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. 2022 Jun:49:100504.
doi: 10.1016/j.spasta.2021.100504. Epub 2021 Mar 27.

A spatio-temporal model based on discrete latent variables for the analysis of COVID-19 incidence

Francesco Bartolucci  1 , Alessio Farcomeni  2
Affiliations

A spatio-temporal model based on discrete latent variables for the analysis of COVID-19 incidence

Francesco Bartolucci et al. Spat Stat. 2022 Jun.

Abstract

We propose a model based on discrete latent variables, which are spatially associated and time specific, for the analysis of incident cases of SARS-CoV-2 infections. We assume that for each area the sequence of latent variables across time follows a Markov chain with initial and transition probabilities that also depend on latent variables in neighboring areas. The model is estimated by a Markov chain Monte Carlo algorithm based on a data augmentation scheme, in which the latent states are drawn together with the model parameters for each area and time. As an illustration we analyze incident cases of SARS-CoV-2 collected in Italy at regional level for the period from February 24, 2020, to January 17, 2021, corresponding to 48 weeks, where we use number of swabs as an offset. Our model identifies a common trend and, for every week, assigns each region to one among five distinct risk groups.

Keywords: Data augmentation; Hidden Markov models; MCMC; SARS-CoV-2; Swabs.

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Figures

Fig. 1
Fig. 1
Positive rate for twelve regions, together with the Italian tendency (in red). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Fig. 2
Fig. 2
Positive rate for nine regions, together with the Italian tendency (in red). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Fig. 3
Fig. 3
Trajectories corresponding to the 5 latent states suitably ordered together with the Italian trend (dashed curve).
Fig. 4
Fig. 4
Heatmap of the predicted latent state for each region at each week. Darker is associated with worse predicted risk.
See this image and copyright information in PMC

References

    1. Alaimo Di Loro P., Divino F., Farcomeni A., Jona Lasinio G., Lovison G., Maruotti A., Mingione M. 2020. Nowcasting COVID-19 incidence indicators during the Italian first outbreak. arXiv:2010.12679. - PMC - PubMed
    1. Anderson G., Farcomeni A., Pittau M.G., Zelli R. Rectangular latent Markov models for time-specific clustering, with an analysis of the well being of nations. J. R. Stat. Soc. C. 2019;68:603–621.
    1. Bartolucci F., Farcomeni A. A multivariate extension of the dynamic logit model for longitudinal data based on a latent Markov heterogeneity structure. J. Amer. Statist. Assoc. 2009;104:816–831.
    1. Bartolucci F., Farcomeni A. A discrete time event-history approach to informative drop-out in mixed latent Markov models with covariates. Biometrics. 2015;71:80–89. - PubMed
    1. Bartolucci F., Farcomeni A. 2021. A hidden Markov space-time model for mapping of the dynamics of global access to food.