Sains Malaysiana 40(5)(2011): 527–535

Pemetaan Kes Kemortalan Bayi di Semenanjung Malaysia Menggunakan Kaedah Bayes Empirik

(Mapping of Infant Mortality Cases in Peninsular Malaysia using Empirical Bayes Method)

Nuzlinda Abdul Rahman*

Pusat Pengajian Sains Matematik Universiti Sains Malaysia, 11800 USM, Penang, Malaysia

Abdul Aziz Jemain, Kamarulzaman Ibrahim& Ahmad Mahir Razali

Pusat Pengajian Sains Matematik, Universiti Kebangsaan Malaysia

43600 UKM Bangi, Selangor D.E., Malaysia

Received: 22 December / Accepted: 20 May 2010

ABSTRAK

Kajian ini bertujuan untuk memetakan kes kemortalan bayi mengikut daerah di Semenanjung Malaysia bagi tahun 1991 hingga 2000. Penganggaran risiko relatif berdasarkan kaedah Bayes empirik telah digunakan dalam kajian ini. Tiga kaedah penganggaran parameter dihuraikan iaitu kaedah momen, kaedah kebolehjadian maksimum dan kaedah penganggaran gabungan momen dan kebolehjadian maksimum. Keteguhan anggaran parameter yang diperoleh diuji menggunakan kaedah Bootstrap. Hasil kajian mendapati jurang antara kawasan berisiko rendah dengan kawasan berisiko tinggi adalah lebih besar pada awal dekad 2000 berbanding pada awal dekad 1990-an walaupun pada dasarnya kadar mortaliti bayi secara keseluruhannya adalah semakin berkurangan pada peringkat nasional. Kawasan pantai timur Semenanjung Malaysia masih pada takuk yang sama iaitu masih berada dalam kategori berisiko tinggi sepanjang tempoh yang dikaji. Seterusnya, gambaran terdapatnya tompokan risiko juga turut terpapar dalam peta yang dihasilkan. Berdasarkan kaedah Bootstrap, parameter-parameter yang dianggarkan dalam kajian ini adalah teguh.

Kata kunci: Bootstrap; kaedah Bayes empirik; kemortalan bayi; risiko relative

ABSTRACT

The objective of this study was to map the infant mortality cases over Peninsular Malaysia by district for the period of 1991 to 2000. Relative risks estimation based on empirical Bayes method was used in this study. Three methods of estimation were described which include moment method, maximum likelihood method and combination of moment and maximum likelihood method. The robustness of the parameters estimation was examined using Bootstrap method. The study indicated that the gap between the low risk areas and the high risk areas are larger in the early decade of 2000 compared to the early 1990s eventhough the infant mortality rate is declining at the national level. The east coast areas of the Peninsular Malaysia still remain in the high risk category over the period of the study. Moreover, the maps obtained indicated the occurrence of clustering effect in the infant mortality risk. Based on the Bootstrap method, all parameters estimation obtained in this study were robust.

Keywords: Bootstrap; empirical bayes method; infant mortality; relative risk

REFERENCES

Ainsworth, L.M. & Dean, C.B. 2006. Approximate inference for disease mapping. Computational Statistics & Data Analysis 50: 2552-2570.

Berke, O. 2005. Exploratory spatial relative risk mapping. Preventive Veterinary Medicine 71: 173-182.

Biggeri, A., Dreassi, E., Lagazio, C. & Bohning, D. 2003. A transitional non-parametric maximum pseudo-likelihood estimator for disease mapping. Computational Statistics & Data Analysis 41: 617-629.

Bohning, D. 1995. A review of reliable maximum likelihood algorithms for semiparametric mixture models. Journal of Statistical Planning and Inference 47: 5-28.

Bohning, D., Dietz, E. & Schlattmann, P. 1998. Recent developments in computer-assisted analysis of mixture. Biometrics 54: 525-536.

Bohning, D., Schlattmann, P. & Lindsay, B. 1992. Computer-assisted analysis of mixtures (C.A.MAN): Statistical algorithms. Biometrics 48: 283-303.

Cano-Serral, G., Azlor, E., Rodriguez-Sanz, M., Pasarin, M.I., Martinez, J.M., Puigpinos, R., Muntaner, C. & Borrel, C. 2009. Socioeconomic inequalities in mortality in Barcelona: A study based on census tract (MEDEA Project). Health & Place 15(1): 186-192.

Chandrasekaran, S.K. & Arivarignan, G. 2006. Disease mapping using mixture distribution. Indian Journal of Medical Research 123(6): 788-798.

Clayton, D. & Kaldor, J. 1987. Empirical Bayes estimates of age-standardized relative risks for use in disease mapping. Biometrics 43: 671-681.

Hasselblad, V. 1969. Estimation of finite mixtures of distributions from the exponential family. Journal of the American Statistical Association 64: 1459-1471.

Jabatan Perangkaan Malaysia. 1991. Perangkaan Penting Malaysia.

Jabatan Perangkaan Malaysia. 2000. Perangkaan Penting Malaysia.

Kaluzny, S.P., Vega, S.C., Cardoso, T.P. & Shelly, A.A. 1998. S+ Spatial Stats User’s manual for Windows and UNIX. New York: Springer.

Koch, T. & Denike, K. 2001. GIS approaches to the problem of disease clusters: a brief commentary. Social Science & Medicine 52: 1751-1754.

Kraak, M.J. & Ormeling, F.J. 1996. Cartography: Visualization of spatial data. England: Longman.

Lawson, A.B. & Williams, F.L.R. 2001. An Introductory Guide to Disease Mapping. Chichester: John Wiley & Sons.

Lawson, A.B., Browne, W.J. & Rodeiro, C.L.V. 2003. Disease Mapping with WinBUGS and MlwiN. New York: Wiley.

Marshall, R.J. 1991. Mapping disease and mortality rates using empirical Bayes estimators. Applied Statistics 40: 283-294.

Meza, J.L. 2003. Empirical Bayes estimation smoothing of relative risks in disease mapping. Journal of Statistical Planning and Inference 112: 43-62.

Monmonier, M. 1993. Mapping it Out. Chicago: The University of Chicago Press.

Ng, S. & McLachlan, G.J. 2004. Speeding up the EM algorithm for mixture model-based segmentation of magnetic resonance images. Pattern Recognition 37: 1573-1589.

Rattanasiri, S., Bohning, D., Rojanavipart, P. & Athipanyakom, S. 2004. A mixture model application in disease mapping of malaria. Southeast Asian Journal Trop. Med. Public. Health 35: 38-47.

Robbins, H. 1964. The empirical Bayes approach to statistical decision problems. Annals of Mathematical Statistics 35: 1-20.

Schlattmann, P. & Bohning, D. 1993. Mixture models and disease mapping. Statistics in Medicine 12: 1943-1950.

Schlattmann, P., Dietz, E. & Bohning, D. 1996. Covariate adjusted mixture models and disease mapping ith the program Dismapwin. Statistics in Medicine 12: 919-929.

Schroder, W. 2006. GIS, geostatistics, metadata banking and tree-based models for data analysis and mapping in environmental monitoring and epidemiology. International Journal of Medical Microbiology 296: 23-36.

Slocum, T.A. 1999. Thematic Cartography and Visualization. Upper Saddle River, NJ: Prentice Hall.

Staubach, C., Schmid, V., Knorr-Held, L. & Ziller, M. 2002. A Bayesian model for spatial wildlife disease prevalence data. Preventive Veterinary Medicine 56: 75-87.

Tsutakawa, R.K. 1985. Estimation of cancer mortality rates: A Bayesian analysis of small frequencies. Biometrics 41: 69-79.

United Nations. 1986. Economic and Social Survey of Asia and the Pacific. New York: United Nations.

United Nations. 2002. Economic and Social Survey of Asia and the Pacific. New York: United Nations.

Waller, L.A. & Gotway, C.A. 2004. Applied Spatial Statistics for Public Health Data. New Jersey: John Wiley & Sons.

*Corresponding author; email: nuzlinda@usm.my