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Register a new userParametric Modeling Approach to COVID-19 Pandemic Data
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Added by
Nofiu Badmus
Publication date
2021
fields
Mathematical Statistics
and research's language is
English
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The problem of skewness is common among clinical trials and survival data which has being the research focus derivation and proposition of different flexible distributions. Thus, a new distribution called Extended Rayleigh Lomax distribution is constructed from Rayleigh Lomax distribution to capture the excessiveness of some survival data. We derive the new distribution by using beta logit function proposed by Jones (2004). Some statistical properties of the distribution such as probability density function, cumulative density function, reliability rate, hazard rate, reverse hazard rate, moment generating functions, likelihood functions, skewness, kurtosis and coefficient of variation are obtained. We also performed the expected estimation of model parameters by maximum likelihood; goodness of fit and model selection criteria including Anderson Darling (AD), CramerVon Misses (CVM), Kolmogorov Smirnov (KS), Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC) and Consistent Akaike Information Criterion (CAIC) are employed to select the better distribution from those models considered in the work. The results from the statistics criteria show that the proposed distribution performs better with better representation of the States in Nigeria COVID-19 death cases data than other competing models.
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It is well known that the minimax rates of convergence of nonparametric density and regression function estimation of a random variable measured with error is much slower than the rate in the error free case. Surprisingly, we show that if one is willing to impose a relatively mild assumption in requiring that the error-prone variable has a compact support, then the results can be greatly improved. We describe new and constructive methods to take full advantage of the compact support assumption via spline-assisted semiparametric methods. We further prove that the new estimator achieves the usual nonparametric rate in estimating both the density and regression functions as if there were no measurement error. The proof involves linear and bilinear operator theories, semiparametric theory, asymptotic analysis regarding Bsplines, as well as integral equation treatments. The performance of the new methods is demonstrated through several simulations and a data example.
We show that the COVID-19 pandemic under social distancing exhibits universal dynamics. The cumulative numbers of both infections and deaths quickly cross over from exponential growth at early times to a longer period of power law growth, before eventually slowing. In agreement with a recent statistical forecasting model by the IHME, we show that this dynamics is well described by the erf function. Using this functional form, we perform a data collapse across countries and US states with very different population characteristics and social distancing policies, confirming the universal behavior of the COVID-19 outbreak. We show that the predictive power of statistical models is limited until a few days before curves flatten, forecast deaths and infections assuming current policies continue and compare our predictions to the IHME models. We present simulations showing this universal dynamics is consistent with disease transmission on scale-free networks and random networks with non-Markovian transmission dynamics.
Pooled testing offers an efficient solution to the unprecedented testing demands of the COVID-19 pandemic, although with potentially lower sensitivity and increased costs to implementation in some settings. Assessments of this trade-off typically assume pooled specimens are independent and identically distributed. Yet, in the context of COVID-19, these assumptions are often violated: testing done on networks (housemates, spouses, co-workers) captures correlated individuals, while infection risk varies substantially across time, place and individuals. Neglecting dependencies and heterogeneity may bias established optimality grids and induce a sub-optimal implementation of the procedure. As a lesson learned from this pandemic, this paper highlights the necessity of integrating field sampling information with statistical modeling to efficiently optimize pooled testing. Using real data, we show that (a) greater gains can be achieved at low logistical cost by exploiting natural correlations (non-independence) between samples -- allowing improvements in sensitivity and efficiency of up to 30% and 90% respectively; and (b) these gains are robust despite substantial heterogeneity across pools (non-identical). Our modeling results complement and extend the observations of Barak et al (2021) who report an empirical sensitivity well beyond expectations. Finally, we provide an interactive tool for selecting an optimal pool size using contextual information
COVID-19--a viral infectious disease--has quickly emerged as a global pandemic infecting millions of people with a significant number of deaths across the globe. The symptoms of this disease vary widely. Depending on the symptoms an infected person is broadly classified into two categories namely, asymptomatic and symptomatic. Asymptomatic individuals display mild or no symptoms but continue to transmit the infection to otherwise healthy individuals. This particular aspect of asymptomatic infection poses a major obstacle in managing and controlling the transmission of the infectious disease. In this paper, we attempt to mathematically model the spread of COVID-19 in India under various intervention strategies. We consider SEIR type epidemiological models, incorporated with India specific social contact matrix representing contact structures among different age groups of the population. Impact of various factors such as presence of asymptotic individuals, lockdown strategies, social distancing practices, quarantine, and hospitalization on the disease transmission is extensively studied. Numerical simulation of our model is matched with the real COVID-19 data of India till May 15, 2020 for the purpose of estimating the model parameters. Our model with zone-wise lockdown is seen to give a decent prediction for July 20, 2020.
Complex biological processes are usually experimented along time among a collection of individuals. Longitudinal data are then available and the statistical challenge is to better understand the underlying biological mechanisms. The standard statistical approach is mixed-effects model, with regression functions that are now highly-developed to describe precisely the biological processes (solutions of multi-dimensional ordinary differential equations or of partial differential equation). When there is no analytical solution, a classical estimation approach relies on the coupling of a stochastic version of the EM algorithm (SAEM) with a MCMC algorithm. This procedure needs many evaluations of the regression function which is clearly prohibitive when a time-consuming solver is used for computing it. In this work a meta-model relying on a Gaussian process emulator is proposed to replace this regression function. The new source of uncertainty due to this approximation can be incorporated in the model which leads to what is called a mixed meta-model. A control on the distance between the maximum likelihood estimates in this mixed meta-model and the maximum likelihood estimates obtained with the exact mixed model is guaranteed. Eventually, numerical simulations are performed to illustrate the efficiency of this approach.
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