CoChat
Sign Up
Cited by 16Survey Sampling and Estimation TechniquesOptimal Experimental Design MethodsSpatial and Panel Data Analysis

Efficient design of geographically-defined clusters with spatial autocorrelation

Open access
I. Watson, Samuel·2022·Journal of Applied Statistics
DOI 10.1080/02664763.2021.1941807PMC PMC9543073
Open this paper in CoChat — free accountOpen PDF

Abstract

Clusters form the basis of a number of research study designs including survey and experimental studies. Cluster-based designs can be less costly but also less efficient than individual-based designs due to correlation between individuals within the same cluster. Their design typically relies on ad hoc choices of correlation parameters, and is insensitive to variations in cluster design. This article examines how to efficiently design clusters where they are geographically defined by demarcating areas incorporating individuals and households or other units. Using geostatistical models for spatial autocorrelation, we generate approximations to within cluster average covariance in order to estimate the effective sample size given particular cluster design parameters. We show how the number of enumerated locations, cluster area, proportion sampled, and sampling method affect the efficiency of the design and consider the optimization problem of choosing the most efficient design subject to budgetary constraints. We also consider how the parameters from these approximations can be interpreted simply in terms of ‘real-world’ quantities and used in design analysis.

The claims and statistics of this paper haven’t been checked yet.

Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.

A few free checks a day · papers already verified open instantly · results are public

Integrity signals

Registry

Crossref · 10.1080/02664763.2021.1941807

Cites

1 of 1 references verified0 citation errors · 0 not checkable

Statistics

Claims the paper makes

The claims and statistics of this paper haven’t been checked yet.

Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.

A few free checks a day · papers already verified open instantly · results are public

Self-check

Percentages, sums and reported differences re-computed from the paper’s own numbers.

The self-check needs the paper’s full text.

Cites

Flagged first, then by citations

Research works printed but not linked: 37

  1. [1]S. Basu and T. G. Thibodeau, Analysis of spatial autocorrelation in house prices, J. Real Estate Financ. Econom. 17 (1998), pp. 61– 85. DOI: 10.1023/A:1007703229507. · DOI
  2. [2]R. Benedetti, F. Piersimoni, and P. Postiglione, Spatially balanced sampling: A review and A reappraisal, Int. Stat. Rev. 85 (Dec 2017), pp. 439– 454. DOI: 10.1111/insr.12216. · DOI
  3. [4]J. R. Carr, R. E. Bailey, and E. D. Deng. Use of indicator variograms for an enhanced spatial analysis. J. Int. Assoc. Math. Geol, 17 (8) (Nov 1985), pp. 797– 881. DOI: 10.1007/BF01034062 · DOI
  4. [5]L.-W. Chao, H. Szrek, K. Peltzer, S. Ramlagan, P. Fleming, R. Leite, J. Magerman, G. B. Ngwenya, N. Sousa Pereira, and J. Behrman, A comparison of EPI sampling, probability sampling, and compact segment sampling methods for micro and small enterprises, J. Dev. Econ. 98 (May 2012), pp. 94– 107. DOI: 10.1016/j.jdeveco.2011.08.007. 22582004 PMC3347860 · DOI
  5. [6]Lei Chen, Yong Gao, Di Zhu, Yihong Yuan, and Yu Liu. Quantifying the scale effect in geospatial big data using semi-variograms. PLOS ONE, 14 (11) (Nov 2019) pp. e0225139. DOI: 10.1371/journal.pone.0225139. 31725781 PMC6855636 · DOI
  6. [7]J.P. Chilès and P. Delfiner, Geostatistics: Modeling Spatial Uncertainty, 2nd ed., John Wiley & Sons, Inc., 2012. DOI: 10.1002/9781118136188. · DOI
  7. [8]M. Chipeta, D. Terlouw, K. Phiri, and P. Diggle, Inhibitory geostatistical designs for spatial prediction taking account of uncertain covariance structure, Environmetrics 28 (Feb 2017), pp. e2425. DOI: 10.1002/env.2425. · DOI
  8. [9]E. Delmelle. Spatial Sampling. The SAGE Handbook of Spatial Analysis, 2009, pp. 183– 206.
  9. [10]P. J. Diggle and E. Giorgi, Model-Based geostatistics for prevalence mapping in low-Resource settings, J. Am. Stat. Assoc. 111 (Jul 2016), pp. 1096– 1120. DOI: 10.1080/01621459.2015.1123158. · DOI
  10. [11]O. Dubrule. Indicator variogram models: do we have much choice? Math. Geosci., 49 (4) (May 2017) pp. 441– 465. DOI: 10.1007/s11004-017-9678-x · DOI
  11. [12]S. Eldridge and S. Kerry, A Practical Guide to Cluster Randomised Trials in Health Services Research, Wiley, Chichester, UK, 2012.
  12. [13]J. P. Elhorst and K. Zigova, Competition in research activity among economic departments: evidence by negative spatial autocorrelation, Geogr. Anal. 46 (Apr 2014), pp. 104– 125. DOI: 10.1111/gean.12031. · DOI
  13. [14]F. Fowler Survey Research Methods, 4th ed., 2012. DOI: 10.4135/9781452230184. · DOI
  14. [15]A. Grafström, N. L. P. Lundström, and L. Schelin, Spatially balanced sampling through the Pivotal method, Biometrics 68 (Jun 2012), pp. 514– 520. DOI: 10.1111/j.1541-0420.2011.01699.x. 22040115 · DOI
  15. [16]A. Grafström and Y. Tillé, Doubly balanced spatial sampling with spreading and restitution of auxiliary totals, Environmetrics 17 (2013), pp. 61– 85. DOI: 10.1002/env.2194. · DOI
  16. [17]D. A. Griffith, Effective geographic sample size in the presence of spatial autocorrelation, Ann. Assoc. Amer. Geogr. 95 (Dec 2005), pp. 740– 760. DOI: 10.1111/j.1467-8306.2005.00484.x. · DOI
  17. [18]M. C. Gulliford, O. C. Ukoumunne, and S. Chinn, Components of variance and intraclass correlations for the design of community-based surveys and intervention studies: data from the health survey for England 1994, Am. J. Epidemiol. 149 (May 1999), pp. 876– 883. DOI: 10.1093/oxfordjournals.aje.a009904. 10221325 · DOI
  18. [19]K. Hemming, S. Eldridge, G. Forbes, C. Weijer, and M. Taljaard, How to design efficient cluster randomised trials, BMJ 358 (Jul 2017), pp. j3064. DOI: 10.1136/bmj.j3064. 28710062 PMC5508848 · DOI · Paper page
  19. [20]K. Hemming, J. Kasza, R. Hooper, A. Forbes, and M. Taljaard, A tutorial on sample size calculation for multiple-period cluster randomized parallel, cross-over and stepped-wedge trials using the Shiny CRT calculator, Int. J. Epidemiol. 49 (Feb 2020), pp. 979– 995. DOI: 10.1093/ije/dyz237. 32087011 PMC7394950 · DOI
  20. [21]R. Hooper, S. Teerenstra, E. de Hoop, and S. Eldridge, Sample size calculation for stepped wedge and other longitudinal cluster randomised trials, Stat. Med. 35 (Nov 2016), pp. 4718– 4728. DOI: 10.1002/sim.7028. 27350420 · DOI
  21. [22]N. Z. Janjua, M. I. Khan, and J. D. Clemens, Estimates of intraclass correlation coefficient and design effect for surveys and cluster randomized trials on injection use in Pakistan and developing countries, Tropical Medicine and International Health 11 (2006), pp. 1832– 1840. DOI: 10.1111/j.1365-3156.2006.01736.x 17176348 · DOI
  22. [23]C. Jarvis, G. L. Di Tanna, D. Lewis, N. Alexander, and W. J. Edmunds, Spatial analysis of cluster randomised trials: a systematic review of analysis methods, Emerg. Themes. Epidemiol. 14 (Dec 2017), pp. 12. DOI: 10.1186/s12982-017-0066-2. 28947911 PMC5609008 · DOI
  23. [24]Jin-Feng Wang, A. Stein, Bin-Bo Gao, and Yong Ge. A review of spatial sampling. Spatial Statistics, 2 (Dec 2012), pp. 1– 14. DOI: 10.1016/j.spasta.2012.08.001. · DOI
  24. [25]S. Kul, K. Vanhaecht, and M. Panella, Intraclass correlation coefficients for cluster randomized trials in care pathways and usual care: hospital treatment for heart failure, BMC. Health. Serv. Res. 14 (2014), pp. 376. DOI: 10.1186/1472-6963-14-84 24565441 PMC3974056 · DOI
  25. [26]V. Lorant, I. Thomas, D. Deliege, and R. Tonglet, Deprivation and mortality: the implications of spatial autocorrelation for health resources allocation, Soc. Sci. Med. 53 (Dec 2001), pp. 1711– 1719. DOI: 10.1016/S0277-9536(00)00456-1. 11762895 · DOI
  26. [27]M. Manton, Collecting Spatial Data: Optimal Design of Experiments for Random Fields, 3rd ed. Eos, Transactions American Geophysical Union, 2008. DOI: 10.1029/2008eo160009 · DOI
  27. [28]P. Milligan, A. Njie, and S. Bennett, Comparison of two cluster sampling methods for health surveys in developing countries, Int. J. Epidemiol. 33 (2004), pp. 469– 476. DOI: 10.1093/ije/dyh096. 15020569 · DOI · Paper page
  28. [29]I. Molho, Spatial autocorrelation in British unemployment, J. Reg. Sci. 35 (Nov 1995), pp. 641– 658. DOI: 10.1111/j.1467-9787.1995.tb01297.x. · DOI
  29. [30]R. L. Munasinghe and R. D. Morris, Localization of disease clusters using regional measures of spatial autocorrelation, Stat. Med. 15 (Apr 1996), pp. 893– 905. DOI: 10.1002/(SICI)1097-0258(19960415)15:7/9¡893::AID-SIM258¿3.0.CO;2-M. 8861158 · DOI
  30. [31]D. M. Murray, Design and Analysis of Group Randomised Trials, Oxford University Press Inc., New York NY, 1998.
  31. [32]A. O'Hagan, Eliciting expert beliefs in substantial practical applications [Read before the royal statistical society at ameeting on 'Elicitation' on Wednesday, April 16th, 1997, the president, professor A. F. M. Smithin the chair], J. R. Stat. Soc.: Ser. D (The Stat.) 47 (Mar 1998), pp. 21– 35. DOI: 10.1111/1467-9884.00114. · DOI
  32. [33]S. Riley, Large-Scale spatial-Transmission models of infectious disease, Science 316 (Jun 2007), pp. 1298– 1301. DOI: 10.1126/science.1134695. 17540894 · DOI
  33. [34]R. Shahid, S. Bertazzon, M. L. Knudtson, and W. A. Ghali, Comparison of distance measures in spatial analytical modeling for health service planning, BMC. Health. Serv. Res. 9 (Dec 2009), pp. 200. DOI: 10.1186/1472-6963-9-200. 19895692 PMC2781002 · DOI
  34. [35]C. J. Skinner, Design effects of two-Stage sampling, J. R. Stat. Soc., Ser. B (Methodological) 48 (1986), pp. 89– 99.
  35. [36]S. E. Spielman and E.-H. Yoo, The spatial dimensions of neighborhood effects, Soc. Sci. Med. 68 (Mar 2009), pp. 1098– 1105. DOI: 10.1016/j.socscimed.2008.12.048. 19167802 · DOI
  36. [37]P.-J. Tsai, M.-L. Lin, C.-M. Chu, and C.-H. Perng, Spatial autocorrelation analysis of health care hotspots in Taiwan in 2006, BMC. Public. Health. 9 (Dec 2009), pp. 464. DOI: 10.1186/1471-2458-9-464 20003460 PMC2799414 · DOI
  37. [38]E. A. Yfantis, G. T. Flatman, and J. V. Behar, Efficiency of kriging estimation for square, triangular, and hexagonal grids, Math. Geol. 19 (1987), pp. 183– 205. DOI: 10.1007/BF00897746. · DOI

Cited by

Sorted by citations

Authors
I. Watson, S.
Affiliations
University of Birmingham, Birmingham, UK
Venue
Journal of Applied Statistics
Publisher
Informa UK Limited
Published
2021-06-17
Volume
49
Issue
13
Pages
3300-3318
ISSN
  • 0266-4763 (ISSN-L)
  • 1360-0532
DOI
10.1080/02664763.2021.1941807
PMC
PMC9543073
OpenAlex
W3093624613
Cited by
16
References
1
Citations by year
2026: 3 · 2025: 6 · 2023: 4 · 2022: 3
FWCI
1.31
Type
journal article
Language
en
Open access
Licence
Locations
  • Journal of Applied Statistics (publishedVersion, cc-by-nc-nd)
  • PubMed Central (publishedVersion, cc-by-nc-nd)
  • PubMed (publishedVersion)
  • arXiv (Cornell University) (submittedVersion)
  • RePEc: Research Papers in Economics (submittedVersion)
  • University of Birmingham Research Portal (University of Birmingham) (submittedVersion, cc-by-nc-nd)
  • arXiv (Cornell University) (cc-by)
Funders
NIHR (16/136/87)
Topics
  • Physical Sciences › Mathematics › Statistics and Probability › Survey Sampling and Estimation Techniques
  • Social Sciences › Decision Sciences › Management Science and Operations Research › Optimal Experimental Design Methods
  • Social Sciences › Economics, Econometrics and Finance › Economics and Econometrics › Spatial and Panel Data Analysis
Keywords
cluster sampling, spatial autocorrelation, effective sample size, geostatistical models, sampling fraction

About these checks

Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.

Statistics and arithmetic are recomputed, not judged.

Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.

What counts as a claim ›How we measure confidence ›How we check this ›

Are you an author, or do you see a problem with this page? Request a review