GEOGRAPHICAL ANALYSIS OF MALARIA-ATTRIBUTABLE MORTALITY AMONG MALAWIAN CHILDREN

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1 Malawi J. Sci. & Technol., 2009, 10(1):1-6 ISSN: print GEOGRAPHICAL ANALYSIS OF MALARIA-ATTRIBUTABLE MORTALITY AMONG MALAWIAN CHILDREN L.N. Kazembe 1, P.M.G. Mpeketula 2 1 Department of Mathematical Sciences, Chancellor College, University of Malawi, P.O. Box 280, Zomba, Malawi, and 2 Department of Biology, Chancellor College, University of Malawi, P.O. Box 280, Zomba, Malawi Malawi J. Sci. & Technol., 2009, 10(1):1-6 ABSTRACT Background. Since 2002, following the establishment of the health management information system, the Ministry of Health in Malawi started to investigate geographical distribution of malaria-related indicators by district, among other diseases. However, spatial heterogeneity due to lack of uniformity in reporting rates, varying population sizes and differences in health seeking behaviour, can be misleading if not accounted for when mapping disease rates. Methods. This paper applied a statistical modelling approach to malaria case fatality ratio data for 30 Malawian districts for to assess spatial contrasts. A Poisson model incorporating Bayesian mapping techniques was used to smooth data, and was compared against the standardized mortality ratio technique. Results and Conclusion. The risk of malaria deaths varied across districts, with significant high risk in Lilongwe and Zomba, whereas low risk areas were observed in Salima, Phalombe and Mulanje. Factors contributing to such patterns warrant further research, probably at a much smaller scale, but may include increasing anti-malarial drug resistance, inavailability or inaccessibility of prompt effective treatment at primary health care level. This model could easily be adapted to other malariometric and tropical diseases indicators where geographical variability is of epidemiological importance. Key words and phrases: Malaria attributable mortality, spatial analysis, Malawi, surveillance, Bayesian hierarchical model, Markov Chain Monte Carlo simulation techniques 1. INTRODUCTION In order to inform the performance of the health care delivery in Malawi, the Ministry of Health has been collecting data on key health indicators, including those on the disease burden, through the health management information system (HMIS) (Chaulagai et al., 2005). Since 2002, the Ministry started to display certain disease information using maps to describe their geographical variability (Government of Malawi, 2003), highlighting areas of high and low incidence or mortality rates. These can also used to detect spatial clusters, which would generate aetiological hypotheses about possible causes for apparent differences in risk. Disease mapping, an age-old epidemiological technique, can inform planning of monitoring and evaluation activities of the Ministry. Mapping of crude incidence or mortality rates, however, can be misleading because of variability in population sizes, lack of uniformity in reporting rates from health facilities to the district health office, and differences in health seeking behaviour (Cameron and Trivedi, 1998; Ugarte et al., 2006; Chilundo et al., 2004). These misrepresent the real risk heterogeneity among regions, making it difficult to distinguish genuine differences from chance variability. Appropriate geographical monitoring and evaluation of impact of interventions would be enhanced by applying statistical models that allow a more accurate display of true rates of the disease. The most Corresponding author: L. Kazembe, Department of Mathematical Sciences, Chancellor College, University of Malawi, P.O. Box 280, Zomba, Malawi. lkazembe@chanco.unima.mw widely used strategy, to account for spatial heterogeneity, is to estimate the spatial distribution of risk by means of simulation based on Bayesian hierarchical models (Clayton and Kaldor, 1987). This approach enables relative risk maps to be estimated by smoothing criteria. There are several methods for generating estimates in Bayesian hierarchical models, however, the conditional autoregressive (CAR) model (Besag et al., 1991; Ugarte et al., 2006), is commonly used. In this article, we apply Bayesian hierarchical models (Fahrmeir and Lang, 2001), to analyse geographical variability of malaria attributable deaths, using health facility data, aggregated at district level. Specifically, a Poisson regression model for count data, incorporating random effects for each district, is applied to allow modelling of overdispersion, spatial heterogeneity and correlation. Neglecting or inappropriate modelling of these issues would result in biased estimates (Cameron and Trivedi, 1998). Malaria in Malawi, as elsewhere in the sub-saharan Africa region, remains one of the leading causes of mortality in children under the age of five, contributing over 40% of all deaths in children under the age of two (Government of Malawi, 2002). Control efforts aim to halve the burden of malaria by the year 2010 and a further 50% by Among others, the key indicators of successful malaria control will include reduced malaria-specific mortality among under-five children by at least 25% by 2006 and 50% by 2010; and reduced age-structured, malaria case-fatality rate by 25% by 2006 and 50% by 2010 (Government of Malawi, 2002). Mapping district-

2 2 Kazembe et al., Analysis of malaria-attributable mortality specific mortality rates may identify districts that are of high risk. In our analysis we tried to answer the following questions: 1. What is the pattern of malaria deaths in the country. Is there any spatially structured variation or unstructured heterogeneity in the data? 2. Are there any districts with spatially significant mortality rates? Are there any possible outliers or clustering depicted by the data? Identifying hot spot districts would allow further assessment of aetiological factors attributive to the patterns of the disease. More importantly this could guide the malaria control program to classify districts where resources are needed most to reduce the burden of the disease further. 2. MATERIALS AND METHODS 2.1. Malaria mortality data Cases were sourced from the Malawi HMIS database. The HMIS is a surveillance database of most common diseases in Malawi, including malaria (Chaulagai et al., 2005). Within the HMIS, a network of district health offices (DHO) report monthly or quarterly to the system, depending on the nature of the disease. Each DHO in turn, is fed weekly by a network of health facilities under its jurisdiction. At each health facility, registers are used to enter relevant indicators and are supposedly analyzed at the close of each day to assess trends and anomalies arising in the data, and for immediate decision-making in case of epidemics. For our study, we used district-aggregated malaria attributed mortality data, recorded monthly between 2000 and A total of 30 districts (including the 4 cities of Zomba, Lilongwe, Blantyre and Mzuzu), were used as units for spatial analysis. A mean total for each district was used in our analysis. The outcome variable analysed was the case fatality rate (CFR), defined as the ratio of the total number of individuals who died in hospital due to the malaria to the total number of admissions in the district. We restrict our analysis to children under the age of five realizing that this is the group of highest risk, and any results from this study would be of epidemiological importance (Roll Back Malaria, 2000). Figure 1 shows the crude CFR by district Statistical analysis Two approaches were used to estimate the geographical distribution of risk. The first approach used the classical standardized mortality ratio (SMR) (Clayton and Kaldor, 1987). The SMR measures local deviation of the disease risk. For observed count O i, and expected counts E i in the ith district, the SMR is calculated as the ratio between observed and expected deaths, i.e., and its standard error is SMR O i /E i, (1) se(smr) = N i /E i, (2) where N i is the corresponding population at risk (i.e., the total number of children hospitalised) in each district i = 1,..., 30. The working assumption with SMR is that Fig. 1. Choropleth map of raw case fatality rates of malaria mortality, at district level in Malawi, for children aged under-five years from January 2000 to December Areas with no or insufficient data are marked with diagonal solid lines. the observed counts are independent and drawn from a Poisson distribution, O i Po(θ i E i ), with mean θe i where θ i is the relative risk (RR). The expected number of cases in each district is calculated as E i = N i ( Oi Ni ). The SMR is therefore an estimator of θ. The second approach applied the Bayesian hierarchical model fitted via Markov chain Monte Carlo (MCMC) methods. The counts model considered, in term of the mean, is log θ i = log E i + α 0 + f geo (s i ). (3) where log E i is the offset and α 0 is a fixed effect. Here exp(α 0 ) represents the average risk of mortality over all the health districts. If area covariates are available these can be incorporated into the model as fixed effects (w i γ) or smooth functions for continuous variables f ij (x ij ). The component f geo (s i ), s i {1,..., S} is the spatial component, with S the maximum number of areas considered. The component f geo (s i ) can be split further into two random variables, such that f geo (s i ) = f unstr (s i ) + f str (s i ). The first random variable, f unstr (s i ), is assumed to be independently and identically distributed for all districts. This permits within district heterogeneity due to differences in healthseeking behaviour (possibly based on remoteness of facility), admission policies (possibly based on DHO policy) and reporting of statistics (possibly reflecting (in)competencies of responsible personnel) since these may not necessarily be similar for adjacent districts. The

3 MJST 2009, 10(1):1-6 3 second component, the structured component- f str (s i ), represents a spatial process or correlation, and allows large scale similarities between districts to be estimated. The general model becomes log θ i = log E i +α 0 +f ij (x ij )+f unstr (s i )+f str (s i )+w iγ. (4) We considered the following three models: Model 0: Homogeneity model Model 1: Homogeneity + f str (District) Model 2: Homogeneity + f str (District) + f unstr (District) Model 0 is a basic model testing for spatial homogeneity in the relative risk across districts. This is given by log Deaths i = log Admitted i + α 0 with the intercept as the only variable. Model 1 assessed the hypothesis of spatially structured risk. In model 2 we combined and simultaneously estimated the two spatial effects, yielding: log Deaths i = log Admitted i + α 0 + f str (s i ) + f unstr (s i ). Estimation of the parameters of the models is through the Bayesian approach, thus equation (3) or (4) forms the first level of a hierarchical Bayesian model. To complete the formulation, prior distributions are assigned to all parameters at the second level of hierarchy. The fixed effect, α 0, was assigned flat prior distributions. The district effects f str were fitted as spatially structured effects through the CAR prior (Besag et al., 1991). This assumes that contiguous areas, i.e., districts sharing a common boundary, have similar risk patterns. The CAR prior has the form f str (s) {f str (t), t s} N( s i, τ 2 str/m s ) (5) where M s is the number of adjacent districts and t is the neighbour of district s, s i is the mean of area s pooled from neighbouring districts, τstr 2 is a spatial variance. The random effects f unstr were assigned a zero mean Gaussian prior distribution: f unstr (s) N(0, τunstr). 2 The degree of heterogeneity was controlled by τunstr. 2 To complete the Bayesian hierarchy, hyper-parameters should be specified. Standard choice for the hyperparameters for the variance components, τi 2 (in the CAR model and the unstructured component) is the Inverse Gamma prior, IG(a, b) where a = and b = Bayesian inference is based on the analysis of posterior distribution of the model parameters. In general the posterior is highly dimensional and analytically intractable, which makes direct inference almost impossible. This problem is circumvented by using MCMC simulation techniques, whereby samples are drawn from the full conditional distribution of parameters given the rest of the data. Full details of the simulation techniques can be found elsewhere (Fahrmeir and Lang, 2001). The models were implemented in BayesX (Brezger et al., 2005), a public-domain software for analysing structured additive regression models. Convergence was visually assessed by plotting cumulative path plots for each of the monitored parameters (Yu and Mykland, 1998). For model comparisons we used the Deviance Information Criterion (DIC) (Spiegelhalter et al., 2002), based on the Bayesian posterior distribution of the deviance statistic D. A model s fit is summarized by the posterior expectation of the deviance D, and the model s complexity is captured by p D, the effective number of parameters. The DIC is then defined as DIC = D + p D. Smaller values of DIC indicate a better fitting model. Results from the best fitting model were mapped. The smoothed RR estimates were plotted together with a map of posterior probabilities. This map assessed areas of significantly lower or greater risk compared to the overall mean of the whole area (RR=1). The posterior probabilities were divided into <20%, 20 80% and >80%, by applying Richardson s criterion (Richardson et al., 2004). Values of greater than 80% strongly indicate that the risk was higher than the mean of the whole area, and values of less than 20% indicate that the area had risk lower than the mean risk of entire area. Intermediate values (20 80%) indicate that there was not enough evidence to differentiate from the overall risk RAW SMR SMOOTH Fig. 2. Clouds of points (scatterplots) representing the estimates from the three approaches used: the raw case fatality ratio (RAW), standardized mortality ratio (SMR), and the Bayesian hierarchical model (SMOOTH). 3. RESULTS A total of 12, 349 children were recorded to have died of malaria between January 2000 and December 2001 in all districts of Malawi. This represented about 7.9% of all children hospitalized of the disease. The mean total number of children who died per district was 671 from an average total of 8283 hospitalized children per district. Table 1 shows summaries of observed, expected cases, and raw case fatality ratio. The mean across districts of the number of deaths was (range: ), and median was The raw CFR ranged from 0.95 to 19.22, with a mean of 7.86 and median of Figure 1 shows a map of the raw CFR. The district of highest risk was Kasungu (black area), while Chiradzulu had the lowest risk (white area). Districts of relatively high risk included Rumphi, Balaka, Nsanje, Machinga and Mulanje. No data were available for Blantyre district and Blantyre city. Table 1 also gives SMR estimates. The mean RR was

4 4 Kazembe et al., Analysis of malaria-attributable mortality TABLE 1 Summary statistics for the raw rates, unsmoothed relative risk (standardised mortality ratio) and smoothed relative risk of malaria mortality among children at district level in Malawi. Statistics Observed cases Expected cases CFR (%) Unsmoothed RR Smoothed RR Minimum st quartile Median Mean rd quartile Maximum CFR=Case fatality rate; RR=Relative risk TABLE 2 Deviance information criterion (DIC) values for the different models of malaria mortality in Malawian districts, for the year Model: D pd DIC Model Model Model (a) (b) Fig. 3. Maps showing (a) standardized case fatality rate and (b) the corresponding standard error. Areas with no or insufficient data are marked with diagonal solid lines (range: ), and the median was A modest shift downwards in smoothed rate values can be seen compared to the raw rates (Figure 2). Figure 3 shows choropleth maps of the SMR and the corresponding standard errors for each district based on equations 1 and 2. The SMR gave a slightly heterogeneous map (Figure 3a), further suggesting that the pattern was strongly influenced by random variability in the distribution of malaria cases. The standard error of SMRs were high for isolated areas, e.g., Salima, Nsanje and Mulanje (Figure 3b), reflecting how extreme values may influence the standard error estimates (Eq.2). The geographical distribution of risk is similar to the raw CFR (Figure 1). This is not surprising since the correlation coefficients between the raw CFR and SMR was r =1.00. Figure 2 shows the combined representation of the cloud of points (scatterplot) corresponding to the results for each pair of estimators. The data points for RAW versus SMR are aligned along the diagonal line, indicating perfect correlation. Based on the DIC values (Table 2), model 2 (model with both structured and unstructured spatial variation) was better than others. The assumption of spatial homogeneity is rejected (DIC=593.47) for spatial heterogeneity (DIC=571.72). However, model 1 and 2 can not be distinguished. In other words, the inclusion of unstructured spatial effects in the model adds very little to the model fit. We therefore report the results on model 1. The overall relative risk across districts was RR=0.13 (based on α 0 = 2.06), but was not significant at both 80% and 95% credible intervals. The summary of relative risk estimates from model 1 are shown in Table 1. The mean RR was estimated at 0.84 (range: ), and the median was Compared to the unsmoothed RR, these estimates are shrunk towards the overall mean (RR=1.00). In fact the correlation between the unsmoothed and smoothed RR was r = This is also evident in Figure 2, indicating the smoothing effect of the Bayesian hierarchical model on the SMR estimates. Figure 4(a) shows the smoothed RR, with the corresponding significance map (Figure 4b), highlighting hot spot districts. These RR show less spatial variation in risk and probable clusters of high and low RR can be seen from the plot. Notable in the map (Figure 4a and b), are the high RR observed in Lilongwe and Zomba districts, while low RR were observed in Salima, Mulanje and Phalombe districts. Major changes due to the smoothing effect, when comparing the SMR and smoothed RR, are observed in Dedza, Kasungu, Salima, Rumphi, Mwanza and Phalombe districts. It can also be noted that Blantyre has an estimate, an expected result of the model, due to pooling of information from neighbouring areas. 4. DISCUSSION This paper has answered a number of questions on the geographical variability of malaria-related mortality at district level in Malawi. We applied, a Bayesian hierarchical model to describe the distribution of risk of dying of malaria for children under the age of five. This case study is but one example of many conceivable applications of such models in malaria research and in general in public health research. It is evident that mortality

5 MJST 2009, 10(1):1-6 5 risk estimates based on the raw or standardized mortality ratio estimators can be misleading. The correlation between estimates from SMR or raw approach and the model approach support this assertion (Figure 2). This seems to suggest that spatial correlation was strong in the data, and failure to account for this may lead to erroneous conclusions. The smoothed estimates, through the Bayesian hierarchical model, are easy to interpret, despite the fact that the posterior estimates are conservative, with high specificity and low sensitivity (Richardson et al., 2004). This has its own advantage as it avoids false positives thereby producing true clusters in the maps. Put differently, the smoothed malaria risk estimates give a more stable pattern of the underlying risk of disease than that provided by the raw estimates (Ugarte et al., 2006; Richardson et al., 2004). (a) Fig. 4. (a) Smoothed relative risk (RR) and (b) the corresponding posterior probability for RR >1: <20 (white areas: significantly lower); 20-80% (grey areas: no significance); >80% (black areas: significantly higher). The maps are based on Model 1 in Table 2. In this analysis, we saw that the risk of dying of malaria is varied between districts, and even among districts that neighbour each other. Factors contributing to this pattern are a matter of conjecture. Unmeasured socioeconomic differences might be some of the factors related to this pattern. Rural masses are at increased risk of malaria infection and death because they are not able to pay for effective malaria drugs nor afford transport to a health facility for prompt treatment of malaria (Koef et al., 2004). The further the village is from the health centre, the more disadvantaged the households are in terms (b) of getting early health care. Rurality is, therefore, one of the factors worth considering in future research. Medical services are often concentrated around trading centres, most far removed from those in need. The growing levels of anti-malarial drug resistance may also contribute to differences in the risk of in-hospital mortality. It has been argued that increases in malaria deaths in Africa can be attributed to increase in drug failure (Zucker et al., 1996, 2003). The full extent of such effects are not known in Malawi, since data are only available at few sentinel sites, but, in another study, using hospital register data, the effect of treatment regimes on malaria-attributed mortality was inconclusive (Kazembe et al., 2006). The geographical pattern can also be explained by variability in health seeking behaviour. Health seeking behaviour plays a critical role in accessing prompt and effective care. Home based care or traditional medicines are the first sources of care in most communities because of traditional beliefs, difficulties in accessing and unavailability of formal health services (Munthali, 2005). Only when the disease is perceived to be severe or near fatal, do people seek modern biomedical care at health facilities (De Savigny et al., 2004). This may further be compounded by delayed referrals, making such children worse-off when they arrive at the hospital (Kazembe et al., 2008). This is the first analysis to examine the geographical distribution of malaria mortality risk in Malawi. No prior studies of this nature, except to model malaria incidence risk (Kazembe, 2007), have been carried out in this area, and it shows the potential HMIS data can give for informed decision making in malaria control in Malawi. However, as with all routinely collected data there are known limitations on data quality in terms of completeness, correctness and consistency. As stated above, health facility data under-report malaria cases that occur in the community because most people resort to home or community-based care (Chilundo et al., 2004; Chaulagai et al., 2005; De Savigny and Binka, 2004). It is therefore reasonable to interpret the risk pattern realized in this study as representing the risk of dying from severe malaria (Roll Back Malaria, 2000, 2005). When considered necessary, under-reporting can be adjusted for in the analysis (Chaulagai et al., 2005). This will be the focus of further future study. Moreover, there is need in future models to consider models suited for abrupt discontinuities in RR. A closer look at the results show highly elevated RR for Lilongwe and Zomba which have relatively lower SMR but neighbouring districts (Kasungu, Dedza, Salima; Mulanje, Balaka, Machinga with high SMR) have highly reduced RR. Thus there is not only smoothing and shrinking of RR estimates but also possible flipping, and may be attributed to the choice of the model. Indeed as suggested by the referee to this paper, one may consider an alternative Besag et al. (1991) specification using heavy-tailed, double-exponential distribution than the Gaussian distribution and/or semi-parametric spatial models, see Denison and Holmes (2001); Knorr-Held and Rasser (2000); Green and Richardson (2002). Fortunately, some software to implement such models are available, and we plan to address this problem in our future research and implement it in BDCD software (Knorr-Held and Rasser,

6 6 Kazembe et al., Analysis of malaria-attributable mortality 2000). In conclusion, this study has filled a significant gap in the knowledge of geographical distribution of mortality attributed to malaria in Malawi. Spatial analysis of health events can help health researchers visualise problems and identify solutions. The maps identified districts that were of high risk of malaria mortality, and demonstrates the significance of using disease mapping techniques in a surveillance system. This has important potential implications for research and health policy planning purposes. First, the maps can generate leads for indepth epidemiologic or geographic studies that may shed light on factors contributing to malaria risk. Secondly, findings may help policy decision makers to pinpoint high-risk areas with specific health problems. Thirdly, the maps may contribute to developing and prioritizing health targets at the district -area level. Fourthly, results of this study could form basis for distributing and targeting interventions across geographical zones (Benach et al., 2003; Carter et al., 2000). For instance, the national malaria control programme may want to explore why the risk of malaria is higher in Lilongwe and Zomba, while in Salima, Mulanje and Phalombe the risk is significantly lower than other districts. ACKNOWLEDGEMENT LNK would like to acknowledge research training grant received from WHO/TDR for the year We thank the HMIS specialists at districts for making the records accessible. We would also like to thank the anonymous referees for their careful scrutiny of the original manuscript and thus contributed tremendous to the readability of the final version of the manuscript. ETHICAL CLEARANCE This study was approved by the Ministry of Health Ethics Committee. Benach, J., Yasui, Y., Borrell, C. (2003). Examining geographic patterns of mortality: The atlas of mortality in small areas in Spain ( ). European J. Public Health 31: Besag, J., York, J. and Mollie, A. (1991). Bayesian image restoration with two applications in spatial statistics (with discussion). Ann. Instit. Stat. Math. 43: Brezger, A., Kneib, T. and Lang, S. (2005). BayesX: Analyzing Bayesian structured additive regression models. J. Stat. Soft. 14:11. Cameron, A and Trivedi, P. (1998). Regression analysis of count data. Cambridge University Press, New York. Carter, R., Mendis, K.N., Roberts, D. (2000). Spatial targeting of interventions against malaria. Bull. World Health Organ. 78: Chaulagai, C.N., Moyo, C.M., Koot, J., Moyo, H.B., Sambakunsi, T.C., Khunga, F.M., Naphini, P.D. (2005). Design and implementation of a health management information system in Malawi: issues, innovations and results. Health Policy Plan. 20: Chilundo, B., Sundby, J., Aanestad, M. (2004). Analysing the quality of routine malaria data in Mozambique. Malaria J. 3:3. Clayton, D. and Kaldor, J. (1987). Empirical Bayes estimates of age-standardized relative risks for use in disease mapping. Biometrics 43: De Savigny, D., Mayombana, C., Mwageni, E., Masanja, H. (2004). Care-seeking patterns for fatal malaria in Tanzania. Malaria J. 3:27. De Savigny, D., Binka, F. (2004). Monitoring future impact of malaria burden in sub-saharan Africa. Am. J. Trop. Med. Hyg. 71S: Denison, D.G.T., Holmes, C.C. (2001). Bayesian partinioning for estimating disease risk. Biometrics. 57: Fahrmeir, L., Lang, S. (2001). Bayesian inference for generalized additive mixed models based on Markov random field priors. J. Royal Statist. Soc. C (Appl. Stat.) 50: Government of Malawi. (2002). Malaria Policy. National Malaria Control Programme. Community Health Sciences Unit. Government of Malawi, Lilongwe. Government of Malawi (2003). Health Information Annual Bulletin Ministry of Health and Population. Lilongwe, Malawi. Green, P.J., Richardson, S. (2002). Hidden Markov models and disease mapping. J. Am. Stat. Assoc. 97: Kazembe, L.N., Kleinschmidt, I., Sharp, B.L. (2006). Patterns of malaria-related hospital admissions and mortality among Malawian children: an example of spatial modelling of hospital register data. Malaria J. 5:93 REFERENCES Kazembe, L.N. (2007). Spatial modelling and risk factors of malaria incidence in northern Malawi. Acta Trop. 102: Kazembe, L.N., Chirwa, T.F., Simbeye, J.S., Namangale, J.J. (2008). Applications of Bayesian approach in modelling risk of malaria-attributable hospital mortality. BMC Medical Research Methodol. 8:7. Knorr-Held, L., Rasser, G. (2000). Bayesian detection of clusters and discontinuities in disease maps. Biometrics. 56: Kofoed PE, Rodrigues, A., Co, F., Hedegaard, K., Rombo, L., Aaby, P. (2004). Which children come to the health centre for treatment of malaria? Acta Trop. 90: Munthali, A.C. (2005). Managing malaria in under-five children in a rural Malawian village. Nordic J African Stud, 14: Roll Back Malaria. (2000). Framework for monitoring progress and evaluating outcomes and impact. Roll Back Malaria, World Health Organisation: WHO/CDS/RBM/ Roll Back Malaria Partnership. (2004). Monitoring and Evaluation Reference Group (MERG), Morbidity Task Force Meeting on Proposed method of estimating malaria incidence at country level (October 2004) minutes available at partnership/ wg/ wg-monitoring/. Richardson, S., Thomson, A., Best, N., Elliott, P. (2004). Interpreting posterior relative risk estimates in disease-mapping studies. Environ. Health Perspect. 112: Spiegelhalter, D.J., Best, N.G., Carlin, B.P and van der Linde, A. (2002). Bayesian measures of model complexity and fit. J. R. Stat. Soc. B (with discussion 64: Ugarte, M.D., Ibanez, B., Militino, A.F. (2006). Modelling risks in disease mapping. Stat. Meth. Med. Res. 15: Yu, B., Mykland, P. (1998). Looking at Markov samplers through CUSUM path plots: A simple diagnostic idea. Statistics and Computing 8: Zucker, J.A., Ruebush, T.K., Obonyo, C. (2003). The mortality consequences of the continued use of chloroquine in Africa: Experience in Siyaya, Western Kenya. Am. J. Trop. Med. and Hyg. 68: Zucker, J.R., Lackritz, E.M., Ruebush, T.K. (1996). Childhood mortality during and after hospitalization in western Kenya: effect of malaria treatment regimens. Am. J. Trop. Med. and Hyg. 55:

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