Abstract
Model-based disease mapping remains a fundamental policy-informing tool in the fields of public health and disease surveillance. Hierarchical Bayesian models have emerged as the state-of-the-art approach for disease mapping since they are able to both capture structure in the data and robustly characterise uncertainty. When working with areal data, e.g. aggregates at the administrative unit level such as district or province, current models rely on the adjacency structure of areal units to account for spatial correlations and perform shrinkage. The goal of disease surveillance systems is to track disease outcomes over time. This task is especially challenging in crisis situations which often lead to redrawn administrative boundaries, meaning that data collected before and after the crisis are no longer directly comparable. Moreover, the adjacency-based approach ignores the continuous nature of spatial processes and cannot solve the change-of-support problem, i.e. when estimates are required to be produced at different administrative levels or levels of aggregation. We present a novel, practical, and easy to implement solution to solve these problems relying on a methodology combining deep generative modelling and fully Bayesian inference: we build on the recently proposed PriorVAE method able to encode spatial priors over small areas with variational autoencoders by encoding aggregates over administrative units. We map malaria prevalence in Kenya, a country in which administrative boundaries changed in 2010.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
Any kernel can be used. We use RBF only as an example.
References
Bernadinelli, L., Pascutto, C., Best, N.G., Gilks, W.R.: Disease mapping with errors in covariates. Stat. Med. 16(7), 741–752 (1997)
Bernardinelli, L., Montomoli, C.: Empirical Bayes versus fully Bayesian analysis of geographical variation in disease risk. Stat. Med. 11(8), 983–1007 (1992)
Besag, J.: Spatial interaction and the statistical analysis of lattice systems. J. Roy. Stat. Soc.: Ser. B (Methodol.) 36(2), 192–225 (1974)
Besag, J., York, J., Mollié, A.: Bayesian image restoration, with two applications in spatial statistics. Ann. Inst. Stat. Math. 43, 1–20 (1991)
Bhatt, S., et al.: The effect of malaria control on Plasmodium falciparum in Africa between 2000 and 2015. Nature 526(7572), 207–211 (2015)
Bhatt, S., Cameron, E., Flaxman, S.R., Weiss, D.J., Smith, D.L., Gething, P.W.: Improved prediction accuracy for disease risk mapping using gaussian process stacked generalization. J. Roy. Soc. Interface 14(134), 20170520 (2017)
Bingham, E., et al.: Pyro: deep universal probabilistic programming. J. Mach. Learn. Res. 20, 28:1–28:6 (2019). http://jmlr.org/papers/v20/18-403.html
Bradbury, J., et al.: JAX: composable transformations of Python+NumPy programs (2018). http://github.com/google/jax
Clayton, D.G.: Bayesian methods for mapping disease risk. In: Geographical and Environmental Epidemiology: Methods for Small-Area Studies, pp. 205–220 (1992)
Clayton, D.G., Bernardinelli, L., Montomoli, C.: Spatial correlation in ecological analysis. Int. J. Epidemiol. 22(6), 1193–1202 (1993)
Cressie, N.: Statistics for Spatial Data. Wiley, Hoboken (2015)
Gelman, A., Carlin, J.B., Stern, H.S., Rubin, D.B.: Bayesian Data Analysis. Chapman and Hall/CRC (1995)
Gemperli, A., et al.: Mapping malaria transmission in West and Central Africa. Trop. Med. Int. Health 11(7), 1032–1046 (2006)
Gosoniu, L., Vounatsou, P., Sogoba, N., Smith, T.: Bayesian modelling of geostatistical malaria risk data. Geospat. Health 1(1), 127–139 (2006)
Hassan, M.: A state of change: district creation in Kenya after the beginning of multi-party elections. Polit. Res. Q. 69(3), 510–521 (2016)
Hay, S.I., et al.: A world malaria map: plasmodium falciparum endemicity in 2007. PLoS Med. 6(3), e1000048 (2009)
Johnson, O., Diggle, P., Giorgi, E.: A spatially discrete approximation to log-Gaussian Cox processes for modelling aggregated disease count data. Stat. Med. 38(24), 4871–4887 (2019)
Kang, S.Y., Cramb, S.M., White, N.M., Ball, S.J., Mengersen, K.L.: Making the most of spatial information in health: a tutorial in Bayesian disease mapping for areal data. Geospat. Health 11(2), 190–198 (2016)
Kingma, D.P., Welling, M.: Auto-encoding variational bayes. arXiv preprint arXiv:1312.6114 (2013)
Leroux, B.G., Lei, X., Breslow, N.: Estimation of disease rates in small areas: a new mixed model for spatial dependence. In: Halloran, M.E., Berry, D. (eds.) Statistical Models in Epidemiology, the Environment, and Clinical Trials. IMA, vol. 116, pp. 179–191. Springer, New York (2000). https://doi.org/10.1007/978-1-4612-1284-3_4
MacNab, Y.C.: Bayesian disease mapping: past, present, and future. Spatial Stat. 50, 100593 (2022)
Martins, T.G., Simpson, D., Lindgren, F., Rue, H.: Bayesian computing with INLA: new features. Comput. Stat. Data Anal. 67, 68–83 (2013)
Mishra, S., Flaxman, S., Berah, T., Pakkanen, M., Zhu, H., Bhatt, S.: \(pi\)VAE: encoding stochastic process priors with variational autoencoders. Stat. Comput. (2022)
Phan, D., Pradhan, N., Jankowiak, M.: Composable effects for flexible and accelerated probabilistic programming in NumPyro. arXiv preprint arXiv:1912.11554 (2019)
Reid, H., et al.: Mapping malaria risk in Bangladesh using Bayesian geostatistical models. Am. J. Trop. Med. Hyg. 83(4), 861 (2010)
Riebler, A., Sørbye, S.H., Simpson, D., Rue, H.: An intuitive Bayesian spatial model for disease mapping that accounts for scaling. Stat. Methods Med. Res. 25(4), 1145–1165 (2016)
Robert, C.P., Casella, G., Casella, G.: Monte Carlo Statistical Methods, vol. 2. Springer, New York (1999). https://doi.org/10.1007/978-1-4757-4145-2
Semenova, E., et al.: PriorVAE: encoding spatial priors with variational autoencoders for small-area estimation. J. R. Soc. Interface 19(191), 20220094 (2022)
Semenova, E., Verma, P., Cairney-Leeming, M., Solin, A., Bhatt, S., Flaxman, S.: PriorCVAE: scalable MCMC parameter inference with Bayesian deep generative modelling. arXiv preprint arXiv:2304.04307 (2023)
Snow, R.W., et al.: The prevalence of Plasmodium falciparum in sub-Saharan Africa since 1900. Nature 550(7677), 515–518 (2017)
Tanaka, Y., et al.: Spatially aggregated gaussian processes with multivariate areal outputs. In: Advances in Neural Information Processing Systems, vol. 32 (2019)
U.S. President’s Malaria Initiative. U.S. president’s malaria initiative Kenya malaria operational plan FY 2022 (2022). www.pmi.gov
Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., Bürkner, P.-C.: Rank-normalization, folding, and localization: an improved R for assessing convergence of MCMC (with discussion). Bayesian Anal. 16(2), 667–718 (2021)
Wakefield, J.C., Best, N.G., Waller, L.: Bayesian approaches to disease mapping. In: Spatial Epidemiology: Methods and Applications, vol. 59 (2000)
Weiss, D.J., et al.: Mapping the global prevalence, incidence, and mortality of Plasmodium falciparum, 2000–17: a spatial and temporal modelling study. The Lancet 394(10195), 322–331 (2019)
Yousefi, F., Smith, M.T., Alvarez, M.: Multi-task learning for aggregated data using Gaussian processes. In: Advances in Neural Information Processing Systems, vol. 32 (2019)
Zhu, H., et al.: Aggregated Gaussian processes with multiresolution earth observation covariates. arXiv preprint arXiv:2105.01460 (2021)
Acknowledgments
E.S. acknowledges supported in part by the AI2050 program at Schmidt Futures (Grant [G-22-64476]). S.F. and E.S. acknowledge the EPSRC (EP/V002910/2). SM acknowledges support from the National Research Foundation via The NRF Fellowship Class of 2023 Award (NRF-NRFF15-2023-0010). H.J.T.U acknowledges funding from the MRC Centre for Global Infectious Disease Analysis (reference MR/X020258/1), funded by the UK Medical Research Council (MRC). This UK funded award is carried out in the frame of the Global Health EDCTP3 Joint Undertaking. S.B. acknowledges funding from the MRC Centre for Global Infectious Disease Analysis (reference MR/X020258/1), funded by the UK Medical Research Council (MRC). This UK funded award is carried out in the frame of the Global Health EDCTP3 Joint Undertaking. S.B. acknowledges support from the National Institute for Health and Care Research (NIHR) via the Health Protection Research Unit in Modelling and Health Economics, which is a partnership between the UK Health Security Agency (UKHSA), Imperial College London, and the London School of Hygiene & Tropical Medicine (grant code NIHR200908). (The views expressed are those of the authors and not necessarily those of the UK Department of Health and Social Care, NIHR, or UKHSA.). S.B. acknowledges support from the Novo Nordisk Foundation via The Novo Nordisk Young Investigator Award (NNF20OC0059309). SB acknowledges the Danish National Research Foundation (DNRF160) through the chair grant. S.B. acknowledges support from The Eric and Wendy Schmidt Fund For Strategic Innovation via the Schmidt Polymath Award (G-22-63345).
Author information
Authors and Affiliations
Corresponding authors
Editor information
Editors and Affiliations
Ethics declarations
Data and Code Availability
Data containing administrative boundaries of Kenya are publicly available: current boundaries (https://data.humdata.org/dataset/2c0b7571-4bef-4347-9b81-b2174c13f9ef/resource/03df9cbb-0b4f-4f22-9eb7-3cbd0157fd3d/download/ken_adm_iebc_20191031_shp.zip) and old boundaries (https://www.wri.org/data/kenya-gis-data) can be freely downloaded. Malaria prevalence data was obtained from DHS 2015 survey and contains information on locations of clusters and test positivity to calculate district-specific prevalence; it can be requested from the DHS programme (https://dhsprogram.com/). Code to reproduce the results is available at https://github.com/MLGlobalHealth/aggVAE.
Disclosure of Interests
Authors do not have any competing interests to declare. Any opinions, findings and conclusions or recommendations expressed in this material are those of the author(s) and do not reflect the views of the National Research Foundation, Singapore
Rights and permissions
Copyright information
© 2024 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this paper
Cite this paper
Semenova, E., Mishra, S., Bhatt, S., Flaxman, S., Unwin, H.J.T. (2024). Deep Learning and MCMC with aggVAE for Shifting Administrative Boundaries: Mapping Malaria Prevalence in Kenya. In: Cuzzolin, F., Sultana, M. (eds) Epistemic Uncertainty in Artificial Intelligence . Epi UAI 2023. Lecture Notes in Computer Science(), vol 14523. Springer, Cham. https://doi.org/10.1007/978-3-031-57963-9_2
Download citation
DOI: https://doi.org/10.1007/978-3-031-57963-9_2
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-031-57962-2
Online ISBN: 978-3-031-57963-9
eBook Packages: Computer ScienceComputer Science (R0)