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Assessing the predictive causality of individual based models using Bayesian inference intervention analysis: an application in epidemiology

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Abstract

Understanding dynamics in time and the predominant underlying factors that shape them is a central question in biological and medical sciences. Data are more ubiquitous and richer than ever before and population biology in the big data era need to integrate novel methods. Calibrated Individual Based Models (IBMs) are powerful tools for process based predictive modelling. Intervention analysis is the analysis in time series of the potential impact of an event such as an extreme event or an experimentally designed intervention on the time series, for example vaccinating a population. A method for big data analytics (causal impact) that implements a Bayesian intervention approach to estimating the causal effect of a designed intervention on a time series is used to quantify the deviance between data and IBM outputs. Having quantified the deviance between IBM outputs and data, IBM scenarios are used to predict the counterfactual. The counterfactual is how the IBM response metric would have evolved after the intervention if the intervention had never occurred. The method is exemplified to quantify the deviance between a calibrated IBM outputs and epidemiological data of Bovine Tuberculosis with changing the cattle TB testing frequency as the intervention covariate. The advantage of IBM data validation and uncertainty assessment as time series is also discussed.

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References

  • Aanensen DM, Huntley DM, Feil EJ, al-Own Fa, Spratt BG (2009) EpiCollect: linking smartphones to web applications for epidemiology, ecology and community data collection. PLoS ONE 4:e6968

    Article  Google Scholar 

  • Albuquerque MTD, Gerassis S, Sierra C, Taboada J, Martín JE, Antunes IMHR, Gallego JR (2017) Developing a new Bayesian risk index for risk evaluation of soil contamination. Sci Total Environ 603–604:167–177

    Article  Google Scholar 

  • Andre FE, Booy R, Bock HL, Clemens J, Datta SK, John TJ, Lee BW, Lolekha S, Peltola H, Ruff T (2008) Vaccination greatly reduces disease, disability, death and inequity worldwide. Bull World Health Org 86:140–146

    Article  CAS  Google Scholar 

  • Aznar I, Frankena K, More SJ, O’Keeffe J, McGrath G, de Jong MCM (2018) Quantification of mycobacterium bovis transmission in a badger vaccine field trial. Prev Vet Med 149:29–37

    Article  CAS  Google Scholar 

  • Begon M, Townsend CA, Harper JL (2005) Ecology: from individuals to ecosystems. Wiley, Oxford

    Google Scholar 

  • Bollerslev T (1986) Generalized autoregressive conditional heteroskedasticity. J Econom 31:307–327

    Article  Google Scholar 

  • Briggs, H. 2015. Testing ‘more effective’ than badger cull. http://www.bbc.com/news/science-environment-30820579: BBC

  • Brodersen KH, Gallusser F, Koehler J, Remy N, Scott SL (2015) Inferring causal impact using Bayesian structural time-series models. Ann Appl Stat 9:247–274

    Article  Google Scholar 

  • Brooks-Pollock E, Roberts GO, Keeling MJ (2014) A dynamic model of bovine tuberculosis spread and control in Great Britain. Nature 511:228–231

    Article  CAS  Google Scholar 

  • Burnham KP, Anderson DR (2002) Model selection and multimodel inference. Springer, New York

    Google Scholar 

  • Carter SP, Chambers MA, Rushton SP, Shirley MDF, Schuchert P, Pietravalle S, Murray A, Rogers F, Gettinby G, Smith GC, Delahay RJ, Hewinson RG, McDonald RA (2012) BCG vaccination reduces risk of tuberculosis infection in vaccinated badgers and unvaccinated badger cubs. PLoS ONE 7:e49833

    Article  CAS  Google Scholar 

  • Claridge J, Diggle P, McCann CM, Mulcahy G, Flynn R, McNair J, Strain S, Welsh M, Baylis M, Williams DJL (2012) Fasciola hepatica is associated with the failure to detect bovine tuberculosis in dairy cattle. Nat Commun 3:853

    Article  Google Scholar 

  • Congdon P (2017) Representing spatial dependence and spatial discontinuity in ecological epidemiology: a scale mixture approach. Stoch Environ Res Risk Assess 31:291–304

    Article  Google Scholar 

  • Daliakopoulos IN, Katsanevakis S, Moustakas A (2017) Spatial downscaling of alien species presences using machine learning. Front Earth Sci 5:60

    Article  Google Scholar 

  • Damos P (2016) A stepwise algorithm to detect significant time lags in ecological time series in terms of autocorrelation functions and ARMA model optimisation of pest population seasonal outbreaks. Stoch Environ Res Risk Assess 30:1961–1980

    Article  Google Scholar 

  • DEFRA (2016a) Annex—Background and methodology to the National Statistics on the Incidence of Tuberculosis (TB) in Cattle in Great Britain

  • DEFRA (2016b) Bovine TB testing intervals, 2016. https://www.gov.uk/guidance/bovine-tb-testing-intervals-2016

  • DEFRA. 2016c. Monthly publication of National Statistics on the Incidence of Tuberculosis (TB) in Cattle to end August 2016 for Great Britain

  • Diebold FX (1998) Elements of forecasting. Citeseer, Harrisburg

    Google Scholar 

  • Dunson DB (2001) Commentary: practical advantages of Bayesian analysis of epidemiologic data. Am J Epidemiol 153:1222–1226

    Article  CAS  Google Scholar 

  • Edwards JK, Lesko CR, Keil AP (2017) Invited commentary: causal inference across space and time—quixotic quest, worthy goal, or both? Am J Epidemiol 186:143–145

    Article  Google Scholar 

  • Edwards W, Lindman H, Savage LJ (1963) Bayesian statistical inference for psychological research. Psychol Rev 70:193

    Article  Google Scholar 

  • Enright J, O’Hare A (2017) Reconstructing disease transmission dynamics from animal movements and test data. Stoch Environ Res Risk Assess 31:369–377

    Article  Google Scholar 

  • Eum H-I, Cannon AJ, Murdock TQ (2017) Intercomparison of multiple statistical downscaling methods: multi-criteria model selection for South Korea. Stoch Environ Res Risk Assess 31:683–703

    Article  Google Scholar 

  • Evans MR, Benton TG, Grimm V, Lessells CM, O’Malley MA, Moustakas A, Weisberg M (2014) Data availability and model complexity, generality, and utility: a reply to Lonergan. Trends Ecol Evol 29:302–303

    Article  Google Scholar 

  • Evans MR, Bithell M, Cornell SJ, Dall SRX, Díaz S, Emmott S, Ernande B, Grimm V, Hodgson DJ, Lewis SL, Mace GM, Morecroft M, Moustakas A, Murphy E, Newbold T, Norris KJ, Petchey O, Smith M, Travis JMJ, Benton TG (2013) Predictive systems ecology. Proc R Soc B Biol Sci 280:20131452

    Article  Google Scholar 

  • Evans MR, Moustakas A (2016) A comparison between data requirements and availability for calibrating predictive ecological models for lowland UK woodlands: learning new tricks from old trees. Ecol Evol 6:4812–4822

    Article  Google Scholar 

  • Evans MR, Moustakas A (2017) Plasticity in foraging behaviour as a possible response to climate change. Ecol Inf. https://doi.org/10.1016/j.ecoinf.2017.08.001

    Article  Google Scholar 

  • Fan J, Han F, Liu H (2014) Challenges of big data analysis. Natl Sci Rev 1:293–314

    Article  Google Scholar 

  • Ginsburg O, Bray F, Coleman MP, Vanderpuye V, Eniu A, Kotha SR, Sarker M, Huong TT, Allemani C, Dvaladze A (2017) The global burden of women’s cancers: a grand challenge in global health. Lancet 389:847–860

    Article  Google Scholar 

  • Goicoa T, Adin A, Ugarte MD, Hodges JS (2018) In spatio-temporal disease mapping models, identifiability constraints affect PQL and INLA results. Stoch Environ Res Risk Assess. https://doi.org/10.1007/s00477-017-1405-0

    Article  Google Scholar 

  • Greenwood B (2014) The contribution of vaccination to global health: past, present and future. Philos Trans R Soc B Biol Sci 369:20130433

    Article  Google Scholar 

  • Guarte JM, Barrios EB (2006) Estimation under purposive sampling. Commun Stat Simul Comput 35:277–284

    Article  Google Scholar 

  • Hampton SE, Strasser CA, Tewksbury JJ, Gram WK, Budden AE, Batcheller AL, Duke CS, Porter JH (2013) Big data and the future of ecology. Front Ecol Environ 11:156–162

    Article  Google Scholar 

  • Harper JL (1977) Population biology of plants. Academic Press, Cambridge

    Google Scholar 

  • Heguan Z (1986) Application of arima time series model in tree growing forecast. Sci Silvae Sin 1:011

    Google Scholar 

  • Hernán MA (2016) Does water kill? A call for less casual causal inferences. Ann Epidemiol 26:674–680

    Article  Google Scholar 

  • Hernán MA (2017) Invited commentary: selection bias without colliders. Am J Epidemiol 185:1048–1050

    Article  Google Scholar 

  • Hinckley S, Parada C, Horne JK, Mazur M, Woillez M (2016) Comparison of individual-based model output to data using a model of walleye pollock early life history in the Gulf of Alaska. Deep Sea Res Part II Top Stud Oceanogr 132:240–262

    Article  Google Scholar 

  • Huang J, Malone BP, Minasny B, McBratney AB, Triantafilis J (2017) Evaluating a Bayesian modelling approach (INLA-SPDE) for environmental mapping. Sci Total Environ 609:621–632

    Article  CAS  Google Scholar 

  • Juan P, Díaz-Avalos C, Mejía-Domínguez NR, Mateu J (2017) Hierarchical spatial modeling of the presence of Chagas disease insect vectors in Argentina. A comparative approach. Stoch Environ Res Risk Assess 31:461–479

    Article  Google Scholar 

  • Kane MJ, Price N, Scotch M, Rabinowitz P (2014) Comparison of ARIMA and random forest time series models for prediction of avian influenza H5N1 outbreaks. BMC Bioinf 15:276

    Article  Google Scholar 

  • Kazmin D, Nakaya HI, Lee EK, Johnson MJ, van der Most R, van den Berg RA, Ballou WR, Jongert E, Wille-Reece U, Ockenhouse C (2017) Systems analysis of protective immune responses to RTS, S malaria vaccination in humans. Proc Natil Acad Sci 114:201621489

    Google Scholar 

  • Keyes KM, Tracy M, Mooney SJ, Shev A, Cerdá M (2017) Invited commentary: agent-based models—bias in the face of discovery. Am J Epidemiol 186:146–148

    Article  Google Scholar 

  • Krebs JR, Anderson R, Clutton-Brock T, Morrison I, Young D, Donnelly CA, Frost S, Woodroffe R (1997) Bovine tuberculosis in cattle and badgers. Report to the Rt Hon Dr Jack Cunningham MP by The Independent Scientific Review Group, London, p 191

  • Lange M, Thulke H-H (2017) Elucidating transmission parameters of African swine fever through wild boar carcasses by combining spatio-temporal notification data and agent-based modelling. Stoch Environ Res Risk Assess 31:379–391

    Article  Google Scholar 

  • Levins R (1966) The strategy of model building in population biology. Am Sci 54:421–431

    Google Scholar 

  • Loglisci C, Malerba D (2017) Leveraging temporal autocorrelation of historical data for improving accuracy in network regression. Stat Anal Data Min ASA Data Sci J. https://doi.org/10.1002/sam.11336

    Article  Google Scholar 

  • Lonergan M (2014) Data availability constrains model complexity, generality, and utility: a response to Evans et al. Trends Ecol Evol 29:301–302

    Article  Google Scholar 

  • Lowe R, Cazelles B, Paul R, Rodó X (2016) Quantifying the added value of climate information in a spatio-temporal dengue model. Stoch Environ Res Risk Assess 30:2067–2078

    Article  Google Scholar 

  • Lucas TA, Doña RA, Jiang W, Johns GC, Mann DJ, Seubert C, Webster NB, Willens CH, Davis SD (2017) An individual-based model of chaparral vegetation response to frequent wildfires. Theor Ecol 10:217–233

    Article  Google Scholar 

  • Lux SA, Wnuk A, Vogt H, Belien T, Spornberger A, Studnicki M (2016) Validation of individual-based markov-like stochastic process model of insect behavior and a “Virtual Farm” concept for enhancement of site-specific IPM. Front Physiol 7:363

    Article  Google Scholar 

  • Lynch SM, Moore JH (2016) A call for biological data mining approaches in epidemiology. BioData Mining 9:1

    Article  Google Scholar 

  • Mazaris AD (2017) Open data and the future of conservation biology. Ethics Sci Environ Pol 17:29–35

    Article  Google Scholar 

  • Mazaris AD, Fiksen Ø, Matsinos YG (2005) Using an individual-based model for assessment of sea turtle population viability. Popul Ecol 47:179–191

    Article  Google Scholar 

  • Mazaris AD, Matsinos YG (2006) An individual based model of sea turtles: investigating the effect of temporal variability on population dynamics. Ecol Model 194:114–124

    Article  Google Scholar 

  • McCormick TH, Ferrell R, Karr AF, Ryan PB (2014) Big data, big results: knowledge discovery in output from large-scale analytics. Stat Anal Data Min ASA Data Sci J 7:404–412

    Article  Google Scholar 

  • Medawar P (1984) The limits of science. Oxford University Press, Oxford

    Google Scholar 

  • Moland E, Ulmestrand M, Olsen E, Stenseth N (2013) Long-term decrease in sex-specific natural mortality of European lobster within a marine protected area. Mar Ecol Prog Ser 491:153–164

    Article  Google Scholar 

  • Moustakas A (2016) The effects of marine protected areas over time and species’ dispersal potential: a quantitative conservation conflict attempt. Web Ecol 16:113–122

    Article  Google Scholar 

  • Moustakas A (2017) Spatio-temporal data mining in ecological and veterinary epidemiology. Stoch Environ Res Risk Assess 31:829–834

    Article  Google Scholar 

  • Moustakas A, Evans M (2015) Coupling models of cattle and farms with models of badgers for predicting the dynamics of bovine tuberculosis (TB). Stoch Environ Res Risk Assess 29:623–635

    Article  Google Scholar 

  • Moustakas A, Evans MR (2013) Integrating evolution into ecological modelling: accommodating phenotypic changes in agent based models. PLoS ONE 8:e71125

    Article  CAS  Google Scholar 

  • Moustakas A, Evans MR (2016) Regional and temporal characteristics of bovine tuberculosis of cattle in Great Britain. Stoch Environ Res Risk Assess 30:989–1003

    Article  Google Scholar 

  • Moustakas A, Evans MR (2017) A big-data spatial, temporal and network analysis of bovine tuberculosis between wildlife (badgers) and cattle. Stoch Environ Res Risk Assess 31:315–328

    Article  Google Scholar 

  • Moustakas A, Silvert W (2011) Spatial and temporal effects on the efficacy of marine protected areas: implications from an individual based model. Stoch Environ Res Risk Assess 25:403–413

    Article  Google Scholar 

  • Murray EJ, Robins JM, Seage GR, 3rd, Lodi S, Hyle EP, Reddy KP, Freedberg KA, Hernan MA (2017a) Using observational data to calibrate simulation models. Medical decision making: an international journal of the Society for Medical Decision Making: 272989x17738753

  • Murray EJ, Robins JM, Seage GR, Freedberg KA, Hernán MA (2017b) A comparison of agent-based models and the parametric g-formula for causal inference. Am J Epidemiol 186:131–142

    Article  Google Scholar 

  • Najafabadi MM, Villanustre F, Khoshgoftaar TM, Seliya N, Wald R, Muharemagic E (2015) Deep learning applications and challenges in big data analytics. J Big Data 2:1–21

    Article  Google Scholar 

  • Nelson JC, Shortreed SM, Yu O, Peterson D, Baxter R, Fireman B, Lewis N, McClure D, Weintraub E, Xu S, Jackson LA (2014) On behalf of the Vaccine Safety Datalink, p. 2014. Integrating database knowledge and epidemiological design to improve the implementation of data mining methods that evaluate vaccine safety in large healthcare databases. Stat Anal Data Min ASA Data Sci J 7:337–351

    Article  Google Scholar 

  • Nkiaka E, Nawaz NR, Lovett JC (2018) Effect of single and multi-site calibration techniques on hydrological model performance, parameter estimation and predictive uncertainty: a case study in the Logone catchment, Lake Chad basin. Stoch Environ Res Risk Assess. https://doi.org/10.1007/s00477-017-1466-0

    Article  Google Scholar 

  • Pananos AD, Bury TM, Wang C, Schonfeld J, Mohanty SP, Nyhan B, Salathé M, Bauch CT (2018) Critical dynamics in population vaccinating behavior. Proc Natl Acad Sci. https://doi.org/10.1073/pnas.1704093114

    Article  Google Scholar 

  • Perles-Ribes JF, Ramón-Rodríguez AB, Moreno-Izquierdo L, Torregrosa Martí MT (2016) Winners and losers in the Arab uprisings: a Mediterranean tourism perspective. Curr Issues Tour. https://doi.org/10.1080/13683500.2016.1225697

    Article  Google Scholar 

  • Proietti T, Hillebrand E (2017) Seasonal changes in central England temperatures. J R Stat Soc Ser A 180:769–791

    Article  Google Scholar 

  • Punt AE, Hilborn R (2001) BAYES-SA. Bayesian stock assessment methods in fisheries. User’s manual: FAO

  • R Development Core Team (2017) R; A language and environment for statistical computing. Vienna, Austria: R Foundation for Statistical Computing

  • Riad MH, Scoglio CM, McVey DS, Cohnstaedt LW (2017) An individual-level network model for a hypothetical outbreak of Japanese encephalitis in the USA. Stoch Environ Res Risk Assess 31:353–367

    Article  Google Scholar 

  • Rue H, Martino S, Chopin N (2009) Approximate Bayesian inference for latent Gaussian models by using integrated nested Laplace approximations. J R Stat Soc Ser B 71:319–392

    Article  Google Scholar 

  • Sak H, Yang G, Li B, Li W (2017) A copula-based model for air pollution portfolio risk and its efficient simulation. Stoch Environ Res Risk Assess 31:2607–2616

    Article  Google Scholar 

  • Scott SL, Varian HR (2014) Predicting the present with bayesian structural time series. Int J Math Model Numer Optim 5:4–23

    Google Scholar 

  • Silvert W (2001) Modelling as a discipline. Int J Gen Syst 30:261–282

    Article  Google Scholar 

  • Soranno PA, Schimel DS (2014) Macrosystems ecology: big data, big ecology. Front Ecol Environ 12:3

    Article  Google Scholar 

  • Stichel D, Middleton AM, Müller BF, Depner S, Klingmüller U, Breuhahn K, Matthäus F (2017) An individual-based model for collective cancer cell migration explains speed dynamics and phenotype variability in response to growth factors. NPJ Syst Biol Appl 3:5

    Article  Google Scholar 

  • Wagner HH (2013) Rethinking the linear regression model for spatial ecological data. Ecology 94:2381–2391

    Article  Google Scholar 

  • Wu S, Gao Y-J, Ge Z-Z (2017) Optimal use of polyethylene glycol for preparation of small bowel video capsule endoscopy: a network meta-analysis. Curr Med Res Opin 33:1149–1154

    Article  CAS  Google Scholar 

  • Young D, Dye C (2006) The development and impact of tuberculosis vaccines. Cell 124:683–687

    Article  CAS  Google Scholar 

  • Zenner C, Herrnleben-Kurz S, Walach H (2014) Mindfulness-based interventions in schools—a systematic review and meta-analysis. Front Psychol 5:603

    Article  Google Scholar 

  • Zuur AF, Ieno EN, Walker NJ, Saveliev AA, Smith GM (2009) Limitations of linear regression applied on ecological data. In Mixed effects models and extensions in ecology with R, pp 11–33. Springer, Berlin

    Google Scholar 

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Comments from two anonymous reviewers considerably improved an earlier manuscript draft.

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Correspondence to Aristides Moustakas.

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Moustakas, A. Assessing the predictive causality of individual based models using Bayesian inference intervention analysis: an application in epidemiology. Stoch Environ Res Risk Assess 32, 2861–2869 (2018). https://doi.org/10.1007/s00477-018-1520-6

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