Modelling the COVID-19 Infection Trajectory: A Piecewise Linear Quantile Trend Model

Jiang, Feiyu; Zhao, Zifeng; Shao, Xiaofeng

doi:10.1111/rssb.12453

Cited by 19 publications

(10 citation statements)

References 42 publications

(81 reference statements)

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“…Recently, Jiang et al [ 24 , 25 ] propose piecewise linear quantile models that detect multiple change-points, where an SN-based test statistic is above the properly chosen threshold, for capturing the ever-changing growth rate of daily new cases of COVID-19. Note that our segmentation scheme has two distinct advantages over those used in these models: (a) automatic: it does not require any prior hyperparameters and (b) model-agnostic: it can be applicable to any ODE-based epidemic models, including non-linear fitting models.…”

Section: Related Workmentioning

confidence: 99%

Simple epidemic models with segmentation can be better than complex ones

2022

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Given a sequence of epidemic events, can a single epidemic model capture its dynamics during the entire period? How should we divide the sequence into segments to better capture the dynamics? Throughout human history, infectious diseases (e.g., the Black Death and COVID-19) have been serious threats. Consequently, understanding and forecasting the evolving patterns of epidemic events are critical for prevention and decision making. To this end, epidemic models based on ordinary differential equations (ODEs), which effectively describe dynamic systems in many fields, have been employed. However, a single epidemic model is not enough to capture long-term dynamics of epidemic events especially when the dynamics heavily depend on external factors (e.g., lockdown and the capability to perform tests). In this work, we demonstrate that properly dividing the event sequence regarding COVID-19 (specifically, the numbers of active cases, recoveries, and deaths) into multiple segments and fitting a simple epidemic model to each segment leads to a better fit with fewer parameters than fitting a complex model to the entire sequence. Moreover, we propose a methodology for balancing the number of segments and the complexity of epidemic models, based on the Minimum Description Length principle. Our methodology is (a) Automatic: not requiring any user-defined parameters, (b) Model-agnostic: applicable to any ODE-based epidemic models, and (c) Effective: effectively describing and forecasting the spread of COVID-19 in 70 countries.

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Section: Related Workmentioning

confidence: 99%

Simple epidemic models with segmentation can be better than complex ones

2022

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“…A change point is a location or time at which observations or data obey two different models: before and after. Detecting change points is a nontrivial problem and has been studied by many authors; see a book treatment in [ 1 ] and recent advances in CUSUM-based change point tests [ 2 , 3 , 4 ]. In real problems, we may know some prior information about the location of the change point, say at the right or left tail of the sequence.…”

Section: Introductionmentioning

confidence: 99%

A New Class of Weighted CUSUM Statistics

Shi

Wang

Reid

2022

Entropy

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A change point is a location or time at which observations or data obey two different models: before and after. In real problems, we may know some prior information about the location of the change point, say at the right or left tail of the sequence. How does one incorporate the prior information into the current cumulative sum (CUSUM) statistics? We propose a new class of weighted CUSUM statistics with three different types of quadratic weights accounting for different prior positions of the change points. One interpretation of the weights is the mean duration in a random walk. Under the normal model with known variance, the exact distributions of these statistics are explicitly expressed in terms of eigenvalues. Theoretical results about the explicit difference of the distributions are valuable. The expansions of asymptotic distributions are compared with the expansion of the limit distributions of the Cramér-von Mises statistic and the Anderson and Darling statistic. We provide some extensions from independent normal responses to more interesting models, such as graphical models, the mixture of normals, Poisson, and weakly dependent models. Simulations suggest that the proposed test statistics have better power than the graph-based statistics. We illustrate their application to a detection problem with video data.

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“…Change point analysis is a powerful tool for handling structural changes since the seminal work by Page (1955). It received considerable attentions in recent years and has a lot of real applications in various fields including genomics (Liu et al, 2020), social science (Roy, Atchadé and Michailidis, 2017), financial contagion (Pesaran and Pick, 2007) in economy, and even for the recent COVID-19 pandemic studies (Jiang, Zhao and Shao, 2021). Motivated by this, in this paper, we study the change point testing and estimation problem in the high-dimensional linear regression setting.…”

mentioning

confidence: 99%

Change Point Detection for High-dimensional Linear Models: A General Tail-adaptive Approach

Liu¹,

Qi²,

Zhang³

et al. 2022

Preprint

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We study the change point detection problem for high-dimensional linear regression models. The existing literature mainly focuses on the change point estimation with stringent sub-Gaussian assumptions on the errors. In practice, however, there is no prior knowledge about the existence of a change point or the tail structures of errors. To address these issues, in this paper, we propose a novel tail-adaptive approach for simultaneous change point testing and estimation. The method is built on a new loss function which is a weighted combination between the composite quantile and least squared losses, allowing us to borrow information of the possible change points from both the conditional mean and quantiles. For the change point testing, based on the adjusted L 2 -norm aggregation of a weighted score CUSUM process, we propose a family of individual testing statistics with different weights to account for the unknown tail structures. Through a combination of the individual tests, a tail-adaptive test is further constructed that is powerful for sparse alternatives of regression coefficients' changes under various tail structures. For the change point estimation, a family of argmax-based individual estimators is proposed once a change point is detected. In theory, for both individual and tail-adaptive tests, bootstrap procedures are proposed to approximate their limiting null distributions. Under some mild conditions, we justify the validity of the new tests in terms of size and power under the high-dimensional setup. The corresponding change point estimators are shown to be rate optimal up to a logarithm factor. Moreover, combined with the wild binary segmentation technique, a new algorithm is proposed to detect multiple change points in a tail-adaptive manner. Extensive numerical results are conducted to illustrate the competitive performance of the proposed method.

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Modelling the COVID-19 Infection Trajectory: A Piecewise Linear Quantile Trend Model

Cited by 19 publications

References 42 publications

Simple epidemic models with segmentation can be better than complex ones

Simple epidemic models with segmentation can be better than complex ones

A New Class of Weighted CUSUM Statistics

Change Point Detection for High-dimensional Linear Models: A General Tail-adaptive Approach

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