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Detecting Interaction Between Random Region and Fixed Age Effects in Disease Mapping

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  • C. B. Dean
  • M. D. Ugarte
  • A. F. Militino

Abstract

Summary. The purpose of this article is to draw attention to the possible need for inclusion of interaction effects between regions and age groups in mapping studies. We propose a simple model for including such an interaction in order to develop a test for its significance. The assumption of an absence of such interaction effects is a helpful simplifying one. The measure of relative risk related to a particular region becomes easily and neatly summarized. Indeed, such a test seems warranted because it is anticipated that the simple model, which ignores such interaction, as is in common use, may at times be adequate. The test proposed is a score test and hence only requires fitting the simpler model. We illustrate our approaches using mortality data from British Columbia, Canada, over the 5‐year period 1985–1989. For this data, the interaction effect between age groups and regions is quite large and significant.

Suggested Citation

  • C. B. Dean & M. D. Ugarte & A. F. Militino, 2001. "Detecting Interaction Between Random Region and Fixed Age Effects in Disease Mapping," Biometrics, The International Biometric Society, vol. 57(1), pages 197-202, March.
    • Handle: RePEc:bla:biomet:v:57:y:2001:i:1:p:197-202
    DOI: 10.1111/j.0006-341X.2001.00197.x
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    1. R. W. Farebrother, 1984. "A Remark on Algorithms as 106, as 153 and as 155 the Distribution of a Linear Combination of X2 Random Variables," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 33(3), pages 366-369, November.
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    Cited by:

    1. Nicoletta D’Angelo & Antonino Abbruzzo & Giada Adelfio, 2021. "Spatio-Temporal Spread Pattern of COVID-19 in Italy," Mathematics, MDPI, vol. 9(19), pages 1-14, October.
    2. Ana Isabel Ribeiro & Ludivine Launay & Elodie Guillaume & Guy Launoy & Henrique Barros, 2018. "The Portuguese version of the European Deprivation Index: Development and association with all-cause mortality," PLOS ONE, Public Library of Science, vol. 13(12), pages 1-13, December.
    3. Maria Dolores Ugarte, 2015. " Banerjee , S. Carlin , B. P. , and Gelfand , A. E. Hierarchical Modeling and Analysis for Spatial Data. Second Edition . CRC Press/Chapman & Hall . Monographs on Statistics and Applied Probability 13," Biometrics, The International Biometric Society, vol. 71(1), pages 274-277, March.
    4. Lee, Dae-Jin & Durbán, María, 2009. "Smooth-CAR mixed models for spatial count data," Computational Statistics & Data Analysis, Elsevier, vol. 53(8), pages 2968-2979, June.
    5. G. Vicente & T. Goicoa & P. Fernandez‐Rasines & M. D. Ugarte, 2020. "Crime against women in India: unveiling spatial patterns and temporal trends of dowry deaths in the districts of Uttar Pradesh," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 183(2), pages 655-679, February.
    6. Dean, C. B. & Ugarte, M. D. & Militino, A. F., 2004. "Penalized quasi-likelihood with spatially correlated data," Computational Statistics & Data Analysis, Elsevier, vol. 45(2), pages 235-248, March.
    7. Geert Verbeke & Geert Molenberghs, 2003. "The Use of Score Tests for Inference on Variance Components," Biometrics, The International Biometric Society, vol. 59(2), pages 254-262, June.
    8. Maria Dolores Ugarte, 2015. "Banerjee , S. Carlin , B. P. , and Gelfand , A. E. Hierarchical Modeling and Analysis for Spatial Data. Second Edition . CRC Press/Chapman & Hall . Monographs on Statistics and Applied Probability 135," Biometrics, The International Biometric Society, vol. 71(1), pages 274-277, March.
    9. T. Goicoa, 2019. "Comments on: Modular regression - a Lego system for building structured additive distributional regression models with tensor product interactions," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(1), pages 40-42, March.
    10. Ugarte, M.D. & Goicoa, T. & Militino, A.F., 2009. "Empirical Bayes and Fully Bayes procedures to detect high-risk areas in disease mapping," Computational Statistics & Data Analysis, Elsevier, vol. 53(8), pages 2938-2949, June.
    11. Naeimehossadat Asmarian & Seyyed Mohammad Taghi Ayatollahi & Zahra Sharafi & Najaf Zare, 2019. "Bayesian Spatial Joint Model for Disease Mapping of Zero-Inflated Data with R-INLA: A Simulation Study and an Application to Male Breast Cancer in Iran," IJERPH, MDPI, vol. 16(22), pages 1-13, November.
    12. Lee, Dae-Jin & Durbán, María, 2008. "Smooth-car mixed models for spatial count data," DES - Working Papers. Statistics and Econometrics. WS ws085820, Universidad Carlos III de Madrid. Departamento de Estadística.

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