Study the Trend Pattern in COVID-19 using Spline-Based Time Series Model: A Bayesian Paradigm

Agiwal, Varun; Kumar, J.; Yip, Yau Chun

doi:10.20944/preprints202007.0306.v1

Cited by 4 publications

(4 citation statements)

References 12 publications

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“…Splines allow for smooth transitions and subtle structural shifts by piecing together different polynomial line segments, which is an alternative model to deal with the characteristics of COVID-19 case number. Agiwal's study [14] showed spline function is useful to convert the non-linear trend of newly COVID-19 cases into a linear pattern. Sousa et al (2020) [15] proposed an automatic method based on the minimization of the sum of squared residuals plus a penalty to estimate the knot number and locations.…”

Section: Introductionmentioning

confidence: 99%

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An analysis of coronavirus disease 2019 with spline regression at province level during first-level response to major public health emergency out of Hubei, China

Liang

Shen

2021

Epidemiol. Infect.

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This study aims to locate the knots of cumulative coronavirus disease 2019 (COVID-19) case number during the first-level response to public health emergency in the provinces of China except Hubei. The provinces were grouped into three regions, namely eastern, central and western provinces, and the trends between adjacent knots were compared among the three regions. COVID-19 case number, migration scale index, Baidu index, demographic, economic and public health resource data were collected from 22 Chinese provinces from 19 January 2020 to 12 March 2020. Spline regression was applied to the data of all included, eastern, central and western provinces. The research period was divided into three stages by two knots. The first stage (from 19 January to around 25 January) was similar among three regions. However, in the second stage, growth of COVID-19 case number was flatter and lasted longer in western provinces (from 25 January to 18 February) than in eastern and central provinces (from 26 February to around 11 February). In the third stage, the growth of COVID-19 case number slowed down in all the three regions. Included covariates were different among the three regions. Overall, spline regression with covariates showed the different change patterns in eastern, central and western provinces, which provided a better insight into regional characteristics of COVID-19 pandemic.

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Section: Introductionmentioning

confidence: 99%

“…In his study, spline models outperformed cubic ones with each outcome. Sousa et al[15] and Agiwal et al[14] fitted the daily reported COVID-19 cases of European, American and Asian countries with linear and cubic spline terms, identifying the knots of each country. However, change patterns might be different among various regions in a country.…”

mentioning

confidence: 99%

An analysis of coronavirus disease 2019 with spline regression at province level during first-level response to major public health emergency out of Hubei, China

Liang

Shen

2021

Epidemiol. Infect.

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“…Many applications require piecewise polynomial functions, usually referred to as "splines," which interpolate given data points and satisfy additional conditions such as continuity, smoothness, and convexity or concavity. The recent and the ongoing COVID-19 pandemic, spurred advances in spline-related research, specifically, splines have been shoen to be useful for modeling and forecasting of the COVID-19 spread [1][2][3][4], and COVID-19 trend [5]. In [6], splines were used to analyse the relationship between the ambient temperature and the transmission of COVID-19.…”

Section: Introductionmentioning

confidence: 99%

Data Interpolation by Optimal Splines with Free Knots Using Linear Programming

Thakur¹,

Bragin²

2021

Preprint

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Studies have shown that in many practical applications, data interpolation by splines leads to better approximation and higher computational efficiency as compared to data interpolation by a single polynomial. Data interpolation by splines can be significantly improved if knots are allowed to be free rather than at a priori fixed locations such as data points. In practical applications, the smallest possible curvature is often desired. Therefore, optimal splines are determined by minimizing a derivative of continuously differentiable functions comprising the spline of the required order. The problem of obtaining an optimal spline is tantamount to minimizing derivatives of a nonlinear differentiable function over a Banach space on a compact set. While the problem of data interpolation by quadratic splines has been accomplished analytically, interpolation by splines of higher orders or in higher dimensions is challenging. In this paper, to overcome difficulties associated with the complexity of the interpolation problem, the interval over which data points are defined, is discretized and continuous derivatives are substituted by their discrete counterparts. It is shown that as the mesh of the discretization approaches zero, a resulting near-optimal spline approaches an optimal spline. Splines with the desired accuracy can be obtained by choosing an appropriate mesh of the discretization. By using cubic splines as an example, numerical results demonstrate that the linear programming (LP) formulation, resulting from the discretization of the interpolation problem, can be solved by linear solvers with high computational efficiency and resulting splines provide a good approximation to the optimal splines.

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“…Many important applications require interpolation by splines. The recent and ongoing COVID-19 pandemic has spurred advances in spline-related research; specifically, splines have been shown to be useful for modeling and forecasting the spread of COVID-19 [5][6][7][8], and COVID-19 trends [9]. In [10], splines were also used to analyze the relationship between the ambient temperature and the transmission of COVID-19.…”

Section: Introductionmentioning

confidence: 99%

Data Interpolation by Near-Optimal Splines with Free Knots Using Linear Programming

Thakur

Bragin

2021

Mathematics

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The problem of obtaining an optimal spline with free knots is tantamount to minimizing derivatives of a nonlinear differentiable function over a Banach space on a compact set. While the problem of data interpolation by quadratic splines has been accomplished, interpolation by splines of higher orders is far more challenging. In this paper, to overcome difficulties associated with the complexity of the interpolation problem, the interval over which data points are defined is discretized and continuous derivatives are replaced by their discrete counterparts. The l∞-norm used for maximum rth order curvature (a derivative of order r) is then linearized, and the problem to obtain a near-optimal spline becomes a linear programming (LP) problem, which is solved in polynomial time by using LP methods, e.g., by using the Simplex method implemented in modern software such as CPLEX. It is shown that, as the mesh of the discretization approaches zero, a resulting near-optimal spline approaches an optimal spline. Splines with the desired accuracy can be obtained by choosing an appropriately fine mesh of the discretization. By using cubic splines as an example, numerical results demonstrate that the linear programming (LP) formulation, resulting from the discretization of the interpolation problem, can be solved by linear solvers with high computational efficiency and the resulting spline provides a good approximation to the sought-for optimal spline.

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Study the Trend Pattern in COVID-19 using Spline-Based Time Series Model: A Bayesian Paradigm

Cited by 4 publications

References 12 publications

An analysis of coronavirus disease 2019 with spline regression at province level during first-level response to major public health emergency out of Hubei, China

An analysis of coronavirus disease 2019 with spline regression at province level during first-level response to major public health emergency out of Hubei, China

Data Interpolation by Optimal Splines with Free Knots Using Linear Programming

Data Interpolation by Near-Optimal Splines with Free Knots Using Linear Programming

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