1 Swiss Tropical Institute, Basel, Switzerland.
2 Medical Research Council, Durban, South Africa.
3 Faculté de Médicine de Pharmacie et dOtondo-Stomatologie, Université du Mali, Bamako, Mali.
Received for publication August 30, 2002; accepted for publication May 23, 2003.
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ABSTRACT |
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infant mortality; malaria; models, statistical; spatial analysis; variogram
Abbreviations: Abbreviations: DHS, Demographic and Health Surveys; MARA, Mapping Malaria Risk in Africa; OR, odds ratio.
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INTRODUCTION |
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A difficulty with mortality studies is that the verbal autopsies used to assign a cause of death are not very reliable (3). Many deaths in malaria-endemic areas, assigned to other causes, are related to malaria infection (4). Moreover, low birth weight is an important risk factor for infant mortality and is known to arise because of both prematurity and intrauterine growth retardation resulting from malaria infection of the mother during pregnancy (7). It follows that malaria may be a relevant risk factor for many deaths even when it is not the immediate cause. Hence, it is as important to look at the relation of malaria endemicity to all-cause mortality as it is to look at its relation to malaria-specific deaths.
Smith et al. (5) linked published all-cause mortality rates and entomologic inoculation rates across Africa and found an increase in the infant mortality rate with these rates but no clear trend with the child (1259 months of age) mortality rate. The major shortcomings of the study were the small number of sites compared and the fact that they were a convenience sample. Geographic variation in the factors independently affecting both malaria transmission and mortality (such as water availability) introduces ecologic confounding. Analyses linking site-specific mortality data with local malaria indices, which make appropriate adjustment for these ecologic confounders, are clearly needed.
There are a few data sets that allow these types of analysis. The databases we have used for this study are the Mapping Malaria Risk in Africa (MARA) and the Demographic and Health Surveys (DHS) databases. The MARA database consists of surveys recording malariologic information, with over 10,000 collected data points all over Subsaharan Africa, to date. It is currently the most comprehensive database on malariologic surveys in Africa (8). The DHS database, coordinated by Macro International, Inc. (Calverton, Maryland), provides nationally representative household surveys worldwide with large sample sizes of between 5,000 and 30,000 households, typically. It monitors indicators in the areas of demography, health, and nutrition.
We linked the two databases using their site-specific data and developed a geostatistical model that enabled us to investigate spatial patterns of infant mortality risk, to assess its determinants, and to carry out an ecologic analysis examining the relation between infant mortality risk and malaria. We demonstrated the methodology by applying the technique to data collected from Mali. The savanna and Sahel zones of the country represent an appropriate setting for implementing such a methodology, because of the tendency for living conditions to become generally more difficult in the more northerly, drier areas, while malaria transmission is generally expected to be more intense in the wetter, southern areas. Therefore, we cannot properly assess the effect of malaria transmission on infant mortality without adjustment for potential confounders. We believe our approach of linking the two databases to carry out an ecologic analysis of infant mortality risk to be novel. Instead of a district-specific approach (9, 10), we modeled the data at the individual level, using a site-dependent correlation structure, to estimate the various effects without relying on data that are aggregated by administrative boundaries, which would have led to loss of information. This approach provides estimates of the effects of various factors including malaria endemicity, taking into account confounding and spatial correlation. In addition, it allows us to produce maps of infant mortality risk adjusted for socioeconomic factors.
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MATERIALS AND METHODS |
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The DHS database is the most comprehensive database on child survival in Africa, compiled by a survey program in 23 countries funded by the US Agency for International Development and coordinated by Macro International, Inc. The aim of these surveys is to provide data for a range of monitoring and impact evaluation indicators within the population, health, and nutrition sectors. Birth histories since 1960 corresponding to 35,906 infants were extracted from the DHS carried out from November 1995 to April 1996 in Mali. Additionally, year of birth, residence, mothers education, infants sex, birth order, preceding birth interval, and mothers age at infants birth were extracted. Using location information provided by Macro International, we were able to geolocate the 183 distinct survey sites shown in figure 2 by using digital maps and databases, such as the "Africa Data Sampler" (13) and the "Geoname Digital Gazetteer" (14).
Statistical analysis
Logistic regression models were fitted to infant mortality, using SAS version 8.2 software (SAS Institute, Inc., Cary, North Carolina) to identify significant socioeconomic, demographic, and birth-related covariates. The variables chosen were those analyzed by Coulibaly et al. (15) in their report that summarizes the results of the 19951996 DHS survey in Mali in relation to mortality. The mothers age at the childs birth and the date of birth of the child were included in all models. In addition, the following variables showing a significant bivariate association with infant mortality were selected for subsequent spatial multivariate analysis: type of region, mothers education, sex, birth order, and preceding birth interval.
Bayesian hierarchical models were fitted to estimate the amount of spatial heterogeneity in infant mortality as well as associations between risk factors and infant mortality in the presence of spatial correlation. Ignoring this correlation would result in underestimation of the variance of the effects of risk factors (16). We used logistic models with village-specific random effects to assess geographic heterogeneity and the effects of different covariates. Some of the covariates used were at the individual level (socioeconomic, demographic, birth-related covariates) and some were at the village level (malaria prevalence category). Malaria prevalence was not observed at the locations of the mortality data but was estimated using the model by Kleinschmidt et al. (11). These estimates were categorized because explanatory analysis revealed a nonlinear relation between infant mortality and malaria prevalence. The cutoffs were chosen according to the frequency distribution of mortality data and on epidemiologic considerations. Spatial correlation was modeled by assuming that the random effects are distributed according to a multivariate normal distribution with a variance-covariance matrix related to the variogram of the spatial process (17). We used Markov chain Monte Carlo simulation (18, 19) to estimate the model parameters. Simulation-based Bayesian kriging was also applied to produce smoothed maps of mortality risk and of the variance of the map estimates (20). The deviance information criterion (21) was applied to assess the effect of malaria prevalence on infant mortality. The smaller the deviance information criterion values, the better the fit of the model. Further details of this modeling approach are given in the Appendix. The analysis was implemented using software written by the authors in Fortran 95 (Compaq Visual Fortran version 6.1) using International Mathematical and Statistical Libraries (IMSL) numerical libraries (Visual Numerics, Inc., Houston, Texas).
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RESULTS |
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Three spatial Bayesian models were fitted. A baseline model (model 0) included no covariates but an overall constant and site-specific random effects. Model 1 was an extension of the baseline model with the inclusion of year of birth and socioeconomic and demographic variables as potential risk factors. Model 2 included the same parameters as did model 1 but, in addition, adjusted for levels of malaria endemicity. In addition, a Bayesian nonspatial analog of model 2 was fitted for comparative purposes. The parameter estimates obtained from models 1 and 2 and from the nonspatial model are shown in table 1. Estimates of the odds ratios indicate that, in the nonspatial analysis, infant mortality was related to the estimated malaria prevalence after adjustment for the other risk factors. After taking into account the spatial correlation that was present in the infant mortality risk data, we found that the effect of malaria transmission was no longer significant. In fact, the point estimates of the odds ratios change little, but the confidence intervals become wider, confirming the importance of taking spatial correlation into account when analyzing geographic data (16). Model comparison revealed that the model with the smallest deviance information criterion value and, therefore, with the best fit was spatial model 1, which does not include malaria risk.
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The parameters 2 and
(table 1) measure the variance of the spatial process and the rate of correlation decay (smoothing parameter), respectively. Our data set indicates a small value of
with a posterior median of 0.04 (95 percent credible interval: 0.007, 0.24), suggesting a strong spatial correlation, because this parameter measures the range of the geographic dependency, which is defined as the minimum distance at which spatial correlation between locations is below 5 percent. In our exponential setting, it can be calculated as 3/
= 75 degrees of longitude and latitude. This implies a nonvanishing correlation between all sampled points and results in very smooth maps for the predicted random effects.
Figure 1 displays the distribution of malaria surveys. The figure shows that most of the surveys were carried out in the south and southwest of the country. There are very few surveys in the center around the Niger River and no surveys in the north of Mali. Model predictions of malaria risk at the DHS locations (figure 2) indicate a low-malaria-risk zone north of the Niger River that contradicts empirical evidence of high transmission, suggesting that the lack of data leads to imprecise estimates in this part of the country, which may distort the relation between malaria endemicity and infant mortality. The unadjusted map of infant mortality risk (figure 3), obtained by the predictions of the Bayesian model, reveals that the highest infant mortality rates are found in the central and central-east part of the country around the Niger River. Distinct foci of high mortality can be identified in the regions of Nara, Banamba, Dioila, Kadiolo, Kolondieba, and Kenieba. Figure 4 represents the variation in infant mortality that is not explained by socioeconomic differences (on a logit scale). This map is a measure of our estimate of the geographic variation of risk of infant mortality, independent of the particular socioeconomic circumstances of the mother. It therefore reflects the marginal burden of infant mortality that is due to ecologic factors, such as malaria transmission intensity and other diseases, at the map locations. A component of this may be residual socioeconomic factors that our covariate data did not fully take into account. In this map, we can distinguish three zones of high risk: the one in the central and central-east border with Burkina Faso, a zone of south Mali that covers the regions from Nara and Diema to Kolondieba and Bougouni, and a zone in the southwest in the region of Kenieba. Estimates of the variance of the residual spatial variation (figure 5) show lower variance in the estimates near locations with observed mortality.
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DISCUSSION |
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The risk factors that were found to be related to mortality are already well known. The negative association between maternal education and mortality has been previously described by Farah and Preston (22). Higher education may result in greater health awareness, better utilization of health facilities (23), higher income and the ability to purchase goods and services that improve infants health (24), longer birth intervals, and possibly higher maternal ages (25).
Although several studies have investigated the relation between malaria transmission and child mortality, this is the first study to our knowledge that attempts to assess this relation by taking into account the geographic variation that is present for both parameters after adjustment for socioeconomic confounders. In this analysis, we consider malaria prevalence as a measure of malaria transmission. There are alternative indicators of transmission intensity that have been used to study the effects of malaria on mortality. However, the relation between these indicators has not been fully investigated. The most usual measure is the entomologic inoculation rate, which is the product of the vector-biting rate multiplied by the proportion of mosquitoes infected with sporozoite-stage malaria parasites. Beier et al. (26) report that the entomologic inoculation rate is only weakly related to malaria prevalence. To our knowledge, no studies have been carried out on the best measure of transmission to study mortality.
We have estimated for the first time the geographic distribution of the burden of infant mortality in Mali in addition to that which can be attributed to socioeconomic differences. It is plausible that a large measure of this burden is due to the effect of malaria on infant mortality, even though we were not able to demonstrate this directly. The lack of a relation between malaria risk and infant mortality could reflect unmeasured local factors, for instance, variations in health provisions or the availability of a water supply in the dry Sahel region, which could have a stronger influence than malaria risk on infant mortality. Such unmeasured covariates with spatial structure could also explain the residual spatial correlation in the data. Information missing from the database regarding malaria control measures taken at different locations could also confound the analysis. Methodological problems related to the compilation of survey data sets, such as the MARA database, constitute a further limitation to our analysis. The surveys, for example, were carried out at different seasons and include different age groups at the various locations. It may well be that, in areas with seasonal malaria, the effect on mortality would be stronger than in areas with perennial malaria. The model of Kleinschmidt et al. (11) for malaria prevalence did not take seasonal variation into account, although malaria transmission in Mali is known to be highly seasonal (F. C. Tanser, South African Medical Research Council, Hlabisa, South Africa, unpublished manuscript).
An additional problem with the database is the sparsity of the surveys in the central-east part of the country. In this analysis, we used a subset of the data in order to deal with the different age groupings of the surveys at the various locations. Currently we are working on alternative approaches that overcome the limitations of heterogeneous age grouping, without omitting data.
An additional methodological problem is the misalignment of the DHS and MARA surveys in time and space. Our analysis is based on the assumption that spatial patterns of infant mortality and malaria risk are relatively stable in time. Although this assumption can be questioned, statistical analysis of the temporal changes of malaria prevalence over the last 40 years at the country level (27) showed no significant patterns. In addition, our analysis of infant mortality rates indicates a statistically significant time trend only for the early years of 19661971, but it is quite stable for the last 20 years, when over 80 percent of all cases are recorded. To overcome geographic misalignment, we estimated malaria prevalence at the DHS locations using the spatial malaria model of Kleinschmidt et al. (11). Although we believe that this modeling approach gives a good estimate of the general pattern of malaria prevalence in Mali and of the overall populations at risk, we cannot be confident in local malaria predictions, especially in areas remote from sampled locations. In particular, the paucity of sampling points in areas of very high infant mortality, especially in the Niger River delta, may have resulted in poor predictions in these areas. We propose to address this problem by compiling the databases from a larger area of West Africa and analyzing only the data points where misalignment is minimal. Despite these limitations, our study has demonstrated the considerable potential of spatial statistical methods for analyzing the DHS data. To our knowledge, this is the first analysis of infant mortality to use geostatistical models. The methods presented are valuable for both producing smoothed (covariate-adjusted) maps of mortality risk and assessing covariate effects. Such maps are particularly helpful to identify high mortality areas for most efficiently allocating limited resources in child survival programs.
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ACKNOWLEDGMENTS |
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The authors are grateful to the MARA collaboration for making the Mali malaria data available and to Macro International, Inc., for providing the names of the villages of the DHS.
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APPENDIX |
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To complete the Bayesian model specification, we need to adopt prior distributions for the model parameters. We chose noninformative uniform priors for the regression coefficients, that is, ß 1, and the following vague priors for the
2 and
parameters:
2 ~ inverse gamma(a1, b1) and
~ inverse gamma(a2, b2), with a1 = a2 = 2.01, b1 = b2 = 1.01. The model was fitted using Markov chain Monte Carlo simulation and, in particular, Gibbs sampling (18). The posterior distribution of
2 then is conjugate inverse gamma. From the nonstandard one-dimensional conditional distributions of all components of ß, U such as
, we sampled by using a random walk metropolis algorithm having a Gaussian proposal density with the mean equal to the estimate from the previous iteration and the variance derived from the inverse second derivative of the log-posterior. We ran a single chain sampler with a burn-in of 5,000 iterations, with convergence assessed by inspection of ergodic averages of selected model parameters. The chain thereafter sampled every 60th iteration until a sample size of 2,000 had been attained.
For model comparison, we utilize the deviance information criterion (DIC), as recently proposed by Spiegelhalter et al. (21). For a vector of parameters , it is defined by
, with D() being the deviance statistic
is the posterior expectation of D, and
is the posterior expectation of
, with both of them easily estimated from outputs of the Markov chain Monte Carlo simulation. Smaller values of the deviance information criterion indicate better fitting models.
To produce a smooth map of mortality risk, we use Bayesian kriging (16, 20). In particular, we obtain estimates of the mortality risk, Y0 = (Y(s01), Y(s02), ..., Y(s0l)) at any unsampled location s0 = (s01, s02, ..., s0l) by the predictive distribution
where the distribution of U0 at new sites given U at observed sites is normal
with and p(Y(s0i)|ß, U(s0i)) ~ ber(p(s0i)), with logit(p(s0i)) = x(s0i)ß + U(s0i). Equation 1 is the expectation E[P(Y0|ß, U0)P(U0|U,
2,
)] over the posterior distribution P(ß, U,
2,
|Y), which is identified by the Gibbs sampler. Numerically, this expectation is approximated by the average
where (ß(k), U(k), 2(k),
(k)) are samples drawn from the posterior P(ß, U,
2,
| Y). For mapping purposes, predictions were made for 600,000 pixels covering a regular grid of the whole area of Mali south of 18 degrees latitude north.
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NOTES |
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REFERENCES |
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