Surrogate Marker Assessment Using Mediation and Instrumental Variable Analyses in a Case-Cohort Design

The identification of surrogate markers for gold standard outcomes in clinical trials enables future cost-effective trials that target the identified markers. Due to resource limitations, these surrogate markers may be collected only for cases and for a subset of the trial cohort, giving rise to what is termed the case-cohort design. Motivated by a COVID-19 vaccine trial, we propose methods of assessing the surrogate markers for a time-to-event outcome in a case-cohort design by using mediation and instrumental variable (IV) analyses. In the mediation analysis we decomposed the vaccine effect on COVID-19 risk into an indirect effect (the effect mediated through the surrogate marker such as neutralizing antibodies) and a direct effect (the effect not mediated by the marker), and we propose that the mediation proportions are surrogacy indices. In the IV analysis we aimed to quantify the causal effect of the surrogate marker on disease risk in the presence of surrogatedisease confounding which is unavoidable even in randomized trials. We employed weighted estimating equations derived from nonparametric maximum likelihood estimators (NPMLEs) under semiparametric probit models for the time-to-disease outcome. We plugged in the weighted NPMLEs to construct estimators for the aforementioned causal effects and surrogacy indices, and we determined the asymptotic properties of the proposed estimators. Finite sample performance was evaluated in numerical simulations. Applying the proposed mediation and IV analyses to a mock COVID-19 vaccine trial data, we found that 84.2% of the vaccine efficacy was mediated by 50% pseudovirus neutralizing antibody and that neutralizing antibodies had significant protective effects for COVID-19 risk.

Assessing potential insights of an imperfect testing strategy: Parameter estimation and practical identifiability using early COVID-19 data in India.

A deterministic model with testing of infected individuals has been proposed to investigate the potential consequences of the impact of testing strategy. The model exhibits global dynamics concerning the disease-free and a unique endemic equilibrium depending on the basic reproduction number when the recruitment of infected individuals is zero; otherwise, the model does not have a disease-free equilibrium, and disease never dies out in the community. Model parameters have been estimated using the maximum likelihood method with respect to the data of early COVID-19 outbreak in India. The practical identifiability analysis shows that the model parameters are estimated uniquely. The consequences of the testing rate for the weekly new cases of early COVID-19 data in India tell that if the testing rate is increased by 20% and 30% from its baseline value, the weekly new cases at the peak are decreased by 37.63% and 52.90%; and it also delayed the peak time by four and fourteen weeks, respectively. Similar findings are obtained for the testing efficacy that if it is increased by 12.67% from its baseline value, the weekly new cases at the peak are decreased by 59.05% and delayed the peak by 15 weeks. Therefore, a higher testing rate and efficacy reduce the disease burden by tumbling the new cases, representing a real scenario. It is also obtained that the testing rate and efficacy reduce the epidemic's severity by increasing the final size of the susceptible population. The testing rate is found more significant if testing efficacy is high. Global sensitivity analysis using partial rank correlation coefficients (PRCCs) and Latin hypercube sampling (LHS) determine the key parameters that must be targeted to worsen/contain the epidemic.

Agent-based mathematical model of COVID-19 spread in Novosibirsk region: Identifiability, optimization and forecasting

The problem of identification of unknown epidemiological parameters (contagiosity, the initial number of infected individuals, probability of being tested) of an agent-based model of COVID-19 spread in Novosibirsk region is solved and analyzed. The first stage of modeling involves data analysis based on the machine learning approach that allows one to determine correlated datasets of performed PCR tests and number of daily diagnoses and detect some features (seasonality, stationarity, data correlation) to be used for COVID-19 spread modeling. At the second stage, the unknown model parameters that depend on the date of introducing of containment measures are calibrated with the usage of additional measurements such as the number of daily diagnosed and tested people using PCR, their daily mortality rate and other statistical information about the disease. The calibration is based on minimization of the misfit function for daily diagnosed data. The OPTUNA optimization framework with tree-structured Parzen estimator and covariance matrix adaptation evolution strategy is used to minimize the misfit function. Due to ill-posedness of identification problem, the identifiability analysis is carried out to construct the regularization algorithm. At the third stage, the identified parameters of COVID-19 for Novosibirsk region and different scenarios of COVID-19 spread are analyzed in relation to introduced quarantine measures. This kind of modeling can be used to select effective anti-pandemic programs. © 2023 Walter de Gruyter GmbH, Berlin/Boston 2023.

A general modeling framework for quantitative tracking, accurate prediction of ICU, and assessing vaccination for COVID-19 in Chile.

Background: One of the main lessons of the COVID-19 pandemic is that we must prepare to face another pandemic like it. Consequently, this article aims to develop a general framework consisting of epidemiological modeling and a practical identifiability approach to assess combined vaccination and non-pharmaceutical intervention (NPI) strategies for the dynamics of any transmissible disease. Materials and methods: Epidemiological modeling of the present work relies on delay differential equations describing time variation and transitions between suitable compartments. The practical identifiability approach relies on parameter optimization, a parametric bootstrap technique, and data processing. We implemented a careful parameter optimization algorithm by searching for suitable initialization according to each processed dataset. In addition, we implemented a parametric bootstrap technique to accurately predict the ICU curve trend in the medium term and assess vaccination. Results: We show the framework's calibration capabilities for several processed COVID-19 datasets of different regions of Chile. We found a unique range of parameters that works well for every dataset and provides overall numerical stability and convergence for parameter optimization. Consequently, the framework produces outstanding results concerning quantitative tracking of COVID-19 dynamics. In addition, it allows us to accurately predict the ICU curve trend in the medium term and assess vaccination. Finally, it is reproducible since we provide open-source codes that consider parameter initialization standardized for every dataset. Conclusion: This work attempts to implement a holistic and general modeling framework for quantitative tracking of the dynamics of any transmissible disease, focusing on accurately predicting the ICU curve trend in the medium term and assessing vaccination. The scientific community could adapt it to evaluate the impact of combined vaccination and NPIs strategies for COVID-19 or any transmissible disease in any country and help visualize the potential effects of implemented plans by policymakers. In future work, we want to improve the computational cost of the parametric bootstrap technique or use another more efficient technique. The aim would be to reconstruct epidemiological curves to predict the combined NPIs and vaccination policies' impact on the ICU curve trend in real-time, providing scientific evidence to help anticipate policymakers' decisions.

Multiple cohort study of hospitalized SARS-CoV-2 in-host infection dynamics: Parameter estimates, identifiability, sensitivity and the eclipse phase profile.

Within-host SARS-CoV-2 modelling studies have been published throughout the COVID-19 pandemic. These studies contain highly variable numbers of individuals and capture varying timescales of pathogen dynamics; some studies capture the time of disease onset, the peak viral load and subsequent heterogeneity in clearance dynamics across individuals, while others capture late-time post-peak dynamics. In this study, we curate multiple previously published SARS-CoV-2 viral load data sets, fit these data with a consistent modelling approach, and estimate the variability of in-host parameters including the basic reproduction number, R0, as well as the best-fit eclipse phase profile. We find that fitted dynamics can be highly variable across data sets, and highly variable within data sets, particularly when key components of the dynamic trajectories (e.g. peak viral load) are not represented in the data. Further, we investigated the role of the eclipse phase time distribution in fitting SARS-CoV-2 viral load data. By varying the shape parameter of an Erlang distribution, we demonstrate that models with either no eclipse phase, or with an exponentially-distributed eclipse phase, offer significantly worse fits to these data, whereas models with less dispersion around the mean eclipse time (shape parameter two or more) offered the best fits to the available data across all data sets used in this work. This manuscript was submitted as part of a theme issue on "Modelling COVID-19 and Preparedness for Future Pandemics".

Estimating a time-to-event distribution from right-truncated data in an epidemic: A review of methods.

Time-to-event data are right-truncated if only individuals who have experienced the event by a certain time can be included in the sample. For example, we may be interested in estimating the distribution of time from onset of disease symptoms to death and only have data on individuals who have died. This may be the case, for example, at the beginning of an epidemic. Right truncation causes the distribution of times to event in the sample to be biased towards shorter times compared to the population distribution, and appropriate statistical methods should be used to account for this bias. This article is a review of such methods, particularly in the context of an infectious disease epidemic, like COVID-19. We consider methods for estimating the marginal time-to-event distribution, and compare their efficiencies. (Non-)identifiability of the distribution is an important issue with right-truncated data, particularly at the beginning of an epidemic, and this is discussed in detail. We also review methods for estimating the effects of covariates on the time to event. An illustration of the application of many of these methods is provided, using data on individuals who had died with coronavirus disease by 5 April 2020.

Comprehensive investigation of pathway enrichment methods for functional interpretation of LC-MS global metabolomics data.

BACKGROUND: Global or untargeted metabolomics is widely used to comprehensively investigate metabolic profiles under various pathophysiological conditions such as inflammations, infections, responses to exposures or interactions with microbial communities. However, biological interpretation of global metabolomics data remains a daunting task. Recent years have seen growing applications of pathway enrichment analysis based on putative annotations of liquid chromatography coupled with mass spectrometry (LC-MS) peaks for functional interpretation of LC-MS-based global metabolomics data. However, due to intricate peak-metabolite and metabolite-pathway relationships, considerable variations are observed among results obtained using different approaches. There is an urgent need to benchmark these approaches to inform the best practices. RESULTS: We have conducted a benchmark study of common peak annotation approaches and pathway enrichment methods in current metabolomics studies. Representative approaches, including three peak annotation methods and four enrichment methods, were selected and benchmarked under different scenarios. Based on the results, we have provided a set of recommendations regarding peak annotation, ranking metrics and feature selection. The overall better performance was obtained for the mummichog approach. We have observed that a ~30% annotation rate is sufficient to achieve high recall (~90% based on mummichog), and using semi-annotated data improves functional interpretation. Based on the current platforms and enrichment methods, we further propose an identifiability index to indicate the possibility of a pathway being reliably identified. Finally, we evaluated all methods using 11 COVID-19 and 8 inflammatory bowel diseases (IBD) global metabolomics datasets.

The Structural Identifiability of a Humidity-Driven Epidemiological Model of Influenza Transmission.

Influenza epidemics cause considerable morbidity and mortality every year worldwide. Climate-driven epidemiological models are mainstream tools to understand seasonal transmission dynamics and predict future trends of influenza activity, especially in temperate regions. Testing the structural identifiability of these models is a fundamental prerequisite for the model to be applied in practice, by assessing whether the unknown model parameters can be uniquely determined from epidemic data. In this study, we applied a scaling method to analyse the structural identifiability of four types of commonly used humidity-driven epidemiological models. Specifically, we investigated whether the key epidemiological parameters (i.e., infectious period, the average duration of immunity, the average latency period, and the maximum and minimum daily basic reproductive number) can be uniquely determined simultaneously when prevalence data is observable. We found that each model is identifiable when the prevalence of infection is observable. The structural identifiability of these models will lay the foundation for testing practical identifiability in the future using synthetic prevalence data when considering observation noise. In practice, epidemiological models should be examined with caution before using them to estimate model parameters from epidemic data.

Comparison of Hawkes and Seir Models for the Spread of Covid-19

Two models that capture the spread of infectious diseases, the Hawkes point process model and the SEIR compartmental model, are compared with regard to their use in modeling the COVID-19 pandemic. The physical plausibility of the SEIR model is weighed against the parsimony and flexibility of the Hawkes model. The mathematical connection between Hawkes and SEIR models is described.

IDENTIFIABILITY OF INFECTION MODEL PARAMETERS EARLY IN AN EPIDEMIC.

It is known that the parameters in the deterministic and stochastic SEIR epidemic models are structurally identifiable. For example, from knowledge of the infected population time series I(t) during the entire epidemic, the parameters can be successfully estimated. In this article we observe that estimation will fail in practice if only infected case data during the early part of the epidemic (prepeak) is available. This fact can be explained using a well-known phenomenon called dynamical compensation. We use this concept to derive an unidentifiability manifold in the parameter space of SEIR that consists of parameters indistinguishable from I(t) early in the epidemic. Thus, identifiability depends on the extent of the system trajectory that is available for observation. Although the existence of the unidentifiability manifold obstructs the ability to exactly determine the parameters, we suggest that it may be useful for uncertainty quantification purposes. A variant of SEIR recently proposed for COVID-19 modeling is also analyzed, and an analogous unidentifiability surface is derived.

A comparison and calibration of integer and fractional-order models of COVID-19 with stratified public response.

The spread of SARS-CoV-2 in the Canadian province of Ontario has resulted in millions of infections and tens of thousands of deaths to date. Correspondingly, the implementation of modeling to inform public health policies has proven to be exceptionally important. In this work, we expand a previous model of the spread of SARS-CoV-2 in Ontario, "Modeling the impact of a public response on the COVID-19 pandemic in Ontario, " to include the discretized, Caputo fractional derivative in the susceptible compartment. We perform identifiability and sensitivity analysis on both the integer-order and fractional-order SEIRD model and contrast the quality of the fits. We note that both methods produce fits of similar qualitative strength, though the inclusion of the fractional derivative operator quantitatively improves the fits by almost 27% corroborating the appropriateness of fractional operators for the purposes of phenomenological disease forecasting. In contrasting the fit procedures, we note potential simplifications for future study. Finally, we use all four models to provide an estimate of the time-dependent basic reproduction number for the spread of SARS-CoV-2 in Ontario between January 2020 and February 2021.

Limits of epidemic prediction using SIR models.

The Susceptible-Infectious-Recovered (SIR) equations and their extensions comprise a commonly utilized set of models for understanding and predicting the course of an epidemic. In practice, it is of substantial interest to estimate the model parameters based on noisy observations early in the outbreak, well before the epidemic reaches its peak. This allows prediction of the subsequent course of the epidemic and design of appropriate interventions. However, accurately inferring SIR model parameters in such scenarios is problematic. This article provides novel, theoretical insight on this issue of practical identifiability of the SIR model. Our theory provides new understanding of the inferential limits of routinely used epidemic models and provides a valuable addition to current simulate-and-check methods. We illustrate some practical implications through application to a real-world epidemic data set.

Mathematical Model for Medium-Term Covid-19 Forecasts in Kazakhstan

In this paper has been formulated and solved the problem of identifying unknown parameters of the mathematical model describing the spread of COVID-19 infection in Kazakhstan, based on additional statistical information about infected, recovered and fatal cases. The considered model, which is part of the family of modified models based on the SIR model developed by W. Kermak and A. McKendrick in 1927, is presented as a system of 5 nonlinear ordinary differential equations describing the variational transition of individuals from one group to another. By solving the inverse problem, reduced to solving the optimization problem of minimizing the functional, using the differential evolution algorithm proposed by Rainer Storn and Kenneth Price in 1995 on the basis of simple evolutionary problems in biology, the model parameters were refined and made a forecast and predicted a peak of infected, recovered and deaths among the population of the country. The differential evolution algorithm includes the generation of populations of probable solutions randomly created in a predetermined space, sampling of the algorithm's stopping criterion, mutation, crossing and selection.

Understanding the Role of Environmental Transmission on COVID-19 Herd Immunity and Invasion Potential.

COVID-19 is caused by the SARS-CoV-2 virus, which is mainly transmitted directly between humans. However, it is observed that this disease can also be transmitted through an indirect route via environmental fomites. The development of appropriate and effective vaccines has allowed us to target and anticipate herd immunity. Understanding of the transmission dynamics and the persistence of the virus on environmental fomites and their resistive role on indirect transmission of the virus is an important scientific and public health challenge because it is essential to consider all possible transmission routes and route specific transmission strength to accurately quantify the herd immunity threshold. In this paper, we present a mathematical model that considers both direct and indirect transmission modes. Our analysis focuses on establishing the disease invasion threshold, investigating its sensitivity to both transmission routes and isolate route-specific transmission rate. Using the tau-leap algorithm, we perform a stochastic model simulation to address the invasion potential of both transmission routes. Our analysis shows that direct transmission has a higher invasion potential than that of the indirect transmission. As a proof of this concept, we fitted our model with early epidemic data from several countries to uniquely estimate the reproduction numbers associated with direct and indirect transmission upon confirming the identifiability of the parameters. As the indirect transmission possess lower invasion potential than direct transmission, proper estimation and necessary steps toward mitigating it would help reduce vaccination requirement.

STRUCTURAL AND PRACTICAL IDENTIFIABILITY ANALYSES ON THE TRANSMISSION DYNAMICS OF COVID-19 IN THE UNITED STATES∗

We formulate an epidemic model to capture essential epidemiology of COVID-19 and major public health interventions. We start with a system of differential equations involving six compartments, and we use the Goodman and Weare affine invariant ensemble Markov Chain Monte Carlo algorithm (GWMCMC) to identify a simplified version of the full model that consists of only four compartments. We examine well-posedness of the relevant parameter estimation problem for the given observations using the U.S. epidemic data;study the reliability of model selection;analyze the structural identifiability of the selected model;and conduct a practical identifiability analysis on the selected model using the GWMCMC algorithm. Our study shows that the selected model is structurally identifiable for the confirmed cases, and for small measurement errors, key parameters such as the transmission rate are practically identifiable. We also analyze the stability of the selected model and prove the global asymptotic stability of the disease-free equilibrium and the endemic equilibrium by constructing appropriate Lyapunov functions. Our numerical experiments show that the U.S. will undergo damped transit oscillations towards the endemicity. © 2022, Wilmington Scientific Publisher. All rights reserved.

Forecasting COVID-19 and Analyzing the Effect of Government Interventions

We developed DELPHI, a novel epidemiological model for predicting detected cases and deaths in the prevaccination era of the COVID-19 pandemic. The model allows for underdetection of infections and effects of government interventions. We have applied DELPHI across more than 200 geographical areas since early April 2020 and recorded 6% and 11% two-week, out-of-sample median mean absolute percentage error on predicting cases and deaths, respectively. DELPHI compares favorably with other top COVID-19 epidemiological models and predicted in 2020 the large-scale epidemics in many areas, including the United States, United Kingdom, and Russia, months in advance. We further illustrate two downstream applications of DELPHI, enabled by the model's flexible parametric formulation of the effect of government interventions. First, we quantify the impact of government interventions on the pandemic's spread. We predict, that in the absence of any interventions, more than 14 million individuals would have perished by May 17, 2020, whereas 280,000 deaths could have been avoided if interventions around the world had started one week earlier. Furthermore, we find that mass gathering restrictions and school closings were associated with the largest average reductions in infection rates at 29.9 +/- 6.9% and 17.3 +/- 6.7%, respectively. The most stringent policy, stay at home, was associated with an average reduction in infection rate by 74.4 +/- 3.7% from baseline across countries that implemented it. In the second application, we demonstrate how DELPHI can predict future COVID-19 incidence under alternative governmental policies and discuss how Janssen Pharmaceuticals used such analyses to select the locations of its Phase III trial for its leading single-dose vaccine candidate Ad26.Cov2.S.

Estimate of the rate of unreported COVID-19 cases during the first outbreak in Rio de Janeiro.

In this work we fit an epidemiological model SEIAQR (Susceptible - Exposed - Infectious - Asymptomatic - Quarantined - Removed) to the data of the first COVID-19 outbreak in Rio de Janeiro, Brazil. Particular emphasis is given to the unreported rate, that is, the proportion of infected individuals that is not detected by the health system. The evaluation of the parameters of the model is based on a combination of error-weighted least squares method and appropriate B-splines. The structural and practical identifiability is analyzed to support the feasibility and robustness of the parameters' estimation. We use the Bootstrap method to quantify the uncertainty of the estimates. For the outbreak of March-July 2020 in Rio de Janeiro, we estimate about 90% of unreported cases, with a 95% confidence interval (85%, 93%).

Exploring the limits of joint control: the case of COVID-19 digital proximity tracing solutions

Referring to the judgment of the CJEU in Fashion-ID, some scholars have anticipated that, “at this rate everyone will be a [joint] controller of personal data”. This contribution follows this arguably provocative, but not entirely implausible, line of thinking. In the first part of the article, we highlight the ambiguities inherent to the concept of “joint control” and confront them with those pertaining to the notion of “identifiability”. In the second part, we investigate the effects of the broad legal test for joint control on the role of the individual user of BLE-based COVID-19 digital proximity tracing solutions. This offers the possibility to examine, at a theoretical level, whether the impact of the broad notion of joint control differs depending on the architecture of the system (i.e. centralized or decentralized). We found out that the strict application of the joint controllership test could lead to unexpected and, most likely, unintended results. First, an app user could, in theory, qualify as a joint controller with a national health authority regardless of the protocol’s architecture. Second, an actor could, again in theory, be considered as a joint controller of data that is not personal from that actor’s perspective. © 2021 Stephanie Rossello and Pierre Dewitte.

Parameter identifiability and optimal control of an SARS-CoV-2 model early in the pandemic.

We fit an SARS-CoV-2 model to US data of COVID-19 cases and deaths. We conclude that the model is not structurally identifiable. We make the model identifiable by prefixing some of the parameters from external information. Practical identifiability of the model through Monte Carlo simulations reveals that two of the parameters may not be practically identifiable. With thus identified parameters, we set up an optimal control problem with social distancing and isolation as control variables. We investigate two scenarios: the controls are applied for the entire duration and the controls are applied only for the period of time. Our results show that if the controls are applied early in the epidemic, the reduction in the infected classes is at least an order of magnitude higher compared to when controls are applied with 2-week delay. Further, removing the controls before the pandemic ends leads to rebound of the infected classes.

Underdetection in a stochastic SIR model for the analysis of the COVID-19 Italian epidemic.

We propose a way to model the underdetection of infected and removed individuals in a compartmental model for estimating the COVID-19 epidemic. The proposed approach is demonstrated on a stochastic SIR model, specified as a system of stochastic differential equations, to analyse data from the Italian COVID-19 epidemic. We find that a correct assessment of the amount of underdetection is important to obtain reliable estimates of the critical model parameters. The adaptation of the model in each time interval between relevant government decrees implementing contagion mitigation measures provides short-term predictions and a continuously updated assessment of the basic reproduction number.