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