Sains Malaysiana 42(7)(2013): 1003–1010

Spatial Analysis of Infant Mortality in Peninsular Malaysia over

Three Decades Using Mixture Models

(Analisis Reruang bagi Kematian Bayi di Semenanjung Malaysia dalam Tempoh Tiga

Dekad Menggunakan Model Campuran)

Nuzlinda Abdul Rahman*

School of Mathematical Sciences, Universiti Sains Malaysia, 11800 Penang, Malaysia

Abdul Aziz Jemain

School of Mathematical Sciences, Faculty of Science and Technology,

Universiti Kebangsaan Malaysia, 43000 Bangi, Selangor, D.E.Malaysia

Diserahkan: 10 November 2011/Diterima: 25 Januari 2013

ABSTRACT

Infant mortality is one of the central public issues in most of the developing countries. In Malaysia, the infant mortality rates have improved at the national level over the last few decades. However, the issue concerned is whether the improvement is uniformly distributed throughout the country. The aim of this study was to investigate the geographical distribution of infant mortality in Peninsular Malaysia from the year 1970 to 2000 using a technique known as disease mapping. It is assumed that the random variable of infant mortality cases comes from Poisson distribution. Mixture models were used to find the number of optimum components/groups for infant mortality data for every district in Peninsular Malaysia. Every component is assumed to have the same distribution, but different parameters. The number of optimum components were obtained by maximum likelihood approach via the EM algorithm. Bayes theorem was used to determine the probability of belonging to each district in every components of the mixture distribution. Each district was assigned to the component that had the highest posterior probability of belonging. The results obtained were visually presented in maps. The analysis showed that in the early year of 1970, the spatial heterogeneity effect was more prominent; however, towards the end of 1990, this pattern tended to disappear. The reduction in the spatial heterogeneity effect in infant mortality data indicated that the provisions of health services throughout the Peninsular Malaysia have improved over the period of the study, particularly towards the year 2000.

Keywords: Disease mapping; infant mortality; mixture model

ABSTRAK

Mortaliti bayi merupakan salah satu isu penting bagi kebanyakan negara membangun. Di Malaysia, kadar kematian bayi pada peringkat kebangsaan telah bertambah baik sejak beberapa dekad yang lalu. Walau bagaimanapun, isu yang akan diketengahkan adalah untuk mengetahui sama ada penambahbaikan ini berlaku secara seragam di seluruh negara atau sebaliknya. Tujuan kajian ini ialah untuk mengkaji taburan geografi bagi kematian bayi di Semenanjung Malaysia dari tahun 1970 sehingga 2000 menggunakan teknik yang dikenali sebagai pemetaan penyakit. Diandaikan pemboleh ubah rawak kes kematian bayi adalah daripada taburan Poisson. Model campuran digunakan untuk mendapatkan bilangan komponen/kumpulan yang optimum bagi data mortaliti bayi bagi setiap daerah di Semenanjung Malaysia. Setiap komponen diandaikan mempunyai taburan yang sama tetapi parameter yang berbeza. Bilangan komponen yang optimum diperoleh menerusi kaedah kebolehjadian maksimum melalui algoritma EM. Teorem Bayes digunakan untuk mengenal pasti kebarangkalian daerah berada dalam setiap komponen bagi taburan campuran yang disuaikan. Setiap daerah diumpukkan kepada komponen yang mempunyai kebarangkalian posterior tertinggi. Keputusan yang diperoleh dipaparkan menerusi peta. Analisis menunjukkan pada awal tahun 1970-an, kesan heterogen reruang adalah lebih ketara, walau bagaimanapun, pada akhir 1990-an, keadaan tersebut telah semakin berkurangan. Pengurangan kesan heterogen reruang dalam data kematian bayi menunjukkan bahawa kemudahan kesihatan yang disediakan di seluruh Semenanjung Malaysia telah semakin baik sepanjang tempoh yang dikaji, terutamanya menjelang tahun 2000.

Kata kunci: Kematian bayi; model campuran; pemetaan penyakit

RUJUKAN

Adebayo, S.B., Fahrmeir, L. & Klasen, S. 2004. Analyzing infant mortality with geoadditive categorical regression model: A case study for Nigeria. Economics and Human Biology 2: 229-244.

Alves, D. & Belluzzo, W. 2004. Infant mortality and child health in Brazil. Economics and Human Biology 2: 391-410.

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

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.

Estimates of Malaysia Federal Revenue and Expenditure. Ministry of Finance Malaysia. 1970-2000.

Everitt, B.S. & Hand, D.J. 1981. Finite Mixture Distributions. New York: Chapman and Hall.

Laskar, M.S. & Harada, N. 2005. Trends and regional variations in infant mortality rates in Japan, 1973-1998. Public Health 119(7): 659-663.

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.

Mantel, N. & Stark, C.R. 1968. Computation of indirect-adjusted rates in the presence of confounding. Biometrics 24: 997-1005.

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.

Mohamed, W.N., Diamond, I. & Smith, W.F.P. 1998. The determinants of infant mortality in Malaysia: A graphical chain modeling approach. Journal of the Royal Statistical Society A 161(3): 349-366.

Pollard, A.H., Yusuff, F. & Pollard, G.N. 1981. Demographic Techniques. Sydney: Pergamon Press.

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.

Rutstein, S.O. 2005. Effects of preceding birth intervals on neonatal, infant and under-five years mortality and nutritional status in developing countries: Evidence from the demographic and health surveys. International Journal of Gynecology and Obstetrics 89: 7-24.

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.

Social Statistics Bulletin Malaysia, Department of Statistics Malaysia. 1965-2002.

Turrell, G. & Mengersen, K. 2000. Socioeconomic status and infant mortality in Australia: A national study of small urban areas, 1985-1989. Social Science & Medicine 50: 1209-1225.

Vital Statistics Malaysia, Department of Statistics Malaysia. 1964-2000.

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

*Pengarang untuk surat-menyurat; email: nuzlinda@usm.my