The role of children in the spread of COVID-19: Using household data from Bnei Brak, Israel, to estimate the relative susceptibility and infectivity of children.

One of the significant unanswered questions about COVID-19 epidemiology relates to the role of children in transmission. This study uses data on infections within households in order to estimate the susceptibility and infectivity of children compared to those of adults. The data were collected from households in the city of Bnei Brak, Israel, in which all household members were tested for COVID-19 using PCR (637 households, average household size of 5.3). In addition, serological tests were performed on a subset of the individuals in the study. Inspection of the PCR data shows that children are less likely to be tested positive compared to adults (25% of children positive over all households, 44% of adults positive over all households, excluding index cases), and the chance of being positive increases with age. Analysis of joint PCR/serological data shows that there is under-detection of infections in the PCR testing, which is more substantial in children. However, the differences in detection rates are not sufficient to account for the differences in PCR positive rates in the two age groups. To estimate relative transmission parameters, we employ a discrete stochastic model of the spread of infection within a household, allowing for susceptibility and infectivity parameters to differ among children and adults. The model is fitted to the household data using a simulated maximum likelihood approach. To adjust parameter estimates for under-detection of infections in the PCR results, we employ a multiple imputation procedure using estimates of under-detection in children and adults, based on the available serological data. We estimate that the susceptibility of children (under 20 years old) is 43% (95% CI: [31%, 55%]) of the susceptibility of adults. The infectivity of children was estimated to be 63% (95% CI: [37%, 88%]) relative to that of adults.

Application of one-step method to parameter estimation in ODE models.

In this paper, we study application of Le Cam's one-step method to parameter estimation in ordinary differential equation models. This computationally simple technique can serve as an alternative to numerical evaluation of the popular non-linear least squares estimator, which typically requires the use of a multistep iterative algorithm and repetitive numerical integration of the ordinary differential equation system. The one-step method starts from a preliminary n -consistent estimator of the parameter of interest and next turns it into an asymptotic (as the sample size n→∞) equivalent of the least squares estimator through a numerically straightforward procedure. We demonstrate performance of the one-step estimator via extensive simulations and real data examples. The method enables the researcher to obtain both point and interval estimates. The preliminary n -consistent estimator that we use depends on non-parametric smoothing, and we provide a data-driven methodology for choosing its tuning parameter and support it by theory. An easy implementation scheme of the one-step method for practical use is pointed out.

A model-based initial guess for estimating parameters in systems of ordinary differential equations.

The inverse problem of parameter estimation from noisy observations is a major challenge in statistical inference for dynamical systems. Parameter estimation is usually carried out by optimizing some criterion function over the parameter space. Unless the optimization process starts with a good initial guess, the estimation may take an unreasonable amount of time, and may converge to local solutions, if at all. In this article, we introduce a novel technique for generating good initial guesses that can be used by any estimation method. We focus on the fairly general and often applied class of systems linear in the parameters. The new methodology bypasses numerical integration and can handle partially observed systems. We illustrate the performance of the method using simulations and apply it to real data.

Modelling motion energy in psychotherapy: A dynamical systems approach.

In this study we introduce an innovative mathematical and statistical framework for the analysis of motion energy dynamics in psychotherapy sessions. Our method combines motion energy dynamics with coupled linear ordinary differential equations and a measurement error model, contributing new clinical parameters to enhance psychotherapy research. Our approach transforms raw motion energy data into an interpretable account of therapist-patient interactions, providing novel insights into the dynamics of these interactions. A key aspect of our framework is the development of a new measure of synchrony between the motion energies of therapists and patients, which holds significant clinical and theoretical value in psychotherapy. The practical applicability and effectiveness of our modelling and estimation framework are demonstrated through the analysis of real session data. This work advances the quantitative analysis of motion dynamics in psychotherapy, offering important implications for future research and therapeutic practice.

Digital twins and the future of precision mental health.

Science faces challenges in developing much-needed precision mental health treatments to accurately identify and diagnose mental health problems and the optimal treatment for each individual. Digital twins (DTs) promise to revolutionize the field of mental health, as they are doing in other fields of science, including oncology and cardiology, where they have been successfully deployed. The use of DTs in mental health is yet to be explored. In this Perspective, we lay the conceptual foundations for mental health DTs (MHDT). An MHDT is a virtual representation of an individual's mental states and processes. It is continually updated from data collected over the lifespan of the individual, and guides mental health professionals in diagnosing and treating patients based on mechanistic models and statistical and machine learning tools. The merits of MHDT are demonstrated through the example of the working alliance between the therapist and the patient, which is one of the most consistent mechanisms predicting treatment outcome.

Data-driven clustering of infectious disease incidence into age groups.

Understanding the patterns of infectious diseases spread in the population is an important element of mitigation and vaccination programs. A major and common characteristic of most infectious diseases is age-related heterogeneity in the transmission, which potentially can affect the dynamics of an epidemic as manifested by the pattern of disease incidence in different age groups. Currently there are no statistical criteria of how to partition the disease incidence data into clusters. We develop the first data-driven methodology for deciding on the best partition of incidence data into age-groups, in a well defined statistical sense. The method employs a top-down hierarchical partitioning algorithm, with a stopping criteria based on multiple hypotheses significance testing controlling the family wise error rate. The type one error and statistical power of the method are tested using simulations. The method is then applied to Covid-19 incidence data in Israel, in order to extract the significant age-group clusters in each wave of the epidemic.

The role of statisticians in the response to COVID-19 in Israel: a holistic point of view.

The COVID-19 pandemic cast a dramatic spotlight on the use of data as a fundamental component of good decision-making. Evaluating and comparing alternative policies required information on concurrent infection rates and insightful analysis to project them into the future. Statisticians in Israel were involved in these processes early in the pandemic in some silos as an ad-hoc unorganized effort. Informal discussions within the statistical community culminated in a roundtable, organized by three past presidents of the Israel Statistical Association, and hosted by the Samuel Neaman Institute in April 2021. The meeting was designed to provide a forum for exchange of views on the profession's role during the COVID-19 pandemic, and more generally, on its influence in promoting evidence-based public policy. This paper builds on the insights and discussions that emerged during the roundtable meeting and presents a general framework, with recommendations, for involving statisticians and statistics in decision-making.

Separable Nonlinear Least-Squares Parameter Estimation for Complex Dynamic Systems.

Nonlinear dynamic models are widely used for characterizing processes that govern complex biological pathway systems. Over the past decade, validation and further development of these models became possible due to data collected via high-throughput experiments using methods from molecular biology. While these data are very beneficial, they are typically incomplete and noisy, which renders the inference of parameter values for complex dynamic models challenging. Fortunately, many biological systems have embedded linear mathematical features, which may be exploited, thereby improving fits and leading to better convergence of optimization algorithms. In this paper, we explore options of inference for dynamic models using a novel method of separable nonlinear least-squares optimization and compare its performance to the traditional nonlinear least-squares method. The numerical results from extensive simulations suggest that the proposed approach is at least as accurate as the traditional nonlinear least-squares, but usually superior, while also enjoying a substantial reduction in computational time.

A two-stage approach for estimating the parameters of an age-group epidemic model from incidence data.

Age-dependent dynamics is an important characteristic of many infectious diseases. Age-group epidemic models describe the infection dynamics in different age-groups by allowing to set distinct parameter values for each. However, such models are highly nonlinear and may have a large number of unknown parameters. Thus, parameter estimation of age-group models, while becoming a fundamental issue for both the scientific study and policy making in infectious diseases, is not a trivial task in practice. In this paper, we examine the estimation of the so-called next-generation matrix using incidence data of a single entire outbreak, and extend the approach to deal with recurring outbreaks. Unlike previous studies, we do not assume any constraints regarding the structure of the matrix. A novel two-stage approach is developed, which allows for efficient parameter estimation from both statistical and computational perspectives. Simulation studies corroborate the ability to estimate accurately the parameters of the model for several realistic scenarios. The model and estimation method are applied to real data of influenza-like-illness in Israel. The parameter estimates of the key relevant epidemiological parameters and the recovered structure of the estimated next-generation matrix are in line with results obtained in previous studies.

Modelling and parameter inference of predator-prey dynamics in heterogeneous environments using the direct integral approach.

Most bacterial habitats are topographically complex in the micro scale. Important examples include the gastrointestinal and tracheal tracts, and the soil. Although there are myriad theoretical studies that explore the role of spatial structures on antagonistic interactions (predation, competition) among animals, there are many fewer experimental studies that have explored, validated and quantified their predictions. In this study, we experimentally monitored the temporal dynamic of the predatory bacterium Bdellovibrio bacteriovorus, and its prey, the bacterium Burkholderia stabilis in a structured habitat consisting of sand under various regimes of wetness. We constructed a dynamic model, and estimated its parameters by further developing the direct integral method, a novel estimation procedure that exploits the separability of the states and parameters in the model. We also verified that one of our parameter estimates was consistent with its known, directly measured value from the literature. The ability of the model to fit the data combined with realistic parameter estimates indicate that bacterial predation in the sand can be described by a relatively simple model, and stress the importance of prey refuge on predation dynamics in heterogeneous environments.