Presumptive treatment for malaria has historically been the norm throughout much of sub-Saharan Africa (SSA). However, multiple problems plague presumptive treatment of malaria. First, considerable overlap in symptoms exists between malaria and other diseases [e.g., pneumonia; 1]. As a result, people that require treatment for other diseases might be inadvertently treated for malaria and sent home, with important consequences in terms of morbidity (and potentially mortality) and cost to the individual [2–4]. Second, there is substantial concern that presumptive treatment can promote more rapid emergence of anti-malarial drug resistance [5, 6]. Finally, as SSA countries transition to using artemisinin-based combination therapy (ACT) as their primary drugs for malaria treatment, presumptive treatment might be financially unsustainable given the higher costs of ACT [4, 7].

As a result of these concerns, the World Health Organization (WHO) has strongly promoted test and treat [8] as the primary malaria treatment policy for SSA countries. In this policy, “every suspected malaria case should be tested” and “every confirmed case should be treated with a quality-assured anti-malarial medicine” [8]. Because microscopy (the gold standard method in the majority of SSA countries [9]) is often unavailable in remote rural settings, the implementation of test and treat has relied heavily on rapid diagnostic tests (RDTs) for parasitological diagnostics [4, 5]. Recent studies have shown that the use of RDTs can lead to substantially improved targeting of anti-malarials when compared to only clinical diagnosis [10, 11]. In addition, despite the increased costs associated with using RDTs, test and treat might still be a cost-effective approach if it reduces the waste associated with providing ACT to uninfected individuals and if it decreases patient costs associated with repeated visits to health facilities ([2] but see [12]).

Despite the benefits associated with using RDTs, it has been repeatedly documented that providers and patients often ignore negative RDT results because of the potentially high stakes associated with a false negative result [13–15]. Indeed, while presumptive treatment certainly leads to over-treatment, test and treat can lead to both under and over-treatment because of false negative and false-positives RDT results, respectively. A recent Cochrane review indicates that RDTs have good overall performance (i.e., sensitivity greater than 90 % and specificity greater than 95 % on average) but finds considerable variation between studies [16]. In particular, RDT performance varied substantially due to differences in the study population (e.g., treatment-seeking individuals versus a random sample of the population), the reference standard [e.g., microscopy or polymerase chain reaction (PCR)], type of RDT and RDT manufacturer, and environmental conditions (e.g., extreme temperature or humidity may damage RDT lots) [4, 9, 17]. As an example of potential limitations of RDTs, the widely used HRP2-based RDTs (e.g., Paracheck®) are Plasmodium falciparum specific and thus fail to detect other Plasmodium species, will fail to detect P. falciparum if parasites have a mutation or deletion of the HRP-2 gene, and may detect the HRP-2 protein long after parasitaemia has been cleared from the host [18].

The relative merits of test and treat compared to presumptive treatment will depend on multiple factors, including performance characteristics of the diagnostic tests (sensitivity and specificity), baseline infection prevalence, and costs (both direct and indirect) associated with false-positives and false-negatives. In this article, Demographic and Health Survey (DHS) data from Burkina Faso were used to show that there is substantial spatial heterogeneity, even within regions of the same country, in relation to baseline infection prevalence and diagnostic test performance. As a result, a countrywide test and treat policy may yield unacceptably high levels of false-negative results in some regions, suggesting that presumptive treatment might be a better alternative in these settings. Proof-of-concept, web-based tools were developed that can aid policy makers in developing region-specific malaria diagnostic and treatment policies.

Overall, individuals in urban areas tended to have a much lower risk of malaria and this risk tended to increase significantly with age (Fig. 1a). Furthermore, there was considerable heterogeneity between regions regarding malaria risk differences in rural and urban areas (Fig. 1b). In relation to RDT performance, the models indicate that the probability of a true positive RDT result (RDT sensitivity) was not consistently influenced by any of the covariates (Fig. 1c). On the other hand, the probability of a false positive RDT result was significantly higher for older children (two to four years old children) and was lower for individuals in urban areas (Fig. 1e). Both RDT sensitivity and specificity varied considerably from region to region (‘intercept’ in Fig. 1d, f).

What do the findings described above imply in relation to the post-test probability of infection \(p\left( {M |R,X} \right)\)? RDT results substantially changed the probability of infection (red and blue circles in Fig. 2) compared to the pre-test probability of infection (i.e., baseline prevalence; black circles in Fig. 2), which indicate that RDTs are very informative regarding the likelihood of infection. However, individuals with a negative RDT result still have a 20–70 % chance of being infected in rural settings (blue solid circles in Fig. 2a–c). For instance, the infection probability of a four years old child with an RDT-negative result in rural areas of the Hauts Basins region (blue solid circles in Fig. 2c) can be equal to the infection probability of a RDT-positive child of the same age in the same region from an urban area (red solid circles in Fig. 2f). Three regions in Fig. 2 were selected to illustrate the patterns between infection status and the main covariates but an online tool was also developed to enable users to explore all factors included in our analysis for all regions (available through the website [27]).

In addition to variation between urban and rural areas within a particular region, this analysis also identified substantial differences between regions. For instance, RDT results seem more informative in the Sud-Ouest region than in the Sahel region (compare vertical distance between the blue and red solid circles in Fig. 2a, b, d, e). Similarly, although urban areas tend to have lower infection probability than rural areas, there seems to be substantial heterogeneity among urban areas. For example, probability of infection in urban areas of the Hauts Basins region is much lower than that in urban areas in Sud-Ouest and Sahel (compare Fig. 2d–f). These results suggest a complicated relationship between RDT outcomes and post-test probability of infection, indicating that a single malaria diagnosis and treatment policy even just for urban areas in Burkina Faso may not be effective. For instance, a test and treat policy might not be suitable for urban areas in the Sahel region, given the high probability of infection (>0.3) of RDT-negative children, whereas it might be a suitable option for urban areas in the Hauts Basin region.

The relevance of spatial heterogeneity for malaria diagnosis and treatment policy can be illustrated with a hypothetical example. For instance, if policy makers decided that it is unacceptable to use a diagnostic test with a probability of false-negative results above 30 % (for example), then presumptive treatment would be recommended for all rural areas in Burkina Faso and for urban settings in the Sahel and Est regions. In another online tool that we have developed (available through the website [28]), readers can explore the geographic implications regarding recommended presumptive treatment for different thresholds of the probability of false-negative results.

The statistical model for malaria microscopy confirms several of the relationships often described in malaria epidemiology in endemic regions, such as the increase in malaria prevalence with age [29] and generally higher prevalence in rural settings when compared to urban areas [30]. However, the impact of some of these factors (e.g., age and urban vs rural settings) on RDT performance is less commonly explored [but see 23, 31, 32]. The modelling results suggest that RDT specificity is higher for children in urban settings and younger children (Fig. 1e). This might be due to these children being less likely to have had a past malaria infection since false positives will typically arise on individuals with past malaria infections due to the relatively long time that the target antigen persists in the blood [33, 34]. Alternatively, these RDT results might be correct but microscopy might have failed to detect these infected individuals, which is likely to be a common phenomenon for individuals with low parasitaemia levels [35–37]. Finally, substantial geographical variation was observed regarding RDT sensitivity and specificity. Multiple reasons could explain this, including differences in the proportion of individuals with past exposure to malaria, exposure of RDTs to excessive heat and humidity during storage and distribution, intra-species diversity of the target antigen, and the parasite stage-specific expression of the antigen [4, 17, 38].

Most importantly, these multiple statistical models were combined to highlight the substantial spatial heterogeneity in malaria risk given RDT results. Under a countrywide test and treat policy, in some regions children with very similar infection probabilities might be denied treatment in a rural setting (due to a negative RDT result) but receive treatment in an urban setting (due to a positive RDT result). To avoid this, region-specific guidelines for malaria diagnosis and treatment might need to be developed, a process that can be potentially aided by the developed tool. Differently from past approaches that have relied on a threshold for the pre-test probability of clinical malaria [39], the proposed tool focuses on the probability of false-negative results to determine which areas a test and treat policy might be warranted. Obviously there are a number of other considerations that should be taken into account when determining policies for malaria diagnosis and treatment. For instance, the results of this study, in conjunction with direct and indirect cost information, would be very informative for policy makers if used in a decision-theoretic framework. In particular, local heterogeneities (e.g., longer travel times and lower wages in rural settings) may play an important role in determining what is most cost effective in each setting. Nevertheless, this analysis clearly illustrates important shortcomings of a uniform test and treat policy across Burkina Faso.

An important caveat to this study is that the data contain children that were sampled regardless of their symptoms and there was no information on symptoms on the day of the survey. Although presence of fever during the previous two weeks was controlled for (a variable that was surprisingly unimportant), baseline malaria prevalence and RDT performance are likely to be different for individuals that seek help in health facilities due to the presence of symptoms. Thus, using data on syndromic individuals would certainly be more appropriate when designing policies for malaria diagnosis and treatment at health facilities. Unfortunately, data over large geographical regions on treatment-seeking individuals that are tested with multiple diagnostic methods (i.e., microscopy and RDT) are scarce. Additional studies are warranted to determine if similar spatial heterogeneities are found when using syndromic data in Burkina Faso and in other malaria-endemic regions. Nevertheless, the results in this article are relevant for determining where a mass screen and treat strategy is likely to be more effective than a mass drug administration approach, a topic that has received renewed interest by policy makers and researchers and for which evidence is still relatively scarce in moderate to high malaria transmission areas ([40] but see [31, 41]). Finally, although this study focuses on children under five years, similar ideas are likely to be applicable for comparing intermittent screening and treatment (IST) as an alternative approach to diagnosis by symptoms only or intermittent preventive treatment for pregnant women [42–45].

One potential concern regarding this study refers to using microscopy as the gold standard method. Although routine microscopy can yield highly variable results, it is important to note that microscopy was conducted by the parasitology laboratory of the CNRFP, the reference laboratory for malaria in Burkina Faso. Staff at this centre participate in various quality control programmes in parasitology (e.g., proficiency testing programmes to comply with the College of American Pathologists and WHO-AFRO checklists) and are subject to rigorous internal and external quality control [21, 46]. Furthermore, DHS surveys across the majority of the SSA countries have relied on expert microscopy and these microscopy results have been extensively used by the scientific community as the gold standard (e.g., to create national malaria prevalence maps). Finally, expert microscopy is commonly used as the gold standard method against which RDT is evaluated [20, 34, 47, 48]. Although even expert microscopy can miss a large proportion of asymptomatic carriers [41], often because of low total parasite density [35–37], this does not explain the high proportion of positive microscopy but negative RDT results (i.e., false-negative results) found here in some regions.

In other words, among all RDT negative children, at least one out of six will actually be infected with malaria. In this calculation, RDT specificity \(p\left( {R = 0|M = 0} \right)\) was assumed to be 100 % but the probability of false negative results can be even higher for lower values of RDT specificity. Indeed, the above scenario is very optimistic. For instance, using the same DHS data from Burkina Faso, Samadoulougou et al. [20] have shown that RDT sensitivity was actually closer to 90 % (89.9 %, with 95 % confidence interval CI of 89–90.8) and specificity was very low (50.4 %, 95 % CI of 48.3–52.6).

Another important remark is that the 2010 DHS data for Burkina Faso was predominantly collected during the rainy season. As a result, the well documented seasonal differences in malaria risk and RDT performance in Burkina Faso [32, 41, 44, 51–53, 56, 59–65] were not accounted for in the statistical models. These seasonal differences can be as dramatic as the geographical differences described here. For instance, similar to the observed pattern for the urban vs rural areas in the Hauts Basins region, a negative RDT test has been shown to reduce the probability of malaria to almost zero during the dry season but not in the rainy season [51]. An important implication of not taking into account seasonality in our models is that any policy derived from these tools is likely to be applicable only for the rainy season. Finally, DHS data were collected during approximately the same time period for each region except for the Centre, Centre-Nord, Nord, and Plateau Central regions. Because of these differences regarding when data were collected in each region, geographical comparisons involving the regions cited above should be interpreted carefully as they may be confounded with seasonality effects.

Similar to the findings in [39, 51], the analysis presented here suggests that a generalized test-based policy should not be used uniformly across all contexts. In particular, even with improved diagnostic methods (e.g., positive control wells; [66]), the ‘back-of-the-envelope’ calculation above reveals how the probability of false-negative results will still be relatively large when prevalence is high. Unfortunately, because prevalence varies significantly even within the same region (e.g., according to age groups, season, rural vs urban), developing sound and straightforward diagnostic guidelines remains an important challenge. This article has shown how different statistical models can come together to inform context specific guidelines for malaria diagnosis and treatment, potentially improving the use of resources (e.g., reducing wasted RDTs in regions where false-negative probabilities are very high) and reducing malaria burden. Ultimately, bridging the gap between information users and these statistical models will be critical to foster evidence-based decision making and better resource allocation.