Reducing bias in risk indices for COVID-19

Submitted: 4 May 2021
Accepted: 7 August 2021
Published: 14 January 2022
Abstract Views: 2351
PDF: 158
Appendix: 292
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Spatiotemporal modelling of infectious diseases such as coronavirus disease 2019 (COVID-19) involves using a variety of epidemiological metrics such as regional proportion of cases and/or regional positivity rates. Although observing changes of these indices over time is critical to estimate the regional disease burden, the dynamical properties of these measures, as well as crossrelationships, are usually not systematically given or explained. Here we provide a spatiotemporal framework composed of six commonly used and newly constructed epidemiological metrics and conduct a case study evaluation. We introduce a refined risk estimate that is biased neither by variation in population size nor by the spatial heterogeneity of testing. In particular, the proposed methodology would be useful for unbiased identification of time periods with elevated COVID-19 risk without sensitivity to spatial heterogeneity of neither population nor testing coverage.We offer a case study in Poland that shows improvement over the bias of currently used methods. Our results also provide insights regarding regional prioritisation of testing and the consequences of potential synchronisation of epidemics between regions. The approach should apply to other infectious diseases and other geographical areas.



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Bai Y, Yao L, Wei T, Tian F, Jin DY, Chen L, Wang M, 2020. Presumed asymptomatic carrier transmission of COVID-19. JAMA - 323:1406-7. DOI:
Balcan D, Colizza V, Gonçalves B, Hud H, Ramasco JJ, Vespignani A, 2009. Multiscale mobility networks and the spatial spreading of infectious diseases. Proc Natl Acad Sci U S A 106:21484-9. DOI:
Bergquist R, Rinaldi L, 2020. Covid-19: pandemonium in our time. Geospat Health 15:880. DOI:
Bertuzzo E, Mari L, Pasetto D, Miccoli S, Casagrandi R, Gatto M, Rinaldo A, 2020. The geography of COVID-19 spread in Italy and implications for the relaxation of confinement measures. Nat Commun 11:4264. DOI:
Bivand RS, Pebesma E, Gómez-Rubio V, 2013. Applied spatial data analysis with R. Springer, Berlin, Germany. DOI:
Błoński M, 2020a. Kolejne przypadki koronawirusa w kopalniach. Chorzy w Rybniku i Rudzie Śląskiej. Available from:
Błoński M, 2020b. Śląskie: ponad jedna trzecia przebadanych górników z kopalni Bielszowice z koronawirusem. Available from:,689311,slaskie-ponad-jedna-trzecia-przebadanych-gornikow-z-kopalni-bielszowice-z
Briz-Redón Ã, Serrano-Aroca Ã, 2020. A spatio-temporal analysis for exploring the effect of temperature on COVID-19 early evolution in Spain. Sci Total Environ 728:138811. DOI:
Candido DS, Claro IM, de Jesus JG, Souza WM, Moreira FRR, Dellicour S, Mellan TA, du Plessis L, Pereira RHM, Sales FCS, Manuli ER, Thézé J, Almeida L, Menezes MT, Voloch CM, Fumagalli MJ, Coletti TM, da Silva CAM, Ramundo MS, Amorim MR, Hoeltgebaum HH, Mishra S, Gill MS, Carvalho LM, Buss LF, Prete CA, Ashworth J, Nakaya HI, Peixoto PS, Brady OJ, Nicholls SM, Tanuri A, Rossi ÃD, Braga CKV, Gerber AL, de C Guimarães AP, Gaburo N, Alencar CS, Ferreira ACS, Lima CX, Levi JE, Granato C, Ferreira GM, Francisco RS, Granja F, Garcia MT, Moretti ML, Perroud MW, Castiñeiras TMPP, Lazari CS, Hill SC, de Souza Santos AA, Simeoni CL, Forato J, Sposito AC, Schreiber AZ, Santos MNN, de Sá CZ, Souza RP, Resende-Moreira LC, Teixeira MM, Hubner J, Leme PAF, Moreira RG, Nogueira ML, Ferguson NM, Costa SF, Proenca-Modena JL, Vasconcelos ATR, Bhatt S, Lemey P, Wu C-H, Rambaut A, Loman NJ, Aguiar RS, Pybus OG, Sabino EC, Faria NR, 2020. Evolution and epidemic spread of SARS-CoV-2 in Brazil. Science (80-. ):eabd2161. DOI:
Chinazzi M, Davis JT, Ajelli M, Gioannini C, Litvinova M, Merler S, Pastore y Piontti A, Mu K, Rossi L, Sun K, Viboud C, Xiong X, Yu H, Elizabeth Halloran M, Longini IM, Vespignani A, 2020. The effect of travel restrictions on the spread of the 2019 novel coronavirus (COVID-19) outbreak. Science (80-. ):368:395-400. DOI:
Chruścińska-Dragan M, 2020. Procesje Bożego Ciała 2020. Czy się odbędą? W tym roku zastąpią je procesje wokół świątyń i przykościelnych placów. Dz. Zach. Available from:
Cobey S, 2020. Modeling infectious disease dynamics. Science (80-. ) 368:713-4. DOI:
Cordes J, Castro MC, 2020. Spatial analysis of COVID-19 clusters and contextual factors in New York City. Spat Spatiotemporal Epidemiol 34:100355. DOI:
Dalziel BD, Kissler S, Gog JR, Viboud C, Bjørnstad ON, Metcalf CJE, Grenfell BT, 2018. Urbanization and humidity shape the intensity of influenza epidemics in U.S. cities. Science (80-. ) 362:75-9. DOI:
David R, Hayes A, 2019. broom: Convert statistical analysis objects into tidy tibbles. R package version 0.5.2.
Desjardins MR, Hohl A, Delmelle EM, 2020. Rapid surveillance of COVID-19 in the United States using a prospective space-time scan statistic: detecting and evaluating emerging clusters. Appl Geogr 118:102202. DOI:
Franch-Pardo I, Napoletano BM, Rosete-Verges F, Billa L, 2020. Spatial analysis and GIS in the study of COVID-19. A review. Sci Total Environ 739:140033. DOI:
Gatto M, Bertuzzo E, Mari L, Miccoli S, Carraro L, Casagrandi R, Rinaldo A, 2020. Spread and dynamics of the COVID-19 epidemic in Italy: Effects of emergency containment measures. Proc Natl Acad Sci U S A 117:10484-91. DOI:
Gémes K, Talbäck M, Modig K, Ahlbom A, Berglund A, Feychting M, Matthews AA, 2020. Burden and prevalence of prognostic factors for severe COVID-19 in Sweden. Eur J Epidemiol 35:401-9. DOI:
Hatchett RJ, Mecher CE, Lipsitch M, 2007. Public health interventions and epidemic intensity during the 1918 influenza pandemic. Proc Natl Acad Sci U S A 104:7582-7. DOI:
Hohl A, Delmelle EM, Desjardins MR, Lan Y, 2020. Daily surveillance of COVID-19 using the prospective space-time scan statistic in the United States. Spat Spatiotemporal Epidemiol 34:100354. DOI:
Huang R, Liu M, Ding Y, 2020. Spatial-temporal distribution of COVID-19 in China and its prediction: A data-driven modeling analysis. J Infect Dev Ctries 14:246-53. DOI:
Jarynowski A, Wójta-Kempa M, Płatek D, Czopek K, 2020. Attempt to understand public health relevant social dimensions of COVID-19 outbreak in Poland. Soc Regist 4:7-44. DOI:
Jia JS, Lu X, Yuan Y, Xu G, Jia J, Christakis NA, 2020. Population flow drives spatio-temporal distribution of COVID-19 in China. Nature 582:389-94. DOI:
Kassambara A, 2020. ‘ggpubr’: ‘ggplot2’ Based Publication Ready Plots. R Packag. version 0.2.5.
Krzysztofik R, Kantor-Pietraga I, Spórna T, 2020. Spatial and functional dimensions of the COVID-19 epidemic in Poland. Eurasian Geogr Econ 61:573-86. DOI:
Li R, Pei S, Chen B, Song Y, Zhang T, Yang W, Shaman J, 2020. Substantial undocumented infection facilitates the rapid dissemination of novel coronavirus (SARS-CoV-2). Science (80-. ) 368:489-93. DOI:
Lieberman-Cribbin W, Tuminello S, Flores RM, Taioli E, 2020. Disparities in COVID-19 testing and positivity in New York City. Am J Prev Med 59:326-32. DOI:
Medonet, 2020. Poważny błąd w liczbie testów w Kielcach. Szpital wydał oświadczenie, 2020. Available from:,koronawirus--kielce--blad-w-raportowaniu-testow--oswiadczenie,artykul,68822256.html
Miller IF, Becker AD, Grenfell BT, Metcalf CJE, 2020. Disease and healthcare burden of COVID-19 in the United States. Nat Med 26:1212-7. DOI:
Milton Bache S, Wickham H, 2014. Magrittr: a forward-pipe operator for R.
Ministry of Health in Poland, 2020. Report on tests. Available from:
Ministry of Health in Poland - official Twitter profile [WWW Document], Available from:
Mollalo A, Vahedi B, Rivera KM, 2020. GIS-based spatial modeling of COVID-19 incidence rate in the continental United States. Sci Total Environ 728:138884. DOI:
Moran PAP, 1950. Notes on continuous stochastic phenomena. Biometrika 37:17-23. DOI:
Müller K, Wickham H, 2020. tibble: Simple Data Frames. R package version 3.0.1.
Niżankowski R, Myśliwiec M, Szymański P, 2020. Zalecenia w COVID-19. Available from:
Ogiolda K, 2020. Boże Ciało 2020 w Opolu. Biskupi poprowadzili procesję z katedry ‘na górkę.’ Available from:
Omori R, Mizumoto K, Chowell G, 2020. Changes in testing rates could mask the novel coronavirus disease (COVID-19) growth rate. Int J Infect Dis 94:116-8. DOI:
Orlikowski P, 2020. Nowe ognisko koronawirusa. Przebadano 800 osób, uruchomiono mobilną stację. Available from:
Pebesma E, 2018. Simple features for R: Standardized support for spatial vector data. R J 10:439-446. DOI:
Pinkas J, Jankowski M, Szumowski L, Lusawa A, Zgliczynski WS, Raciborski F, Wierzba W, Gujski M, 2020. Public health interventions to mitigate early spread of SARS-CoV-2 in Poland. Med Sci Monit 26:e924730-1-e924730-7. DOI:
Polish Press Agency, 2020a. Szumowski: rekord zachorowań wynika z badań przesiewowych górników i innych ognisk [WWW Document]. Available from:
Polish Press Agency, 2020b. Sasin: od jutra wstrzymamy prace w dwóch kopalniach JSW i w 10 kopalniach PGG [WWW Document]. Available from:
Polsat, 2020. Sasin: ÅšlÄ…sk jest najbezpieczniejszym miejscem w Polsce [WWW Document]. Available from:
Polska Grupa Górnicza, 2020. Wygasa epidemia w Polskiej Grupie Górniczej [WWW Document]. Available from:,Wygasa+epidemia+w+Polskiej+Grupie+Górniczej
Raciborski F, Pinkas J, Jankowski M, SierpiÅ„ski R, ZgliczyÅ„ski WS, Szumowski Å, Rakocy K, Wierzba W, Gujski M, 2020. Dynamics of COVIDâ€19 outbreak in Poland: an epidemiological analysis of the first two months of the epidemic. Polish Arch Intern Med 130:615-21. DOI:
Ramírez-Aldana R, Gomez-Verjan JC, Bello-Chavolla OY, 2020. Spatial analysis of COVID-19 spread in Iran: Insights into geographical and structural transmission determinants at a province level. PLoS Neglect Trop Dis 14:e0008875. DOI:
Ramírez IJ, Lee J, 2020. COVID-19 emergence and social and health determinants in Colorado: A rapid spatial analysis. Int J Environ Res Public Health 17:3856. DOI:
RMF24, 2020. Szumowski: Rozważamy powrót do obostrzeń. Polacy zapomnieli, że mamy epidemię [WWW Document]. Available from:,nId,4543089
Robert Koch Institute, 2021. Information on the designation of international risk areas (18 June 2021). Available from:
Rohleder S, Bozorgmehr K, 2020. Monitoring the spatiotemporal epidemiology of Covid-19 incidence and mortality: a small-area analysis in Germany. Spatial Spatio-Temp Epidemiol 100433. DOI:
Rossman H, Keshet A, Shilo S, Gavrieli A, Bauman T, Cohen O, Shelly E, Balicer R, Geiger B, Dor Y, Segal E, 2020. A framework for identifying regional outbreak and spread of COVID-19 from one-minute population-wide surveys. Nat Med 26:634-8. DOI:
RTL, 2020a. List of countries that have blacklisted Luxembourg. RTL Today. Available from:
RTL, 2020b. Germany declares Luxembourg risk region, cautions against non-essential travel. RTL Today. Available from:
RTL, 2020c. Germany revises Luxembourg’s classification as Covid-19 risk zone. RTL Today. Available from:
Runge A, Kantor-Pietraga I, Runge J, Krzysztofik R, Dragan W, 2018. Can depopulation create urban sustainability in postindustrial regions? A case from Poland. Sustain 10:4633. DOI:
Sievert C, 2018. plotly for R. Available from:
Statistics Poland, 2020. Demographic yearbook of Poland. Available from:
Statistics Poland, 2020. Local Data Bank. Available from:
Tagliazucchi E, Balenzuela P, Travizano M, Mindlin GB, Mininni PD, 2020. Lessons from being challenged by COVID-19. Chaos Solitons Fractals 137:109923. DOI:
Tennekes M, 2018. Tmap: thematic maps. R J Stat Softw 84:1-39. DOI:
TVN24, 2020. Morawiecki: ‘Śmiało idźcie do urn’. A co pokazują dane o pandemii? [WWW Document]. Available from:,110/morawiecki-smialo-idzcie-do-urn-a-co-pokazuja-dane-o-pandemii,1021761.html
Waller LA, Gotway CA, 2004. Applied spatial statistics for Public Health Data, Vol. 368. ed. John Wiley & Sons, New York, NY, USA, 520 pp. DOI:
Watoła J, 2020. Statystyki koronawirusa coraz bardziej fałszywe. Ministerstwu Zdrowia brakuje na Śląsku już 1,1 tys. przypadków. Gaz. Wybor. Available from:,35063,26112008,statystyki-koronawirusa-coraz-bardziej-falszywe-ministerstwu.html
WHO, 2020. Coronavirus disease (COVID-19) advice for the public [WWW Document]. Available from:
Wickham H, 2016. ggplot2 Elegant Graphics for Data Analysis (Use R!). Springer, Berlin, Germany. DOI:
Wickham H, 2007. Reshaping data with the reshape package. J Stat Softw 21:1-20. DOI:
Wickham H, Francois R, Henry L, Kirill M, 2019. dplyr: a grammar of data manipulation. R Packag. version 0.8.3.
Zhang CH, Schwartz GG, 2020. Spatial disparities in coronavirus incidence and mortality in the united states: an ecological analysis as of May. J Rural Health 2020;36:433-45. DOI:

How to Cite

Michalak, M. P., Cordes, J., Kulawik, A., Sitek, S., Pytel, S., Zuzańska-Żyśko, E., & Wieczorek, R. (2022). Reducing bias in risk indices for COVID-19. Geospatial Health, 17(s1).

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