How to Optimally Estimate Malaria Readiness Indicators at the Health district Level? Findings 1 from the Burkina Faso Service Availability and Readiness Assessment (SARA) Cross-Sectional 2 Data 3

: 23 Background: One of the major causes of malaria-related deaths in Sub-Saharan African countries is the 24 limited accessibility to quality care. In these countries, malaria control activities are implemented at the 25 health district level. However, malaria indicators are often regionally representative. This paper provides an approach for estimating health district-level malaria readiness indicators from survey data designed 27 to provide regionally representative estimates. 28 Methods: A binomial hierarchical Bayesian spatial prediction method was applied to Service 29 Availability and Readiness Assessment (SARA) survey data to provide estimates of essential equipment 30 availability and readiness to provide malaria care at the health district level. Predicted values of each 31 indicator were adjusted by the type of health facility, location, and population density. Then, a health 32 district composite readiness profile was built via hierarchical ascendant classification. 33 Results: All surveyed health-facilities were mandated to manage malaria. The spatial distribution of 34 essential equipment and malaria readiness was heterogeneous. Around 62.9% of health districts had a 35 high level of readiness to provide malaria care and prevention during pregnancy. Low-performance 36 scores for managing malaria were found in big cities located in the central and Haut-Bassins regions. 37 The health districts with low coverage for both first-line antimalarial drugs and rapid diagnostic tests 38 were Baskuy, Bogodogo, Boulmiougou, Nongr-Massoum, Sig-Nonghin, Dafra, and Do. 39 Conclusion: We provide health district estimates and reveal gaps in basic equipment and malaria 40 management resources in some districts that need to be filled. By providing local-scale estimates, this 41 approach could be replicated for other types of indicators to inform decision-makers and health program 42 managers and to identify priority areas. 43

6 guidelines for malaria treatment and IPTp, first-line antimalarials in stock, and RDT availability. In the 134 analysis, the variable "health facility provides malaria diagnosis and treatment services" was not 135 included as all (100%) health facilities surveyed provided malaria diagnosis and treatment services. 136 In brief, the availability and readiness indicators were binary variables, taking a value of 1 if the 137 key item was available and in a functional state at the health-facility, and 0 otherwise [8,16]. Data were 138 recorded on a paper questionnaire. After verification and validation, data were entered electronically in 139 a database designed as a Census and Survey Processing System (CSPRO). 140

Current Statistical Analyses Applied to SARA Survey Data in Burkina Faso 141
According to WHO recommendations, both tracer indicators and general and specific indices were 142 used in routine data analysis [8,16,32]. A descriptive analysis was applied to the data to provide 143 regionally and nationally representative estimates; this allowed the percentage of facilities providing 144 specific services with tracer items or owning the equipment on the day of the assessment to be estimated. 145 Beyond these descriptive statistics, health facility readiness indicators are also increasingly being used 146 in SSA countries to assess the health system strengthening through the construction of a composite score 147 In this study, four steps for modeling the SARA survey data were used to create a HBSM 153 framework model for the data. As mentioned above, the availability or readiness variables were binary (denoted ), each with 156 its own Boolean-valued outcome, i.e., success ( is equal to 1 with probability p) or failure ( is equal 157 to 0 with probability q = 1 − p). The Burkina Faso area comprises a set of = 1, … , 70 non-overlapping 158 health districts = { 1 , … … … , }, and availability or readiness indicators are recorded for each health 7 district. Let be the number of health facilities in the health district ( ). In each , the variable 160 is tested (or measured) times, and the number of successful trials among tests is counted. The 161 probability of observing exactly successful trials for the variable among trials in the health 162 district , is: 163 Step 2: Non-Spatial Grouped Binomial Regression (Proportional Counts) and Test for Spatial 165 Autocorrelation 166 Since the analysis assumes that the variable in health district follows a binomial distribution, 167 the following model can be fitted to the data: 168 where is the probability (proportion) of success in health district k ( ) after considering the observed 171 effects for covariates and is the regression coefficients of the covariates. In this step, we fit the spatial dependence in the data by including spatial random effects in the 181 model. In this model, health district random effects are included and region identities are included as 182 random factors to account for inter-regional variance not captured by the fixed effects and health district 183 specific random effects: 184 represents probabilities that are assumed to have prior distributions, ~ ( 1 = 186 1, 2 = 1); = ( 0 , 1 , 2 , 3 ) ~ (0, ) is the unstructured fixed effects; = ( 1 , … , 70 ) 187 represents the health district spatial random effects (i.e., residual area variation arising from unmeasured 188 or unknown factors); and = ( 1 , … , 13 )~(0, 2 ) represents regional area random 189 effects. 2 is the variances of the marginal regional area random effect.
is decomposed as the sum 190 of a structured spatial random effect ( ) and an unstructured random effect ( ) [ denotes the number of neighbors for health district , and 2 and 2 are the variances 203 of the marginal structured and unstructured components, respectively.

Composite Readiness Profile Building Through Hierarchical Ascendant Classification 224
We performed a hierarchical ascending classification (HAC) on the predicted values of availability 225 and readiness to assess the resemblances and differences between health districts from a 226 multidimensional point of view. For the HAC, Euclidean distance and Ward's criterion were used. 227 Ward's criterion is based on the Huygens-Steiner theorem, which allows decomposition of the total 228 inertia between and within group variance. A group or cluster is an aggregation of several similar health 229 districts. In the initial step of the algorithm, all clusters are singletons (clusters containing a single point). 230 Ward's approach consists of aggregating two groups so that the growth within-inertia is minimal in each 231 step of the algorithm. This method minimizes the total within-cluster variance and maximizes the total 232 inter-cluster variance. To simplify the use of the study findings by health system administrators, the 233 final result groups all health districts into clusters or composite readiness profiles. 234 10 3. Results 235 Table 1 shows the repartition of sample size according to region, location, and type of governing 237 authority. About two-thirds of the health facilities were in rural areas and four-fifths were public 238 facilities. 239

Availability Scores for Essential Equipment 240
The predicted values of health district essential equipment rates from HBSM are shown in Figure  241 1 and availability varied widely across the country. The rate was lowest in the health districts located in the 246 Boucle de Mouhoun and Cassade regions (between 22% and 58%), and highest in the health districts 247 located in the central region (>80%) as well as in health districts of Dafra and Dori, among others.  Table S2 summarize the geographical distribution of malaria readiness at the health 250 district level. More than three-quarters of districts require clinical signs for malaria diagnosis (>98%). 251 Overall, health districts located in the political capital, Ouagadougou, and the economic capital, Bobo-252 Dioulasso, had the lowest rates for the use of rapid diagnostic tests. However, in these regions, the level 253 of microscopy use was high. We observed heterogeneity in antimalarial drug availability across the 254 country. For the first-line antimalarial drugs (artemisinin-based combination therapy, ACT for short), 255 25% of health districts had a score less than 94.3%. Health districts located in major cities, such as 256 Ouagadougou and Bobo-Dioulasso, had the lowest rates regarding the ACT in stock. The percentage of 257 health districts with no ACT in stock on the day of survey ranged from 2.4% to 12.4%. 258 The RDT availability rate on the day of the survey ranged from 50% to 95.6%. Health districts in 259 Ouagadougou and Bobo-Dioulasso had the lowest rates of staff training on malaria diagnosis and 260 11 treatment and IPTp. The results show an inter-regional variability for malaria readiness indicators 261 throughout the study area, though the variation was low ( Figure S1). 262

273
This paper provides an alternative method based on HBSM for optimal estimation of subnational 274 indicators drawn from health-facility-based survey data with a much smaller sample size. Since local 275 administrators need information on the operational scale for planning purposes, this alternative method, 276 using advanced statistical methods applied to SARA survey data, offers a useful method for countries 277 with limited resources. This method has been used in other areas to estimate indicators at the subnational 278 level from samples drawn for national or regional estimates [17,18]. 279 Through the application of the Bayesian method, the problem of sample size is minimized [25-29] 280 as Bayesian approaches are not asymptotic-based, which is a feature that can be an obstacle to the use 281 of frequentist methods in small sample contexts. Consideration of the spatial autocorrelation between 282 health districts provides a more reliable estimate. According to this statistical principle, an event in the 283 neighborhood closest to another may not necessarily increase the information available in the data if 284 similar to the one already assessed [48]. Consequently, such assessments only increase the sample size 285 without providing a complete set of information that is independent [49]. 12 This study highlighted the gaps that must be addressed to improve the quality of health-facility-287 based malaria management. The study showed the low rates of basic equipment throughout the study 288 area, especially for two elements: infant weighing scales and light sources. Without an infant weighing 289 scale, health facility staff are often forced to prescribe drugs based on age when determining the optimal 290 dosage of antimalarial drugs. This can lead to under-or over-dosing of drug prescriptions. Local health 291 authorities should strengthen the availability of this equipment in health facilities located in the north, 292 Cassades, and south-central regions. Health districts with high rates of light source availability were 293 mostly located in urban areas, where electricity is more readily available. In rural areas, until the 294 government finds the means to provide electricity, renewable energy sources, such as solar panels, could 295 be an alternative to providing energy for light sources. 296 Notably, the current policy of routine parasitological diagnosis of malaria in Burkina Faso is based 297 on the use of RDT [50]. Although approximately 75% of health districts have an RDT coverage of more 298 than 94.2%, this analysis indicated that RDT availability is not optimal across the country. For health 299 districts located in urban regions, the RDT coverage was low. This suggests that patients continue to be 300 misdiagnosed for malaria and mistreated. The results also showed that health districts located in urban 301 areas had low rates of other malaria readiness indicators, especially the availability of antimalarial drugs. 302 This finding implies that patients in these areas still use other sources of drug supplies, such as private 303 pharmacies, drug stores, and/or private medical centers, where patients can be diagnosed and purchase 304 over-the-counter medications. The disparity in malaria readiness coverage, especially the inadequate 305 coverage of RDTs and ACTs in urban regions, could hinder the effectiveness of the National-Malaria-306 Control-Program (NMCP ) "test, treat, track" strategy; therefore, the NMCP must seek to identify gaps 307 and optimize resource distribution in health districts with low coverage. 308 A limitation of the study was that a cross-sectional survey is used as design, so the availability of 309 basic equipment and malaria readiness service may vary over time.

311
Our study provides estimates at the health district level using existing data designed to be regionally 312 representative. We show that HBSM is a useful tool to enable the use of regionally representative data 313 with a small sample size to estimate rates (with uncertainty) of malaria readiness indicators at the health 314 district level. The results indicate gaps in basic equipment availability and resources in some health 315 districts, which must be addressed. In a limited resource setting, health programs may struggle to operate 316 effectively due to the lack of reliable estimates at the operational level for monitoring purposes. As 317 demonstrated here, our proposed approach could be replicated for other types of indicators to provide 318 local level estimates for local policy makers so that the gaps can be targeted and addressed as a priority. 319 Our results suggest that further investigations should be implemented to assess the impact of the Health 320 district composite readiness score on the spatial distribution of malaria burden. 321 This study used data from the national health facility-based survey on health service delivery conducted 345 periodically (every two years) by the Ministry of Health of Burkina Faso with technical and financial 346 support from WHO and the Global Fund. Before data collection in the field, field supervisors arranged 347 an appointment with heads of facilities personally, in advance to request permission to collect data in 348 their facility at a date and time that is convenient for the facility, avoiding peak hours. At the data 349 collection date, once a presentation of the procedures and objectives of the study was completed using  Table and Figure legends   521   Table 1 Partition of sampled health-facilities by health district, location and governing authority. 522 Table 2 Composite readiness profile characteristics of health districts obtained by hierarchical ascendant 523 classification estimated from posterior means implemented in the Bayesian binomial model. 524