Spatial interaction effects of health indicators on confirmed malaria
cases in sub-Saharan Africa
By Stijn S. Imhof *
Abstract. To extend the existing literature on malaria transmission this paper employs spatial
econometric methods and estimation techniques. Using spatial panel data models we find that the rate of confirmed malaria cases in a sub-Saharan country depends on the rate of confirmed malaria cases in neighboring sub-Saharan countries. A panel dataset of 36 Sub-Saharan countries over the period 2000 – 2010 has been used to investigate the effect of malaria transmission between countries. In addition, the World Health Organization has developed a strategic approach to reduce the number of humans who become infected through the transmission of malaria. We consider the effect of two health indicators, the rate of distributed insecticide treated nets and the total health expenditure as a percentage of GDP, on the rate of confirmed malaria cases.
JEL classification: C21, Q57, I18
Keywords: Malaria, health expenditure, insecticide treated nets, spatial econometrics
* Stijn S. Imhof. Master student in Economics at the University of Groningen, Faculty of Economics
1. Introduction
Malaria is considered to be an infectious disease and through the mode of transmission spatial dependency and proximity are important; not only time but also place determines whether a human becomes infected and in turn how malaria spread through an ecosystem (Wilson, 2001). For sub-Saharan Africa the endemicity of malaria has been largely unchanged for the past hundred years. The burden of the malaria disease and the total number of malaria deaths is greatest in sub-Saharan Africa in addition malaria is considered one of the great diseases of poverty (Carter and Mendis, 2002). To study the endemicity and transmission of malaria in sub-Saharan Africa various scientific disciplines, such as ecology, health geography and medicine, use spatial modeling techniques in order to capture the link between the mode of malaria transmission and spatial dependency. Most studies within the scientific field of ecology and medicine focus on environmental factors in relation to malaria risk and malaria incidence rates (Lindsay and Birley 1996; Tanser et al., 2003; Parham and Michael, 2010). Additional, a wide range of country specific cases studies exist on the topic of malaria transmission using different spatial modeling techniques (Koenraadt and Githeko, 2005; Kazembe, 2007. The impact and development of public health policy decisions in relation to the transmission of malaria are studied using a socioeconomic perspective (Kazembe et al., 2006; Egbendewe-Mondzozo et al., 2011; Karema 2012).
To extend the existing literature on malaria transmission this paper will take up a spatial econometric approach. Through the use of spatial econometric modeling and estimation techniques we develop a framework in which epidemiological phenomena, such as malaria transmission and proposed public health policy decisions, can be studied. Spatial econometric models assume that humans (i.e. spatial units) are distributed across space and time. In turn interaction effects among cross-sectional units can be indentified which can explain why observations associated with a specific location may be dependent on observations at another location. Following the same line of reasoning we could expect that observed malaria cases associated with a specific location may depend on malaria cases at another location. The biting of a human host by an infected female Anopheles mosquito permits transmission of malaria (i.e. the Plasmodium parasite) from a human host to a vector (i.e. the Anopheles female mosquito) and back to a human host.1 The multiplication of the Plasmodium parasites
1 Over thirty female Anopheles mosquito species commonly transmit the Plasmodium parasite. In addition, five
species of parasites of the genus Plasmodium, P. falciparum, P. vivax, P. ovale, P. malariae and P. knowlesi, are
within red blood cells in a human host will cause symptoms including fever, headaches nausea, and dehydration (Snow and Gilles, 2002). In severe cases the symptoms of the malaria disease will progress to coma or death.
A prominent aspect of the dire situation in sub-Saharan Africa is the lack of adequate health care systems to effectively deliver diagnostic test to confirm whether a human is infected with malaria. In addition the implementation of malaria prevention techniques and the continuing supply of antimalarial drugs are inadequate. Sub-Saharan Africa is highly vulnerable to international failure of global institutions which are concerned with malaria as a public health problem (Carter and Mendis, 2002). Two objectives in the management of malaria as a public health problem stand out. The first objective is to determine whether a human is actually infected with malaria such that adequate treatment can be provided. The second objective is to reduce the number of humans who become infected through the transmission of malaria.
This paper will progress as follow. In section 2 we give an overview of the policies which have been pursued by the World Health Organization (henceforth WHO) to combat malaria in sub-Saharan Africa. In addition our research questions are also spelled out in section 2. Next, in section 3, we discuss which ecological and socioeconomic determinants are fundamental for malaria transmission by reviewing the literature on this topic. In Section 4 we present a theoretical overview of the non-spatial and spatial panel data models which we will use to test the research questions. The data and data limitations are discussed in Section 5. Estimation results of the various model specifications are given in Section 6 and we discuss which model(s) have the best fit to describe the data. Section 7 concludes the paper and proposes directions for further research.
2. Background
efficiency of transferring malaria by three native species of mosquitoes (Gillies and Coetzee, 1987).2 The very high efficiency and technical challenges executing the indoor residual spraying technique in combination with the reluctance of individuals to allow spraying of DDT in their homes lead to the abandonment of the Global Malaria Eradication Program in 1969 for sub-Saharan Africa (Olliaro et al., 1996).
In the following three decades the focus shifted to technical issues and research and development of new tools, leading to advances in drug and vaccine development vector control and insecticide treated mosquito nets. Most emerging sub-Saharan African countries struggled to establish broad-based health care systems and as a consequence little global support was received to combat the malaria resurgence (Tanner and de Savigny, 2008). An important feature of the collapse of the Global Malaria Eradication Program is the strategy shift in 1978 of the WHO from malaria eradication to malaria control. By 1992, the combination of a worsening malaria situation and promising technical developments led to renewed global focus on malaria control and by 1998 the WHO setup the Roll Back Malaria initiative, which clearly defined intervention coverage targets for control, designed to eliminate malaria as a public health problem.
For sub-Saharan Africa the WHO has developed a strategic approach from 2000 onward which is divided in two objectives: prevention and case management (World Health Organization, 2012). The chosen objectives are complementary and work in opposite directions; to prevent the transmission from malaria infected mosquitoes to humans (and from malaria infected humans to non-infected mosquitoes). The most broadly applied prevention techniques are indoor residual spraying and the distribution of insecticide treated (mosquito) nets (henceforth ITNs). Both prevention techniques shorten the lifespan of adult female Anopheles mosquitoes and reduce human contact with infected and non infected mosquitoes. Indoor residual spraying is a malaria prevention technique which has already been explained in the above section. The second broadly applied intervention technique is the mass distribution of ITNs to control for the spread of mosquito vectors. ITNs are conventional insecticide nets that are treated with an insecticide. An ITN has a dual function; first, a human sleeping under a net is protected from malaria infection and second, the transmission of malaria among local populations is reduced. Through the new global focus on malaria control and increased international funding between 2000 and 2010 there has been an increase in the rate of ITNs distributed for sub-Saharan Africa as can be seen from Figure 1. Both the total
2 Anopheles gambiae, Anopheles arabiensis and Anopheles funestus have a predominant role in the transmission
number of confirmed malaria cases and the total distributed number of ITNs are divided by the total population of the 36 sub-Saharan countries included in our study.
The second objective of the strategic approach of the WHO to control for malaria in sub-Saharan Africa is case management. The objective of case management focuses on people suspected of having malaria seeking treatment in the health care sector. Suspicion whether a person is infected with the malaria disease can be confirmed with a malaria diagnostic test. In turn confirmed malaria cases should receive appropriate and effective antimalarial drug treatment. Through the objective of case management access to health care facilities that provided diagnostics testing and treatment have been facilitated. The WHO expect that by the end of 2013, in endemic countries, fifty percent of the people with malaria-like symptoms will receive a malaria diagnostic test in the health sector and hundred percent of the confirmed cases will receive treatment with appropriate and effective antimalarial drugs (World Health Organization, 2012).
The WHO objective of prevention through the use of ITNs is a health coverage indicator which reflect the extent to which humans in need actually receive important health interventions (World Health Organization, 2012). In addition the concept of case management is rather broadly defined strategy objective; no direct conceptual measure can be defined. Health care facilities, diagnostic testing and treatment have to be paid for by the population within a country. Total expenditure on health as a percentage of GDP is also a health indicator which in this paper serves as a proxy for the WHO objective of case management. In this paper we will therefore address the following two research questions. First, is spatial dependency important in the spread of observed malaria cases between countries of
sub-0,00 0,03 0,06 0,09 0,12 0,15 2000 2002 2004 2006 2008 2010 out of total populatio n Year
Figure 1. The distribution of ITNs in comparison to the number of confirmed malaria cases
the number of confirmed malaria cases divided by total population
Saharan Africa? Second, do the health indicators, of prevention through the distribution of ITNs and the expenditure on health as a percentage of GDP, have an effect on the observed malaria cases in sub-Saharan Africa?
3. Determinants of malaria transmission
Suspicion whether the mode of malaria transmission has occurred between infected female mosquito and a human host begins with the symptoms described in the previous section. Whether a human host is actually infected with the Plasmodium parasite is determined by clinical confirmation usually performed by medical trained and certified personnel at health care facilities. The method of clinical confirmation is therefore an important indicator in order to establish if the mode of malaria transmission has actually occurred. The only broad indicator of clinical malaria confirmation, which spans multiple yearly time periods and country observations, is provided by the WHO. At current levels of diagnostic testing the WHO makes a clear distinction between the proportion of human hosts with suspected malaria who receive a diagnostic test and in turn have confirmed malaria and the proportion of human hosts treated for malaria without diagnostic testing (World Health Organization, 2012). The results of the diagnostic tests, usually by microscopy confirmation or a rapid diagnostic test, confirm if an individual has been infected with malaria. The diagnostic test performed and their results are maintained at local health care registers such that malaria infections are clearly distinguished from non-malaria illnesses. In turn aggregate data is reported to district and higher administrative levels.
precipitation amounts, temperature and precipitation amounts are considered important components of the malaria transmission cycle in an ecological setting and have an influence on the malaria disease in sub-Saharan Africa.
In order to understand the transmission mechanism of malaria in an ecological system biotic components are also considered (Wilson, 2001; Aron et al, 2001). Biotic components constitute elements that have cellular structures and have the ability to affect other organisms and shape an ecosystem. Biotic components are usually classified by their function within an ecosystem (i.e. autotrophs, heterotrophs and detritivores). Humans are considered to be heterotrophs in an ecological system and through human interaction with the environment ecological systems are modified (Coluzzi, 1993; Wilson, 2001). Abiotic components affect the broad distribution patterns of fungi, plants and animals, biotic components in turn affect the manner in which the physical or chemical conditions of the environment are modified. The change in abiotic or biotic components enhance or retard the rate of malaria transmission by influencing the abundance of Plasmodium parasites, the distribution of mosquito vectors and their behavior or the risk of infection.
As explained above, ecological systems are influenced by human interaction with their environment. Population density, population migration and social-economic development are important factors contributing to the transmission of malaria within the forces of global ecosystem change (Aron et al., 2001). Geographical areas become more densely populated either through the growth of the population within the geographical area itself or migration of people towards a specific geographical area. Increased population density may bring more people into contact with Plasmodium parasites and mosquito vectors. In turn, resettlement of people due population migration, with no prior exposure to malaria may place them in malarious zones without the partial immunity acquired through years of exposure. In addition through population growth, genetic characteristics expressed in the blood cells of local populations may make them more susceptible to infections of malaria parasites (Livingstone, 1984)
biological difference between man and woman is related to the reproductive function. Pregnant woman and their unborn children are more susceptible to malaria infections and the risk of illness due to a reduction in immunity (Steketee et al., 2001). Gender patterns with respect to socioeconomic norms and responsibility are various, some examples are the division of labor between man and woman which in turn affects the exposure to the malaria disease, the division of financial resources between man and woman to prevent or cure the malaria disease and the acceptability and use of ITNs linked to cultural accepted sleeping patterns (Robert et al., 2003).
4. Spatial models and weight matrices
As explained in the introduction, spatial panel data regression analysis can be used to identify interaction effects among cross-sectional units. Three different types of interaction effects may explain why observations associated with a specific location may be dependent on observations at another location. First, the decision of a spatial unit to behave in some way depends on the decision taken by other spatial units, which are called endogenous interaction effects. Second, the decision of a spatial unit to behave in some way depends on independent explanatory variables of the decision taken by other spatial units, which are called exogenous interaction effects. Third, similar unobserved environmental characteristics result in similar behavior, which are called correlated effects (Manski, 1993).
In order to model spatial dependence between the rates of confirmed malaria cases we consider three spatial panel data models: the spatial panel Durbin model, the spatial panel error model and the spatial panel lag model. A full explanation of all available spatial panel data models is presented in Elhorst (2010). The spatial panel Durbin model can be considered the general model and special case of the spatial panel error model and the spatial panel lag model. In turn both the spatial panel error model and spatial panel lag model can be considered more general cases of the OLS model, as can be seen in Figure 2. The linear regression model with spatial specific effects can be written as:
(1)
0
0
0
0
denotes a 1 vector of independent variables. The 1 vector of independent variables is accompanied by a matching 1 vector of fixed but unknown parameters. Specifically, in our linear regression model the rate of confirmed malaria cases in a country depends on a set of observed local characteristics. Spatial specific effects, , are not present in our model specifications since all independent variables are considered space and time specific. Therefore the linear regression model with spatial specific effect reduces to a non-spatial linear regression model which can be estimated by ordinary least square. Any omitted spatial specific effect is considered to be part of the constant in our models. is an independently and identically distributed error term for and with zero mean and variance
.
Second, in order to model the interaction between spatial units we can consider a panel data model where the interaction between spatial units runs via a spatial autocorrelated process. This type of data model is called the spatial panel error model and can be written as:
(2)
∑ (2a)
Spatial panel lag model:
Spatial panel Durbin model:
Spatial panel error model:
OLS model:
The dependent variable depends on a set of observed local characteristics (i.e. the vector of independent variables ). In addition the error terms are correlated across space. The variable, , denotes the spatial autocorrelated error term which depends on the spatial autocorrelated coefficient . The spatial arrangement of units in the sample is described by a spatial weight matrix (where i = 1 or 2), in turn is an element of this spatial weight
matrix . The spatial panel error model is consistent with a situation where determinants which affect the rate of confirmed malaria cases omitted from the model are spatially autocorrelated or with a situation where unobserved shocks (i.e. an epidemic outbreak of malaria cases in a certain country) follow a spatial pattern.
Third, we consider a panel data model which contains a spatially lagged dependent variable, known as the spatial panel lag model and is written as:
∑ (3)
The dependent variable depends on the dependent variable observed in neighboring units and a set of observed local characteristics. The spatial autoregressive coefficient is denoted by and is an element of the spatial weight matrix . Specifically, in the spatial panel lag model the rate of confirmed malaria cases in a country depends on the rate of confirmed malaria cases in neighboring countries and the set of observed local characteristics.
Fourth, we consider the spatial panel Durbin model which includes both a spatially lagged dependent variable and spatially lagged independent variables and is written as:
∑ ∑ (4)
The dependent variable depends on the dependent variable observed in neighboring units. In addition the dependent variable also depends on the set of observed local characteristics in neighboring units. The spatial autoregressive coefficient for the dependent variable is denoted by and is an element of the spatial weight matrix . In addition the spatial autoregressive coefficient for the matrix of independent variables is denoted by which is a
first-order spatial autoregressive process are omitted from the model, and these variables are correlated with independent variables that are included in the model (Seldadyo et al., 2009).
The spatial weight matrix (where i = 1 or 2) is a matrix which describes the spatial arrangement of the units in the sample. In order to make spatial interaction possible two different spatial weight matrices have been setup in advance. A drawback of this approach is that the specifications of the matrices not directly follow from an underlying theory. By setting up two different matrices we investigate whether the results are sensitive to the specification of . Often the definition of a neighbor is based on geographic criteria, such as polygons having a common boundary (contiguity), points being within a critical distance band, or k-nearest neighbors. In order to model the effect of spatial proximity we have chosen two basic spatial weight matrices as a starting point from which to investigate how malaria spreads through an ecosystem. In our paper we consider a binary contiguity matrix and an inverse distance matrix. The binary contiguity matrix is a border contiguity matrix, where contiguous units (i.e. countries with a common border) are assigned weights of 1 and noncontiguous units (i.e. countries absent of a common border) are assigned weights of 0. The diagonal elements of the binary contiguity matrix are 0, such that no country can be a neighbor of itself. The binary contiguity matrix is a minmax-normalized matrix where the
(i, j)th element of becomes where , ], with
being the largest row sum of and being the largest column sum of . Due to scalar normalization symmetry and the basic model specification are preserved. Moreover, normalizing the spatial weight matrix by scalar fixes the scale of the spatial autocorrelated and spatial autoregressive coefficient. Since our binary contiguity matrix is setup in advance and not directly guided by theory, Kelejian and Prucha (2010) point out that normalizing by a vector of row sums (i.e. row-normalization) is not preferred, hence the choice for scalar normalization. The inverse distance matrix is a coordinate matrix and
measures the inverse distance between capital cities of all the sub-Saharan countries in the dataset (based on kilometre-converted great circle distances).3 The off-diagonal elements of the inverse distance matrix are of the form with 1, where is the distance
between two units (i.e. capital cities). Each row sum of the inverse distance matrix is finite. In addition the diagonal elements of the inverse distance matrix are 0.
5. Data
In total 36 sub-Saharan countries (see Appendix A) are included in the dataset which are included by their WHO policy implementation status of malaria control rather than malaria elimination.4 Malaria control is defined as reducing the malaria disease burden to a level at which it is no longer a public health problem. Whereas malaria elimination is characterized by the interruption of mosquito-borne malaria transmission as a result of deliberate human effort such that the incidence rate of infection reduces towards zero over a specific time period (World Health Organization, 2009). The time dimension of the data covers yearly observation from 2000 up to 2010. We use data from the last decennia since most of the data points can only accurately be obtained from this period.
The data on confirmed malaria cases is obtained from the World Malaria Reports 2005, 2008, 2009, 2010, 2011 and 2012 published by the World Health Organization.5 Specifically, we use the malaria country profiles in these reports to obtain the panel data on this variable. In order to make the number of confirmed malaria cases among countries comparable we divided each observation of confirmed malaria cases in a specific country in a specific year by the total population in a specific country in a specific year. Data on the total population in a certain sub-Saharan country for a specific year is taken from the World Development Indicators 2013 published online by the World Bank.6 By adjusting for population size, we end up with the rate of confirmed malaria cases. In turn the rate of confirmed malaria cases is our dependent variable in our study.
The distribution of the number of ITNs is obtained from the same source as the number of confirmed malaria cases (i.e. the World Malaria Reports). In turn the distribution of the number of ITNs is divided by the total population in a specific country in a specific year. By adjusting for population size, we end up with the rate of distributed ITNs. In this paper we consider the rate of distributed ITNs as the prevention objective of the WHO. The rate of distributed ITNs is a health coverage indicator (World Health Organization, 2012). We might expect that an increase in the rate of distributed ITNs would reduce the rate of confirmed malaria cases, since humans who use these ITNs are protected from obtaining malaria and in turn could not spread the disease further. We must note that in the case of confirmed malaria cases and the rate of distributed ITNs data points are missing. Out of the total set of 396
4 The dataset is available upon request from the author
observations in the panel dataset on this variable 62 data points are missing. All the missing data points can be attributed to the reporting inconsistency in the total number of confirmed malaria cases and the total number of distributed ITNs. Adequate knowledge about the confirmation of malaria by medical practitioners and registration of the number of confirmed malaria cases and the number of distributed ITNs are often not fully developed in sub-Saharan African countries and contribute these reporting inconsistencies (World Malaria Report, 2010). Due to the 62 missing data points, especially in the cases of spatial econometric modeling, we have to be cautious making strong inferences about estimation results. In turn these data points were estimated for each individual cross-section using both the techniques of interpolation and predictive mean matching.
The concept of case management, the second objective of the WHO strategy approach, is broadly defined and no direct conceptual measure can be identified. The total expenditure on health as a percentage of GDP serves as a proxy for this second objective since health care facilities, diagnostic testing and treatment have to be paid for by the population within a country. The data on total health expenditure as a percentage of GDP is taken from the Global Health Observatory Data Repository provided online by the World Health Organization.7
Between 2000 and 2010 the average expenditure on health as a percentage of GDP for the set of 36 sub-Saharan countries has increased with approximately one and half percent, as can be seen from Figure 3.
7 See URL: http://apps.who.int/gho/data/view.main
4,5 5 5,5 6 6,5 7 2000 2002 2004 2006 2008 2010 % of GDP Year Total expenditure on health as a percentage of GDP
As already noted in the previous section the existing literature on malaria focuses on the direct and indirect influence of weather and climate variability. As an environmental variable we included average yearly temperature in degree Celsius. Daily temperature observations are obtained from the land-based station dataset of the American National Climate Data Center.8 The global summary of the day of 500 land-bases stations is used to estimate historical yearly temperature averages. In contrast to the amount of available daily temperature observations, there are many missing data points on historical precipitation amounts. We therefore have chosen to exclude historical yearly precipitation averages in this paper.
The interaction of humans can be classified in broad forces on global ecosystem change in this paper we consider population density as a crude proxy for population migration between countries in the dataset and for population growth within a specific country in the dataset. A high population density facilitates greater exposure of humans who are at risk being affected with malaria (Wilson, 2001). The population density for a country is computed by dividing the total population size in a country for a specific year by the total land area in squared kilometers. Just like the data on total population, the data on land area size is obtained from the World Development Indicators 2013 provided online by the World Bank.9
6. Estimation results
In order to find out which spatial panel data model is appropriate to describe the data we estimate an unconstrained spatial panel Durbin model and test whether the model can be simplified (Elhorst et al., 2006; Ertur and Koch, 2007). The spatial panel Durbin model can be considered a more general spatial model and special case of the spatial panel error model and the spatial panel lag model, as can be seen from Figure 2. Only the scalar normalized contiguity matrix is used to facilitate initial model comparison. In this paper we use random effects for all spatial panel model specifications which allows for heterogeneity across spatial units. We assume that the independent variables and the cross-sectional specific error terms are independent of each other. Moreover, random effects offer an advantages over fixed effects in terms of efficiency since it allows for testing with more degrees of freedom and incorporates the information of the between effects estimator. In addition, all independent variables are considered space and time specific such that any omitted spatial specific effect is part of the constant in our models. In turn each non-spatial and spatial model specification has
8 See URL: http://www.ncdc.noaa.gov/cdo-web/
been tested for presence of heteroskedasticity. For all model specification the error terms are heteroskedastic such that the error terms do not have constant variance, we therefore use robust standard errors in all our estimation results. Table 1 reports our estimations results of cross-country differences in the rate of confirmed malaria cases using different non-spatial and spatial model specifications.10
10 We have used Stata/SE 11.2 to estimate our non-spatial and spatial panel data models. Specifically we have
used the XSMLE module developed by F. Belotti, G. Hughes and A.P. Mortari, distributed on the 17th of March 2013.
Table 1. Explaining cross-country differences in the rate of confirmed malaria cases using four different model specifications [where W is a minmax-normalized (border) contiguity matrix]
Determinants (1) (2) (3) (4) OLS model Spatial panel lag model Spatial panel error model Spatial panel Durbin model X X 0.048 (0.59) -0.008 (-0.15) -0.006 (-0.11) -0.013 (-0.23) 0.079 (0.35) 0.007*** (3.09) 0.009* (2.03) 0.009** (2.05) 0.009* (2.03) (-0.07)-0.001 -0.005*** (-2.61) -0.006* (-1.81) -0.006* (-1.86) -0.006* (-1.78) 0.000 (0.64) 0.000*** (3.22) (-0.01)-0.000 (-0.06) -0.000 (-0.28) -0.000 (0.10)0.000 0.178*** (3.57) 0.201* (1.97) 0.226** (2.20) 0.198* (1.81) (--) 0.236* (1.81) (--) (1.57) 0.182 (--) (--) 0.182 (1.33) (--) No. Obs. 396 396 396 396 R 0.138 0.117 0.088 0.108 Log likelihood 531.73 530.86 532.54
The spatial panel Durbin model can be considered the most general model used to estimate the data in this paper. Both endogenous interaction effects among the dependent variables and exogenous interaction effects among the independent variables are included in this model. To test the hypothesis whether the spatial panel Durbin model can be simplified to the spatial panel error model, : 0, we performed a Wald test which is shown in column (8) of Table 2. The result (0.34 with 4 degrees of freedom [df], p = 0.85) indicate that :
0 cannot be rejected (i.e. there is no reason to reject the spatial panel error model in favor of the spatial panel Durbin model). To test the hypothesis whether the spatially lagged independent variable are jointly significant, : 0 we again performed a Wald test which is shown in column (8) of Table 2. The results (0.43 with 4 degrees of freedom [df], p = 0.79) indicate that : 0 cannot be rejected (i.e. there is no reason to reject the spatial panel lag model in favor of the spatial panel Durbin model). Next we consider the spatial panel error model and spatial panel lag model in turn. Column (3) and (2) of Table 1 show the results of the spatial panel error model and spatial panel lag model.
In order to determine whether the spatial panel error or spatial panel lag model is more appropriate to describe the data in comparison to the OLS, we can use the classical Lagrange Multiplier (LM) test proposed by Anselin (1988) as well as the robust Lagrange Multiplier (LM robust) test, proposed by Anselin et al. (1996), which are shown in column (5) of Table 2. Both the classic and the robust tests are based on the residuals of the OLS model and follow a chi-squared distribution with one degree of freedom. The hypothesis of no spatially
Table 2. Lagrange Multiplier and Wald tests for determining which model specification is most likely to explain the data
Lagrange Multiplier test (5) (6) (7) (8) OLS model
Wald test Spatial panel error model
Spatial panel lag model
Spatial panel Durbin model
Spatial error Spatial error F(1, 28) = 1.78 [ : 0] (--) F(4, 24) = 0.34 [ : 0] 1.62 0.46
Spatial lag Spatial lag
(--) F(1, 28) = 3.27* [ : 0] F(4, 24) = 0.43 : 0] 2.99* 1.82
autocorrelated error term cannot be rejected at any significance level using both the classical LM test and the robust LM test. The OLS model is therefore the more appropriate model to describe the data in comparison to the spatial panel error model. Next we consider the hypothesis of no spatially lagged dependent variable. At 10% significance we must reject the hypothesis of no spatially lagged dependent variable, whereas using the robust test, the hypothesis of no spatially lagged dependent variable cannot be rejected. In order to get a clear picture if we can use the spatial panel lag model to describe the data we also perform a Wald test for the spatial panel lag model, using the null hypothesis : 0 shown in column (7) of Table 2. The null hypothesis . . : 0 that the spatial autoregressive coefficient is zero must be rejected at a 10% significance level and under weak assumptions the spatial panel lag model could be an alternative to the OLS model.
From the above discussion both the OLS model and the spatial panel data model are appropriate to describe the data, depending on the significance level used to interpret the Wald and Lagrange Multiplier tests. Under the OLS model specification, the independent variables expenditure on health, average yearly temperature and population density are significant, in contrast the rate of distributed ITNs is insignificant as can be seen from column (1) in Table 1. An increase in total health expenditure as a percentage of GDP increases the rate of confirmed malaria cases by 0.007. Since new malaria cases (i.e. non confirmed malaria cases) are dependent on diagnostic testing and treatment at health care facilities an increase in total health expenditure would result in an increase in the rate of confirmed malaria cases. As explained in section 2 the WHO expects that by the end of 2013 fifty percent of the people with malaria-like symptoms will receive a malaria diagnostic test in the health sector. Hence an increase in total health expenditure would facilitate broader access to malaria diagnostic testing in the health sector which in turn increases the number of confirmed malaria cases. The independent variables average yearly temperature and population density appear also to be significant under the OLS model specification. An increase in average yearly temperature levels decreases the rate of confirmed malaria cases by -0.005. Although our coefficient value does not convey any direct information about temperature ranges on the rate of confirmed malaria cases, the sign of the coefficient indicates the directional relationship.
of confirmed malaria cases in the own country by 0.236. Using the rate of confirmed malaria cases for sub-Saharan countries the transmission of malaria between countries can be shown using the spatial panel lag model. The independent variables expenditure on health and average yearly temperature appear also to be significant but both have lower t-values in comparison to the OLS model. An increase in the expenditure on health, as a percentage of GDP, increases the rate of confirmed malaria cases by 0.009. The coefficient value of expenditure on health under the spatial lag model specification is the same under the OLS model specification. An increase in average yearly temperature levels decreases the rate of confirmed malaria cases by -0.006. The coefficient value of average yearly temperature under the spatial lag specification is slightly smaller than under the OLS model specification. The population density appears not to be significant under the spatial panel lag model specification, although the value of the population density coefficient is positive for all spatial panel model specifications. The rate of distributed ITNs under all model specifications appears not to be significant. From our analysis the distribution of ITNs among populations in sub-Saharan Africa, as a WHO prevention objective, does not appear to have an effect on the rate of confirmed malaria cases. Under the spatial panel model specifications the coefficients of the rate of distributed ITNs are of the expected sign. An increase in the rate of distributed ITNs would reduce the rate of confirmed malaria cases. In addition population density appears only to be significant under the OLS model specification. Because the coefficient values of the variable population density are too small we cannot give a meaningful interpretation of how population density could affect the rate of confirmed malaria cases under each model specification.
In order to get a more complete picture whether the spatial panel lag model can be used we examine whether our model specification is sensitive to the choice of the spatial weight matrix. Table 3 reports the estimation results of two alternative specification of the spatial weight matrix. In column (1) of Table 3 we consider the minmax-normalized contiguity matrix as a benchmark. The second matrix is an inverse distance matrix. The inverse
The coefficient, , denoting the spatial autoregressive effect in the spatial panel lag model increases from 0.236 to 0.752 and becomes insignificant under the inverse distance matrix specification. The minmax-normalized contiguity matrix is more appropriate for our
spatial panel lag model due to the existence of a significant spatial autoregressive effect. Under both matrix specifications total health expenditure appears to be significant and has an effect on the rate of confirmed malaria cases. A percentage increase in total health expenditure will result in an increase in the rate of confirmed malaria cases in the own country and have a direct effect on the rate of confirmed malaria cases in neighboring countries. Alternatively, a percentage increase in total health expenditure in neighboring
Table 3. The rate of confirmed malaria cases (spatial panel lag model) using two alternative spatial weight matrices
Determinants (1) (2) Coefficient -0.008 -0.004 Direct effect -0.009 -0.004 Indirect effect -0.002 -0.001 Coefficient 0.009* 0.009** Direct effect 0.009* 0.010* Indirect effect 0.001 0.000 Coefficient -0.006* -0.006* Direct effect -0.006* -0.006* Indirect effect -0.001 -0.000 Coefficient -0.000 -0.000 Direct effect 0.000 0.000 Indirect effect 0.000 -0.000 Coefficient 0.201* 0.211 Coefficient 0.236* 0.752 No. Obs. 396 396 R 0.118 0.093 Log likelihood 531.73 530.20
countries will also have a direct effect on the rate of confirmed malaria cases in the own country.
7. Conclusion
Through the use of spatial panel data models and econometric techniques we have shown that epidemiological phenomena, such as malaria transmission can be studied. We have found weak evidence that spatial dependency is important for the rate of confirmed malaria cases between sub-Saharan African countries. Under weak assumptions the spatial panel lag model is appropriate to describe the data in comparison to the OLS model. The rate of distributed ITNs, as a health coverage indicator, appears to have no effect on the rate of confirmed malaria cases under all model specification. In contrast, an increase in the total health expenditure as a percentage of GDP has an effect on the rate of confirmed malaria cases. Moreover, there exists a direct interaction effect between sub-Saharan African countries if we consider total health expenditure as a percentage of GDP on the rate of confirmed malaria cases.
In future research it would be of interest to include a mosquito reproduction function (Parham and Michael, 2010; Mordecai et al., 2013) to account for the relationship of epidemiological factors that affect disease dynamics. In addition, through the use of a mosquito reproduction function, population density can also be modeled more consistently since the function allows for an alternative and more advanced modeling approach of human density. Furthermore, the econometric methods and estimation techniques presented in this paper could also be extended to a regional scale such that disease transmission and proposed public health policy can be studied.
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Appendix A
Countries included in our dataset: • Angola
• Benin, Botswana, Burkina Faso, Burundi • Cameroon, Central African Republic, Chad • Democratic Republic of the Congo
• Cote d’Ivoire • Djibouti
• Equatorial Guinea, Eritrea, Ethiopia
• Gabon, The Gambia, Ghana, Guinea, Guinea-Bissau • Kenya
• Liberia
• Malawi, Mali, Mauritania, Mozambique • Namibia, Niger, Nigeria
• Rwanda
• Senegal, Sierra Leone, Swaziland • United Republic of Tanzania • Togo
