Study population and data sources

The data used for this study refer to children resident in mainland Tanzania aged 7–14 during the period 2010–2014. We combine national- and district-level representative data on academic performance among children with district-level estimates of Plasmodium falciparum parasite rates (PfPR) for each year from 2000 to 2015. The latter represent direct metrics of malaria risk, which we calculate based on pixel level estimates from the Malaria Atlas Project (MAP) [24] and pixel level population estimates from the WorldPop Project [25,26]. The MAP data consist of continuous predictions of Plasmodium falciparum parasite rates among 2 to 10 year-olds (hereafter simply referred to as PfPR) at 5 × 5 km spatial resolution. These are generated using a spatiotemporal Bayesian model combining (i) PfPR estimates of 27,573 spatially and temporally unique population clusters obtained from hundreds of community-based or national cross-sectional surveys from across the African continent, (ii) an optimized set of environmental covariates, and (iii) modeled coverage of Insecticide-Treated bed Nets (ITN), Artemisinin-based Combination Therapies (ACT) and Indoor Residual Spraying (IRS). In the modeling process, survey-based estimates of PfPR are adjusted by age, season and type of diagnostic (rapid diagnostic testing/microscopy), and the modelling of ITN coverage includes socio-demographic covariates [24]. Of the 27,573 population clusters 2,678 are from Tanzania (see S4 Fig for a map of clusters).

The WorldPop data consist of predictions of population density at 1x1 km spatial resolution. These predictions are generated using a non-parametric model in which census data are combined with land cover information, climatic data, elevation data, observed lights at night, information on networks of roads and waterways, large water bodies, and protected area delineations [25]. In the case of Tanzania, population grids are available for 2000, 2005, 2010 and 2015. We estimate intermediate years by taking the natural logarithm of the WorldPop estimates, linearly interpolating the missing years, and finally taking the exponential for the individual years. To arrive at annual district-level estimates of PfPR, we aggregate population data to pixels that correspond to the resolution of the MAP data. For each pixel we then multiply PfPR and the population count and overlay the resulting raster with 2002 district boundaries obtained from the Global Administrative Unit Layers initiative [27]. District-level averages are then calculated by summing over all pixels that fall within a district and dividing by the district population size. Fig 1 illustrates the spatial and temporal variation in PfPR for districts within regions of Tanzania during the period 2000–2015. A recent study concluded that the large drop in prevalence between 2000 and 2015 was due primarily to unprecedented levels of intervention coverage during this period [24].

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Fig 1. Developments in Plasmodium falciparum parasite rates for districts within regions of Tanzania, 2000–2015.

Each graph represents a region, and each line a district within a region, with 2002 boundaries obtained from the Global Administrative Unit Layers initiative.

https://doi.org/10.1371/journal.pone.0199542.g001

Data on children’s educational performance come from the 2010–2014 Uwezo cross-sectional surveys for Tanzania [28]. The data are representative at the district level, and cover children aged 7–16, both in and out of school. In the African context, this level of within-country coverage is unparalleled, and it provides a valuable opportunity to analyze developments over time and across space. The tests are designed to measure basic skills in English and Kiswahili literacy as well as numeracy. The numeracy test has six incremental levels: Number recognition, counting, magnitude comparison, addition, subtraction and multiplication. The literacy tests have five incremental levels: Letter recognition, reading words, reading paragraphs, reading a story and comprehension of the story read. For each test, children who fail to pass any of the levels are awarded a score of one. The other children are awarded a score equal to the highest level passed plus one. The difficulty of the tests is fixed and corresponds to the level expected after two years of completed schooling. The tests were developed by a panel of experts from the Tanzanian Institute of Education, the University of Dar Es Salaam, practicing teachers and experts in the subject area. They were refined in consultation with the Ministry of Education and Vocational Training to ensure that they reflect the national second grade curriculum.

The pooled test score dataset, which covers the surveys undertaken annually from 2010 to 2014, includes a total of 199,767 households and reflects a coverage rate of 79 percent relative to the survey design. From the pooled dataset we exclude children born before 2000, as this is the first year for which we have malaria data. Further, as we wish to control for birth-year fixed effects in our analysis (see below), we exclude children born in 2007, as this birth year is only found in the 2014 survey. This gives us a final pooled sample size of 246,325 children. Table 1 presents summary statistics for the main variables included in this study, split by low/high malaria prevalence districts.

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Table 1. Summary of district by birth cohort means, by PfPR category.

https://doi.org/10.1371/journal.pone.0199542.t001

The last data source is the National Centers for Environmental Information (NOAA) [29], which provides data on night-time light density from 1992 to 2013 at pixel level. Since data on economic activity over time and at the sub-country level is very limited or non-existent in low income contexts, night-time light density has been widely used in recent years to investigate variation in development outcomes [30].

Since the study is based entirely on existing, publicly available, anonymized datasets, no ethical approval has been sought.

Procedures and statistical analysis

We investigate the causal link between infection by malaria in early childhood and academic performance in later childhood (7–14 years of age). Thus, the outcomes of interest are performance in numeracy and English and Kiswahili literacy tests.

As a result of the nature of the Uwezo tests, raw test scores are not comparable across ages and survey years. Specifically, since the tests are not age-dependent, the median test scores increase with age (see S1–S3 Figs). By implication, the same raw score may be indicative of median performance among 7 year-olds but be well below median performance for 14 year-olds. Similarly, as there is some variation in the difficulty of tests across the survey years, the same raw test score may be indicative of a different standard of performance for individuals of the same age in different years. To increase the comparability of test score interpretations across individuals in the pooled sample, we therefore center raw test scores by age and year by subtracting the median score of all children of the same age tested in the same year from individual test scores. The centered test scores (hereafter referred to simply as the test scores) then indicate deviations from the median performance of children of the same age in the same year. We chose this transformation rather than the common approach of standardizing test scores by mean and standard deviations, because the test score distributions are highly skewed, and the median is a better measure of central tendency than the mean in skewed distributions.

Our main predictor variable is PfPR at the district level in a child’s birth year. We choose birth-year prevalence as a measure of the risk of contracting malaria in early childhood rather than an average prevalence over a given age range in order to avoid arbitrarily assigning specific weights to risks experienced at distinct ages in early childhood. It should be noted, however, that birth-year prevalence is in fact strongly correlated with the arithmetic mean of the risk experienced at each age prior to school entry (correlation coefficient 0.810). This essentially means that we would not expect to see different results if, instead, we were to use an average prevalence over a given age range (results using average prevalence for the three-year period covering the year before, of and after birth are available in the S1 Table). The decision to use birth year rather than any other year in early childhood was motivated by the facts (i) that for the majority of children, this is when the district-level risk is highest, and (ii) that pre-natal period and infancy are fundamental periods of brain development and hence most likely to be associated with the highest risk of cognitive impairment [31]. Importantly, however, given the strong correlation of district-level PfPR between years, we are not claiming to identify the specific effect of birth-year exposure but rather use birth-year PfPR as a proxy for early life exposure.

The analysis proceeds as follows. First, we present the crude association between birth-year PfPR and test scores graphically, plotting average test scores for groups defined by 0.1 intervals of birth-year PfPR. Second, we assess the relationship between birth-year PfPR and test scores in a multivariate regression framework. In addition to malaria exposure, we expect individual test scores to be determined by individual and household-specific factors, contextual factors in early childhood, and contextual factors in the survey year. To account for these multiple sources of variation, our baseline specification is as follows:

where y is the centered test score of interest, i indexes individuals, h indexes the household to which the child belongs, k indexes the child’s birth cohort (i.e. year or birth), j indexes the district of residence, and t indicates the year of the survey. On the right-side of the model, in addition to the main explanatory variable of interest (PfPR) and residual error (ε), we include five main groups of controls. These are: (1) individual factors (denoted X_i, which are her gender, birth order and a set of dummy variables for child age); (2) household factors (denoted X_h, which are the size of the household, three dummy variables capturing the highest level of education of the mother’s education, and two dummy variables for socio-economic status, based on ownership of assets); (3) district-level nightlights per capita in the child’s year of birth (denoted x_jk), which represents a time-varying measure of economic development at the district level; (4) joint survey year and district fixed effects (denoted λ_jt); (5) birth year given by the penultimate term. Note that the observed covariates were chosen based on the full set of information available in the datasets across all survey rounds (i.e. no controls were initially included but subsequently dropped). Also, fixed effects for each survey year are implicitly included since they are a linear combination of birth year and age.

To estimate the above specification, we rely on ordinary least squares (OLS) methods, treating the various sets of unobserved group-level effects (i.e. birth cohort, district by survey year etc.) as fixed effects. This is implemented in Stata v15.1 using the user-written command reghdfe [32]; a full set of replication files is also available in S1 File. We prefer OLS as its properties are well established and it constitutes a highly robust estimator for conditional means, regardless of the underlying distribution of the data [33]. OLS estimators naturally extend to incorporate multiple fixed effects, and we adopt this treatment of the unobserved terms since random or mixed effects approaches typically require some assumptions to be made about the structure of correlation between the random effects and other covariates. Fixed effects estimators, by contrast, impose no such assumptions and are thus expected to be consistent over a broader range of conditions. Furthermore, we found that the large size of the dataset and the multiple unobserved terms included in our model meant that alternative mixed effects (maximum likelihood) estimators frequently failed to converge.

In the calculation of standard errors for our estimates, we adopt a two-way clustering procedure. Here we follow Abadie and Wooldridge [34] who identify two primary and separate reasons for using clustered standard errors. The first is a sample design rationale, which captures the notion that if there are clusters in the population that are not represented in the sample, one should cluster errors at the level of such ‘missing’ clusters. In our case, these are the PSUs (villages) rather than administrative districts, since all districts are covered by the surveys. The second rationale for clustering arises when some aggregate of units, rather than individuals (or the units of observation), is assigned collectively to a treatment. In our case, following our definition of PfPR, this is the district by cohort birth year. We consider that both these sources of clustering are potentially relevant and, thus, we apply two-way clustering by the PSU and the district by cohort birth year. Note that this delivers more conservative results than clustering by either factor separately.

We recognize that our baseline specification may not capture the full range of factors that potentially confound the relationship between malaria and test scores. For example, high PfPR districts may have been systematically favored in the allocation of health interventions, and if these interventions had independent effects on children’s cognitive development this may have biased our results. To examine whether this source of bias is material, we estimate the relationship between PfPR and test scores using a household fixed effects estimator. This amounts to replacing the set of observed household covariates (X_h) with a general household-specific term, which is also treated as a fixed effect in the estimation. Because children born in different years living in the same household are likely to be less differentially affected by changes that occur between their birth years than children born in different birth years in different households, this should reduce (but may not entirely eliminate) such potential bias. For instance, a mother who receives health care information for her second child may use that information to improve care for her first child. Another mother who has a child in the same year as the first mother’s first child, but does not have a subsequent child, on the other hand, may not receive the improved information at all, and hence may not improve her child’s care. Therefore, substantial variations in estimates with and without these household fixed effects may indicate that some part of the partial correlation between malaria reduction and test scores is driven by other district-specific time-varying factors (such as childhood development interventions). On the other hand, the discovery of similar estimates would strengthen confidence in the assumption that districts have not experienced such differential paths.

In addition to the baseline and household fixed effects specifications, we undertake a series of robustness checks. First, we construct a pseudo-panel at the level of birth cohorts within districts [17,35]. The average outcomes in this panel will be a result of district-birth-year average individual and contextual factors, most of which are absorbed by district and birth-year fixed effects, which we include in a multivariate linear regression. This approach will deliver consistent estimates of the relationship between malaria and test scores provided that we assume that district-specific shocks or developments in the birth-year period covered by our analysis do not affect children born in different years differentially on average. Note that, under the assumption that seasonality in births is constant across the birth years considered, this approach also alleviates concerns that results are confounded by the facts that in the main analysis, (1) individuals born days apart, but in different years, are assigned different risks of malaria; and (2) individuals born within the same year but in seasons with different levels of malaria prevalence are assigned the same risk of malaria.

Next, we address the fact that we have chosen a transformation of data which is not standard in educational research. This may lead to a concern that our results are sensitive to the particular choice of transformation. To address this, we revert to the raw test scores and create a set of binary (dummy) variables, taking a value of 1 if the child scores above each specific increment. So, a child with the lowest test score (none correct) receives a zero for each of these dummy variables; and a child with the highest test score (all correct) receives a one for each. For each dummy variable we re-run our household fixed effects model, which amounts to a linear probability model in each case. Note that this method is similar to the first stage of the approach, set out in [36], used to consistently estimate parameters of an ordered logit model in the presence of fixed effects. The point is that by looking at the various incremental scores separately we take into account the ordinal nature of the raw test scores and allow for unequal differences in ability at each increment (i.e. the difference in ability between children receiving 1 and 2 may be larger or smaller than the difference between children receiving 3 and 4).

The next two robustness checks are a response to the fact that from the modelled PfPR data (Fig 1) it appears that in some districts PfPR increased between 2000 and 2002. While this increase may be an empirical reality, we cannot rule out the possibility that it is due to the specifics of the modelling behind the estimates. To deal with this concern, we test the sensitivity of our results to (i) dropping individuals from districts with an initial rise in PfPR, and (ii) dropping individuals born before 2002. The final robustness check is needed because a reduction in malaria which affects a given cohort in its birth year could also affect adjacent cohorts and thereby introduce imprecision in the measure of birth-year malaria exposure. To address this concern, we restrict the sample to individuals born several years apart who are therefore likely to have experienced different disease environments. In particular, we drop individuals born between 2002 and 2004.