δ* of the trait mean from its optimal value appears and persists due to genetic mutations not aligned with selection; (2) while this deviation is often undetectable at the trait level, it leaves a substantial signature at the locus level by favoring alleles reducing it, resulting in genic selection with mean coefficient s* proportional to Δ* acting pervasively; (3) with stronger selection on the trait, (3a) the value of Δ* is decreased but the intensity of genic selection is increased in inverse proportion, resulting in an essentially constant, non negligible value of s*. We show how the stationary distribution of allelic frequencies can be obtained from Δ*. The latter can then be characterized as the solution to a fixed-point equation. Finally, we quantify several macroscopic observables of interest (genetic variance, description of the fluctuations of the trait mean as an Ornstein-Uhlenbeck process). The orders of magnitude of the macroscopic observables can be derived on a wide region of the parameter space. The model shows good fit and can straightforwardly be extended to accommodate pleiotropy, dominance, and some forms of epistasis. We also discuss the different breakdown which may occur (Bulmer effect, Hill-Robertson effect, breakdown of the Ornstein-Uhlenbeck approximation for the dynamics of the trait mean, depletion of genetic variability due to low mutation rates).Competing Interest StatementThe authors have declared no competing interest.Footnotes* Numbered lines and changed the link to the code to comply with demands from PCI.* https://doi.org/10.5281/zenodo.18877448Funder Information DeclaredInstitut de Biologie de l'École Normale Supérieure, https://ror.org/03mxktp47Centre Interdisciplinaire de Recherche en Biologie, https://ror.org/01mvzn566University of Vienna, https://ror.org/03prydq77

Modelling the evolution of a continuous trait in a biological population is one of the oldest problems in evolutionary biology, which led to the birth of quantitative genetics. With the recent development of GWAS methods, it has become essential to link the evolution of the trait distribution to the underlying evolution of allelic frequencies at many loci, co-contributing to the trait value. The way most articles go about this is to make assumptions on the trait distribution, and use Wright's formula to model how the evolution of the trait translates on each individual locus. Here, we take a gene's eye-view of the system, starting from an explicit finite-loci model with selection, drift, recombination and mutation, in which the trait value is a direct product of the genome. We let the number of loci go to infinity under the assumption of strong recombination, and characterize the limit behavior of a given locus with a McKean-Vlasov SDE and the corresponding Fokker-Planck IPDE. In words, the selection on a typical locus depends on the mean behaviour of the other loci which can be approximated with the law of the focal locus. Results include the independence of two loci and explicit stationary distribution for allelic frequencies at a given locus (under some assumptions on the fitness function).

We present a unifying, tractable approach for studying the spread of viruses causing complex diseases requiring to be modeled using a large number of types (e.g., infective stage, clinical state, risk factor class). We show that recording each infected individual's infection age, i.e., the time elapsed since infection, has three benefits. First, regardless of the number of types, the age distribution of the population can be described by means of a first-order, one-dimensional partial differential equation (PDE) known as the McKendrick-von Foerster equation. The frequency of type \\(i\\) is simply obtained by integrating the probability of being in state \\(i\\) at a given age against the age distribution. This representation induces a simple methodology based on the additional assumption of Poisson sampling to infer and forecast the epidemic. We illustrate this technique using French data from the COVID-19 epidemic. Second, our approach generalizes and simplifies standard compartmental models using high-dimensional systems of ordinary differential equations (ODEs) to account for disease complexity. We show that such models can always be rewritten in our framework, thus, providing a low-dimensional yet equivalent representation of these complex models. Third, beyond the simplicity of the approach, we show that our population model naturally appears as a universal scaling limit of a large class of fully stochastic individual-based epidemic models, where the initial condition of the PDE emerges as the limiting age structure of an exponentially growing population starting from a single individual.