International Journal of Statistics and Applications
p-ISSN: 2168-5193 e-ISSN: 2168-5215
2013; 3(4): 132-140
doi:10.5923/j.statistics.20130304.06
Ebenezer Owusu-Sekyere1, Bonyah Ebenezer2, Ossei Linda3
1Department of Development Studies, University for Development Studies WA, Ghana
2Department of Mathematics and Statistics, Kumasi Polytechnic, Ghana
3Department of Mathematics, Kwame Nkrumah University of Science and Technology, Kumasi, Ghana
Correspondence to: Bonyah Ebenezer, Department of Mathematics and Statistics, Kumasi Polytechnic, Ghana.
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Hypertension is a major health burden worldwide. In Ghana, the Health Service reports that since 2008, hypertension continuous to be the third most common cause of morbidity and mortality in the Ashanti region with the Kumasi Metropolitan Area leading the pack of endemic areas. The aim of this paper was to examine the spatial distribution of the disease in the Kumasi Metropolitan Area using patients’ medical records. Using both quantitative and qualitative approaches, the research revealed that the disease was more profound in low-income suburbs of the metropolis than the high income communities. Again, the research further revealed that prevalence was high among females than males. Lastly, the high incidence of Hypertension was due to sedentary life style due mainly to the higher rate of urbanization. The research concludes that Hypertension is gradually emerging as a leading cause of death in the metropolis and therefore more efforts and resources should be made available to help manage the disease situation.
Keywords: Hypertension, Kriging, Incidence Rate, Metropolis, Blood Pressure
Cite this paper: Ebenezer Owusu-Sekyere, Bonyah Ebenezer, Ossei Linda, Spatial Modeling of Hypertension Disease in the Kumasi Metropolitan Area of Ghana, International Journal of Statistics and Applications, Vol. 3 No. 4, 2013, pp. 132-140. doi: 10.5923/j.statistics.20130304.06.
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![]() | Figure 1. Map of the Study Area |
and the size of the population at risk also be
, where
is the size of the risk entities at
.Following Oliver et al., (1998), towns are referenced geographically by their centroids with the vector of spatial coordinates
, which leads to the actual spatial support (i.e. size and shape of the towns) is not taken into account in the analysis. The empirical incidence rates of Hypertension disease written as :![]() | (1) |
and can be expressed as the realization of a random variables
that follows a Poisson distribution with one parameter (expected of number of count of hypertension disease). This implies the product of the population size
multiplied by the local risk
:![]() | (2) |
is modelled as a stationary random field with mean m, variance
and covariance function
.The conditional mean and variance of the rate variable
are expressed as:![]() | (3) |
![]() | (4) |
is estimated as the following linear combination of K neighbouring observed rates:![]() | (5) |
are determined in order to minimize the mean square error of prediction under the constraint that the estimator is unbiased. These weights are the solution of the following system of linear equations, Poisson Kriging system:![]() | (6) |


if
and 0 otherwise
is the population-weighted mean of the rates. The term
is a Lagrange parameter that is achieved from the minimization of the estimation variance subject to the unbiased constraint on the estimator. The addition of the term,
, for a zero distance deal with variability obtain from population size, leading to smaller weights for less reliable data. This term exactly stand for the difference between the variance of the risk and rate variables. We applied kriging to filter the noise from the observed rates aggregated to the settlement level, but not to estimate the risk within the settlement itself. The prediction variance based on Poisson kriging is computed using the traditional formula for the ordinary kriging variance:![]() | (7) |
or equivalently its semivariogram
. The semivariogram of the risk is estimated as[14]:![]() | (8) |
is the number of pairs of communities separated by vector
. The different spatial increments
are weighted by a function of their respective population sizes,
, a term which is inversely proportional to their standard deviation. We gave preference to pair data with small standard deviations. A permissible model
is then fitted to the experimental variogram so that we obtain the variogram, covariance value. In this work, we modeled using the weighted least-square regression procedure implemented in the SpaceStat 3.5.6 version software developed by BioMedware USA. Weighting scheme is employed to the least-square in fitting of a variogram model to experimental values. This is to ensure that the selected model is the one that minimizes the weighted sum of squares of differences between the experimental and model curves. The L which is the number of classes of distance is expressed as. ![]() | (9) |
|
![]() | Figure 2. Directional variograms for Females and Males hypertension mortality rates and risks with the model fitted |
![]() | Figure 3. Omni-directional variograms for Females and Males hypertension mortality rates and risks with the model fitted |
![]() | Figure 4. Maps of Females hypertension mortality risks estimated by Poisson kriging and the corresponding kriging variance |
![]() | Figure 5. Maps of Males hypertension mortality risks estimated by Poisson kriging and the corresponding kriging variance |
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