dataesr/scientific-paragraphs-categorization huggingface dataset:
nfdi4health. de/task-force-covid-19-2)within the framework of a  DFG-project  ( LO-342/17-1 ). LP, VE funded by  Mathematical and Statistical modelling project  ( MUNI/A/1615/2020 ), Online platform for real-time monitoring, analysis and management of epidemic situations ( MUNI/11/02202001/2020 ); VE also supported by  RECETOX research infrastructure (Ministry of Education, Youth and Sports of the Czech Republic :  LM2018121 ), the  CETOCOEN EXCELLENCE  ( CZ. 02. 1. 01/0. 0/0. 0/17-043/0009632 ), RECETOX   RI  project ( CZ. 02. 1. 01/0. 0/0. 0/16-013/0001761 ). NIB funded by  Health Protection Research Unit  (grant code  NIHR200908 ). SAb, SF funded by  Wellcome Trust  ( 210758/Z/18/Z ). Europe. The conclusions of the paper are well supported by the data and are consistent with findings from studies in other countries.
Data availability All source data were openly available before the study, originally available at: https://github. com/ covid19-forecast-hub-europe/covid19-forecast-hub-europe (copy archived at swh:1:rev:b4d66c495e-07c12d88384506154cf58f08592365). All data and code for this study are openly available on Github: covid19-forecast-hub-europe/euro-hub-ensemble.
The principle of an augmented RCT is to include a small proportion of patients with the exclusion criteria of interest in the RCT. This proportion should be small to minimize the risk incurred by completely allowing patients into the trial, but yet sufficient for effectiveness prediction purposes. Before implementing this methodology in a genuine RCT, we set-out to test its potentials and characteristics through different case studies. A first case study used observational data from a cohort of schizophrenia patients. Multiple RCTs comparing two antipsychotic drugs were simulated using this dataset, and augmented with increasing proportions of patients having specific characteristics often used as exclusion criteria (e. g. , history of suicide attempt, alcohol use disorder). RCTs augmented with 10-20% patients having these characteristics allowed for good effectiveness prediction, highlighting the relevance of this methodology to better predict treatments effectiveness.
General methodology For simplicity, we will call the estimated comparative effect from data similar to a traditional RCT "efficacy" while the observed comparative effect in real world will be called "effectiveness". The RCT augmentation methodology is a step-by-step process starting at the trial design stage when one or several exclusion criteria need to be applied (e. g. , for safety, or ethical reasons) although they are known or suspected TEM. The general methodology is explained below and the specific example used in the present case study is depicted in Fig. 1. In a first step, a preferably large real-world dataset (e. g. , observational cohort, electronic healthcare records) is used to estimate the effectiveness of the investigational treatment considered as the target measure for estimation.
Second, from this real-world dataset patients who fulfil the RCT eligibility criteria are randomly selected. From this, multiple augmented RCTs are simulated by re-including patients who would otherwise be excluded at different proportions of augmentation. In these simulated RCTs, patients who would otherwise be totally excluded owing to specific characteristics are re-included in the RCT at different proportions of augmentation. Third, a predictive model is trained on each simulated augmented RCT and tested on real-world data. Estimation accuracy is then measured, thus providing an estimation of the smallest necessary proportion of patients that would be necessary to augment the RCT so as to allow for good estimation of effectiveness. Ultimately, following the conduct of the genuine augmented RCT, the actual RCT data can be used, not only to measure the efficacy of the investigational treatment, but also to estimate its effectiveness.
Study population A simulated dataset of N = 10 6 patients suffering from rrHL was generated, using the Python programming language (Python Software Foundation, https://www. python. org/) [22]  (details in the Supplemental material). Patients' characteristics were generated at a patient-level using information on their distribution as found in the literature (Table  S1 ): age  [23] [24] [25] [26]  (categorized into 5 groups), gender  [27] , disease stage (III vs. IV)  [28] , severe comorbidity (vs. none)  [23]. The correlation between age and comorbidity was taken into account  [23]. We purposely used a simple framework (directed acyclic graph, Fig. S1 ) in which patients were randomly allocated to either of the two therapeutic options (drug A or B) with a 1:1 ratio. Patients' characteristics were not associated with treatment choice, that is, there was no Fig.
1. Predictive modeling using augmented RCT data and providing an estimation of the statistic in the real world, and error made (RMSE) when compared with the "true" statistic rrHL, relapsed/refractory Hodgkin's Lymphoma; RMST, Restricted Mean Survival Time; RMSE, Root Mean Square Error 1: Augmented RCTs are simulated by extracting 1000 random samples of 1200 patients from the simulated real-world population; for each set of simulations, RCTs are including increasing % older patients (or patients with severe comorbidity) 2: An exponential Cox model is trained using the RCT dataset, providing model parameters 3: The model is tested on the real-world population 4: The estimated statistics are compared with the "real" statistics; estimation accuracy is measured using the RMSE * A practical use of the methodology requires a large real-world dataset.
Simulation of augmented RCTs From the simulated dataset of real-world patients, a sample of n = 600 patients in each therapeutic arm was randomized in a 1:1 ratio (typical sample size for oncology Phase-3 RCTs  [29] ). Follow-up lasted 3 years. No loss to follow-up was considered because dropping out from oncology trials is infrequent  [29]. No patient died prior to cancer progression or end of follow-up. The primary endpoint was PFS. The main statistic of interest was the between-arm difference in Restricted Mean Survival Time (RMST) at 3 years, expressed in years and thereafter called the RMST difference. RMST remains valid for non-proportional hazards  [33]  and is now often recommended as a primary endpoint in clinical trials  [34] [35] [36]. It represents the average survival from Time 0 to a specified point in time (here, 3 years) and may be estimated as the area under the survival curve up to that point; the RMST difference is RMST under treatment B minus RMST under treatment A, at 3 years.
The RCT population was augmented from p min = 0% (i. e. , no augmentation) to p max (proportion of older/severely comorbid patients in the simulated real-world population, i. e. , exclusion criteria not applied). The proportions of older patients used to augment the RCT were successively: 0%, 1%, 2%, 3%, 4%, 5%, 6%, 8%, 10%, 15%, 20% and 30%. The proportions of severely comorbid patients used to augment the RCT were successively: 0%, 1%, 2%, 3%, 4%, 5%, 6%, 8%, 10%, 15%, 20% and 29. 7%. All simulations were performed with R software  [37]. The R script and libraries used are provided in Supplemental material.
Analyses and modeling The simulation process is described in Fig. 1  and detailed in Supplemental material. For each simulation of an augmented RCT, the process was repeated 1000 times to minimize sampling error. In each simulated RCT, an exponential Cox model was trained and ridge regularization was used  [38]. The model was then tested in the simulated dataset thus providing estimated RMST difference and HR. The error made using the model was measured using the Root Mean Square Error (RMSE)  [39] , i. e. , the mean distance between the real value of the statistic and the estimated statistics, RMSE = ̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅ 1 K ∑ K j=1 ( ŝj -s ) 2 √ √ √ √ where K is the number of estimated statistics (here, K = 1000), the real value of the statistic and ŝj the estimated statistics.
Limitations of the method Several limitations need to be pointed out. First, we used the same exponential Cox model to generate the PFS in the generated dataset as in the predictive modeling phase. The model was therefore already partially adapted to the data, which may have yielded overly optimistic results. Second, because our primary focus was to gauge how the magnitude of treatment effect modification impacted predictive model accuracy, we used the two exclusion criteria one at the time to compare two different cases. We did not explore the case in which older age and severe comorbidity are simultaneously used as exclusion criteria. This type of simulation introduces additional statistical questions and requires further exploration. Finally, further studies are needed to explore the question of statistical power.
In the present study fully-generated data were used for illustrating and further exploring specific aspects of the methodology. In a real situation, one should use a large real-world dataset, e. g. , electronic medical records, containing information on the interaction between treatment and key eligibility criteria. Because the treatment of interest might not been launched yet (e. g. , first pre-approval Phase 3 RCT), information on treatment effect modification may be estimated using realworld data on the treatment as prescribed in another indication or on a similar treatment or a treatment of the same class, if this is sensible to believe that treatment effect modification will be similar to that of the investigational treatment. In the absence of adequate data, it is still reasonable to consider a priori that augmenting the RCT with 1-5% otherwise-excluded patients will provide sufficient information for effectiveness prediction purposes.
Solving the polynomial equations required to construct splitting methods with additional stages is not a trivial task, especially for orders 5 and 6. In these cases we have used the Python function fsolve of the SciPy library, with a large number of initial points in the space of parameters to start the procedure. From the total number of valid solutions thus obtained, we have selected those leading to reasonably small values of all quantities (4. 6) and checked them on numerical examples. The corresponding values for the most efficient methods we have found by following this approach have been collected in Table  1 , where N A * [p] s refers to a symmetric-conjugate method of type (4. 4) of order p involving s stages, and N B * [p] s is a similar scheme of type (4. 5). For completeness, we have also included the most efficient integrators of order 4, 6 and 8 with real coefficients for systems satisfying the condition (4.
Acknowledgements The work of JB is supported by  ANR-22-CE40-0016 "KEN " of the  Agence Nationale de la Recherche (France)  and by the region  Pays de la Loire (France)  through the project " MasCan ". SB, FC and AE-T acknowledge financial support by  Ministerio de Ciencia e Innovación (Spain)  through project  PID2019-104927GB-C21 ,  MCIN/AEI/10. 13039/501100011033 ,  ERDF  ("A  way of making Europe "). The authors would also like to thank  Prof. C. Lubich  for his very useful remarks.
[41]  and by the proposed method. Computation with Abaqus is carried out by using 16 shell elements S4R (a 4 nodes doubly curved shell with reduced integration, hourglass control and finite membrane strains). In Figure  9 , one can remark that the three numerical methods give three different instants for the panel buckling. 6a ) to solutions given in Ref. [41] , with Abaqus Explicit software  [48]  and with the proposed method with η = 10 -15 , N=20 and δ = 10 -6. For all the computations, 16 finite elements are considered. To explain this difference, several computations have been performed with Abaqus for a different number of shell elements (varying from 25 to 506). Results are exposed in Figure  10. From this plot, it is observed that solutions computed with Abaqus converge towards the one obtained with the perturbation method when number of finite elements is greater than 300.
5. 10 -5 s and 2. 8. 10 -5 s for 100 and 306 elements, respectively. On this figure, time evolution of the parameter t max (Eq. 6), is also plotted for three distinct meshing, with an increasing number of element ranging from 16 to 100. Let recall this parameter t max evaluates the range of validity of asymptotic expansions. It is observed that t max value is approximately the same for the three meshing. It coincides with the time-step value 4. 5. 10 -5 s used in the Abaqus simulations with 100 elements. 6a ) versus time according to the solutions given in Ref. [41] , with Abaqus Explicit software  [48]  with several number of elements and with the proposed method with η = 10 -15 , N=20 and δ = 10 -6. Even if the value of parameter t max evolves a lot during computations, it seems do not depend on the mesh size as the time-step does with classical time integration schemes.
Greater is this latter, greater is the parameter t max. This has been highlighted in the past when using asymptotic expansions in computational solid mechanics  [26]  or fluid dynamics  [27]. In this dynamic buckling analysis, the perturbation method, based on power series of time, is compared with classical time integration methods available in Abaqus software. Computations with the perturbation method are carried out with 16 shell finite elements. To get same coherent results with Abaqus, it is required more than 300 finite elements (see Figure  10 ). This implies very small time-step values and large number of iterations. In that case, truncation order N has to be greater than 10 to compute the solution with approximately the same number of continuation steps. As with a classical explicit time integration scheme, only a single matrix triangulation is needed for all the continuation step of the perturbation method.
For the second problem, comparisons were carried out with results available in the literature and computed with the commercial Abaqus software. For both problems, it was shown that explicit ANM predictions were very coherent. For the first problem, the wave propagation nature of the solution is preserved. For same meshing, the ANM solution is close to the implicit Newmark based solution computed with the smallest time-step value. For the second problem, influence of the regularization parameter in the external forcing was established and it was demonstrated that a very small value was necessary. ANM solution also described the non-linear dynamics of the panel. Trigger instant of the buckling and postbifurcated displacement were correctly obtained. Surprisingly, this study allowed for questioning some previous well-established results.
*    This research was financed by the  ANR  project  HOSIGRA  ( ANR-17-CE40-0022 ) and the  IFCAM project "Applications of graph homomorphisms " ( MA/IFCAM/18/39 ). The research of the first author was partially financed by the  French government IDEX-ISITE  initiative  16-IDEX-0001  ( CAP 20-25 ). The third author was supported by the project with grant number:  NSFC 11871439 , and was also supported by  Fujian Provincial Department of Science and Technology ( 2020J01268 ). 1.
Thus, a proper value for U which minimizes EP(i, U ) will be chosen between these two extreme cases. The global prediction error for the whole population is computed with EP(U ) = i EP(i, U ). We retain the matrix U which minimizes EP among a trial of tested values and we denote θ, Ψ, b i, i∈ 1, n the corresponding estimator. In the following, we use the subscript M L to denote the ML estimator. For solving the optimization problems required for computing our inner and outer criteria, we use the Nelder-Mead algorithm implemented in the optimr package  Nash (2016). All optimization algorithms used by the estimation methods require a starting guess value. We start from the true parameter value for each of them. By doing so, we aim to do not mix two distinct problems: 1)the numerical stability of the estimation procedures, 2)the intrinsic accuracy of the different estimators.
Real data analysis We now proceed to the estimation using real data presented in  Pasin et al. (2019)  from which the parameter values given in table 4. 3 come from. In  Pasin et al. (2019)  , the estimation is made from cohorts coming from three phase I trials performed in African and European countries. Each subject was vaccinated with two doses, Ad26. ZEBOV (Janssen Vaccines and Prevention) and MVA-BN-Filo (Bavarian Nordic). In these cohorts, both the effect of injection order, either Ad26. ZEBOV first and MVA-BN-Filo second, or MVA-BN-Filo first and Ad26. ZEBOV second, and the delay between, 28 or 56 days, were evaluated. In this study, we focus on an east African subpopulation where Ad26. ZEBOV was injected first and then MVA-BN-Filo with a delay of 28 days between the two doses. As in  Pasin et al.
(2019)  and the simulation section, to stay in the temporal domain of validity of the model we use measurements made seven days after the second dose injection. It leaves us with 5 measurements of antibody concentration between days 7 up to days 330 per subject. The estimation in the original work has been done using the NIMROD software  Prague et al. (2013)  and log-transformed antibody concentration measurement. We now estimate the parameters with our method with the aim to compare our results with the existing one. We used the same prior distribution π(θ) ∼ N                 -1 0 0 -4. 1         ,         25 0 0 0 0 100 0 0 0 0 100 0 0 0 0 1                 for θ = (ψ δS , ψ φS , ψ φL , ψ δAb ) as the one defined in the NIMROD software. We choose our mesh-size such that we get 200 discretization points for each subject on the observation interval and we use U = 10 i.
In addition, bypass- ing estimation of initial conditions represents a clear advantage for partially observed systems comparing to likelihood based approaches, as emphasized in simulations. Still, this benefit in term of estimation accuracy comes with a computational price. On a server with the parallelization package Snow in R language, it takes approximately 10-15 minutes to obtain an estimation for the two-dimensional linear model, 30 minutes for the insulin model and 3-4 hour for the antibody concentration evolution one, whereas it was a matter of minutes for the other approaches. Nevertheless, the use of compiled languages and proper parallelization could reduce the computation time. Moreover, we have willingly separated the formal definition of the optimal control problem required by our method and the numerical procedure used to solve it, in case it may exist better suited approaches for this specific control problem.
Patients Included in This Study We included all patients aged ≥18 years with suspected or proven COVID-19 as evaluated by the recruiting physician; who completed Covidom registration; and who had a date of COVID-19 symptom onset earlier than November 1, 2021. We also considered suspected cases, as during the first months of the pandemic, positive reverse transcription polymerase chain reaction (RT-PCR) tests were not mandatory in the French health authorities' case definition. At that time, RT-PCR testing was not widely available and was reserved for the most severe cases. Eligible patients were matched with 2 complementary databases: the AP-HP data warehouse (Entrepôt de données de santé de l'AP-HP) and the French National Institute of Statistics and Economic Studies lists of deaths  [11].
Evaluation of Covidom Safety To assess the safety of Covidom, we considered alert handling time by type of alert, patient clinical worsening, and medical contacts outside of Covidom, reported by the patients in their follow-up questionnaires. We evaluated the time to alert first response and the time to alert resolution by comparing the values for both normal and high-priority alerts. In addition, we compared the rate of EMS dispatch events in high-and normal-priority alerts to assess the pertinence of priority classification. Clinical worsening was defined as either hospitalization (or, in the case of patients included at hospital discharge, rehospitalization) or death within 30 days after the date of first symptoms and hospital discharge, respectively. This information was obtained either from hospitalization data by matching with the AP-HP data warehouse, from responses to follow-up questionnaires, or from end-of-monitoring reasons when RMRs systematically called back patients who stopped responding to their daily monitoring questionnaires.
Economic Assessment of Covidom We reported the total cost of operating Covidom, including costs related to regional control center, RMRs, and technical support (eg, application development), divided into staff, information technology, and structural and administration costs. We then estimated the health care costs of patients included in Covidom by computing both out-of-hospital and hospitalization costs. The out-of-hospital costs were obtained from the medical contacts reported in day-14 and day-30 follow-up questionnaires and from medical contacts initiated by RMRs. These included consultations, calls to EMS regulation centers, ED visits, and EMS dispatches. The unit costs and sources for cost computations are presented in Multimedia Appendix 2  [13] [14] [15]. Hospitalization costs were estimated for patients included in Covidom and those hospitalized in one of the AP-HP hospitals, as identified through data matching with the AP-HP data warehouse.
Comparison Among Mild COVID-19 Cases Presenting at AP-HP EDs Although it was impossible to compare the total health care costs of patients with mild COVID-19 included in Covidom with a similar population not included in Covidom, the AP-HP data warehouse allowed us to compare the delay until hospitalization and hospitalization costs between these populations. We considered all patients who had an initial consultation for COVID-19 at an AP-HP hospital ED and who were not hospitalized within 24 hours of this initial consultation as mild COVID-19 patients at the time of the consultation and thus eligible to be included in Covidom. We reported the number, age, and sex of these patients. For patients who were later hospitalized, we compared the delay in days from ED consultation to hospitalization and the hospitalization costs between patients effectively included in Covidom and those who were not.
Diagnostic confirmation of the included patients remained low in the first months because of the limited access to RT-PCR tests in France until June 2020 and the prioritization of severe COVID-19 cases over mild cases in accessing tests. During the summer months of 2020, from the end of the first lockdown in May to the uptake of the epidemic in September, the number of inclusions remained low (n=2049 from May 11, 2020, to August 31, 2020), which explains the relatively high number of negative cases included. Tests may also yield false positives, particularly during the early months of the pandemic. As 78% (46,869/60,073) of patients did not answer follow-up questionnaires, there was a risk of missing a significant portion of the health care cost data and a risk of self-selection bias among respondents to the satisfaction questions.
Acknowledgments The authors would like to thank the Nouveal-e Santé team and, in particular,  Falzon Alexandre ,  Fayolle Guillaume ,  Laporte Fanny , and  Amélie Tortel  for their help with the mobile application and regional center surveillance interface development. The authors would also like to thank  Debastard Laurent ,  Grenier Alexandre ,  Hody Julien ,  Penn Thomas , and the  Paris Region Union régionale des professionnels de santé  for their help in the development and spread of the Covidom solution. The authors would like to thank  Banzet Amélie ,  Marchand-Arvier Jerôme ,  Schmidt Nicolas ,  Villie Pascaline , and  Mosquet Nathalie  from  Assistance Publique-Hôpitaux de Paris  headquarters for their invaluable help. Finally, the authors would like to extend their thanks to all the people involved in operating and including patients in Covidom, whose names are listed in Multimedia Appendix 4.