# Spatio-Temporal Bayesian Models for Malaria Risk Using Survey and Health Facility Routine Data in Rwanda

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

#### 2.1. Data Source

#### 2.2. Statistical Analysis

#### 2.2.1. Binomial Model

#### 2.2.2. Modeling Routine Data Only

#### 2.2.3. Modeling Routine Data with Survey Data

#### 2.3. Bayesian Inference

## 3. Results

#### 3.1. Data Exploratory Analysis

#### 3.2. Main Findings

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- World Health Organization. World Malaria Report 2021. Global Report. 2021. Available online: https://www.who.int/publications/i/item/9789240040496 (accessed on 1 May 2022).
- ICF International. Spatial Data Repository. The Demographic and Health Surveys Program. Available online: https://spatialdata.dhsprogram.com (accessed on 16 September 2022).
- Ties Boerma, J.; Sommerfelt, A.E. Demographic and health surveys (DHS: Contributions and limitations. World Health Stat. Q.
**1993**, 46, 222–226. [Google Scholar] - Dieudonne, H.; Ntizimira, C.; Mbituyumuremyi, A.; Hakizimana, E.; Mahmoud, H.; Birindabagabo, P.; Musanabaganwa, C.; Gashumba, D. The impact of COVID-19 on malaria services in three high endemic districts in Rwanda: A mixed-method study. Malar. J.
**2022**, 21, 48. [Google Scholar] - Wagenaar, B.H.; Hirschhorn, L.R.; Henley, C.; Gremu, A.; Sindano, N.; Chilengi, R. Data-driven quality improvement in low-and middle-income country health systems: Lessons from seven years of implementation experience across Mozambique, Rwanda, and Zambia. BMC Health Serv. Res.
**2017**, 17, 830. [Google Scholar] [CrossRef] [PubMed] - WHO. Monitoring and Evaluating Digital Health Interventions: A Practical Guide to Conducting Research and Assessment; World Health Organization: Geneva, Switzerland, 2017. [Google Scholar]
- National Institute of Statistics of Rwanda; Ministry of Health [Rwanda]; ICF International. Rwanda Demographic and Health Survey 2019–2020; NISR: Kigali, Rwanda; MOH: Kigali, Rwanda; ICF International: Reston, VA, USA, 2020.
- Semakula, M.; Niragire, F.; Faes, C. Bayesian spatio-temporal modeling of malaria risk in Rwanda. PLoS ONE
**2020**, 15, e0238504. [Google Scholar] [CrossRef] [PubMed] - Birgit, S.; Leonhard, H. Spatio-temporal disease mapping using INLA. Environmetrics
**2011**, 22, 725–734. [Google Scholar] - Håvard, R.; Sara, M.; Nicolas, C. Approximate Bayesian inference for latent Gaussian models by using integrated nested Laplace approximations. J. R. Stat. Soc. Ser. B (Stat. Methodol.)
**2009**, 71, 319–392. [Google Scholar] - Julian, B.; Peter, G.; David, H.; Kerrie, M. Bayesian computation and stochastic systems. Stat. Sci.
**1995**, 10, 3–41. [Google Scholar] - Andrea, R.; Leonhard, H.; Håvard, R.; Matthias, B. Gender-specific differences and the impact of family integration on time trends in age-stratified Swiss suicide rates. J. R. Stat. Soc. Ser. A (Statistics Soc.)
**2012**, 175, 473–490. [Google Scholar] - Spiegelhalter, D.J.; Best, N.G.; Carlin, B.P.; Van Der Linde, A. Bayesian measures of model complexity and fit. J. R. Stat. Soc. Ser. B (Stat. Methodol.)
**2002**, 64, 583–639. [Google Scholar] [CrossRef] [Green Version] - Lesaffre, E.; Lawson, A.B. Bayesian Biostatistics; John Wiley & Sons: Hoboken, NJ, USA, 2012. [Google Scholar]
- Pettit, L.I. The conditional predictive ordinate for the normal distribution. J. R. Stat. Soc. Ser. B (Stat. Methodol.)
**1990**, 52, 175–184. [Google Scholar] [CrossRef] - Hemingway, J.; Shretta, R.; Wells, T.N.; Bell, D.; Djimdé, A.A.; Achee, N.; Qi, G. Tools and strategies for malaria control and elimination: What do we need to achieve a grand convergence in malaria? PLoS Biol.
**2016**, 14, e1002380. [Google Scholar] [CrossRef] [PubMed] - Rwanda Biomedical Centre. Indoor Residual Spraying (IRS) and Long-Lasting Insecticide-Treated Nets (LLINs) Distributed in High Malaria Burden Districts; RBC Report; Rwanda Biomedical Centre: Kigali, Rwanda, 2020.
- Rumisha, S.F.; Lyimo, E.P.; Mremi, I.R.; Tungu, P.K.; Mwingira, V.S.; Mbata, D.; Malekia, S.E.; Joachim, C.; Mboera, L.E.G. Data quality of the routine health management information system at the primary healthcare facility and district levels in Tanzania. BMC Med. Inform. Decis. Mak.
**2020**, 20, 340. [Google Scholar] [CrossRef] [PubMed] - Sabella, M.; Pepela, W.; Soti, D.; Hillary, K.; Benson, D.; Ties, B. Using health-facility data to assess subnational coverage of maternal and child health indicators, Kenya. Bull. World Health Organ.
**2017**, 95, 683–694. [Google Scholar] - Agiraembabazi, G.; Ogwal, J.; Tashobya, C.; Kananura, R.M.; Boerma, T.; Waiswa, P. Can routine health facility data be used to monitor subnational coverage of maternal, newborn and child health services in Uganda? BMC Health Serv. Res.
**2021**, 21, 512. [Google Scholar] [CrossRef] [PubMed] - Wilson, E.; Hazel, E.; Park, L.; Carter, E.; Moulton, L.H.; Heidkamp, R.; Perin, J. Obtaining district-level health estimates using geographically masked location from Demographic and Health Survey data. Int. J. Health Geogr.
**2020**, 19, 2. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Adane, A.; Adege, T.M.; Ahmed, M.M.; Anteneh, H.A.; Ayalew, E.S.; Berhanu, D.; Berhanu, N.; Beyene, M.G.; Bhattacharya, A.; Bishaw, T.; et al. Routine health management information system data in Ethiopia: Consistency, trends, and challenges. Glob. Health Action
**2021**, 14, 868–961. [Google Scholar] [CrossRef] [PubMed] - Sawadogo-Lewis, T.; Keita, Y.; Wilson, E.; Sawadogo, S.; Téréra, I.; Sangho, H.; Munos, M. Can We Use Routine Data for Strategic Decision Making? A Time Trend Comparison Between Survey and Routine Data in Mali. Glob. Health Sci. Pract.
**2021**, 9, 869–880. [Google Scholar] [CrossRef] [PubMed] - Thwing, J.; Camara, A.; Candrinho, B.; Zulliger, R.; Colborn, J.; Painter, J.; Plucinski, M.M. A Robust Estimator of Malaria Incidence from Routine Health Facility Data. Am. J. Trop Med. Hyg.
**2020**, 102, 811–820. [Google Scholar] [CrossRef] [PubMed] - Nzabakiriraho, J.D.; Gayawan, E. Geostatistical modeling of malaria prevalence among under-five-year old children in Rwanda. BMC Public Health
**2021**, 21, 369. [Google Scholar] [CrossRef] [PubMed] - Masimbi, O.; Schurer, J.M.; Rafferty, E.; Ndahimana, J.D.A.; Amuguni, J.H. A cost analysis of the diagnosis and treatment of malaria at public health facilities and communities in three districts in Rwanda. Malar. J.
**2022**, 21, 150. [Google Scholar] [CrossRef] [PubMed] - World Health Organization. Global Malaria Program; WHO: Geneva, Switzerland, 2022. [Google Scholar]

**Figure 1.**Percentage of children of age 6–59 months that tested positive for malaria in East Africa (Burundi, Kenya, Rwanda, Tanzania, and Uganda at subnational. Source: DHS data).

**Figure 3.**Incidence rate of malaria among children under five years old per 100,000 population. Health facility routine data for year 2019 and 2020.

**Figure 4.**Spatial variation of malaria prevalence among children under five years old in Rwanda, RR posterior means of spatial effects (

**A**) with 95% UL upper limit (

**C**). Lower limit (

**D**). Panel (

**B**) shows exceeding probability of prevalence above 10% (

**B**). Source: DHS 2019-2020.

**Figure 5.**Spatial variation of malaria relative risk incidence among children under five years old in Rwanda (RR), posterior means of spatial effects with 95% upper limit (UL). Source: health facility routine data from 2019 and 2020.

**Figure 6.**Posterior temporal trend effect for malaria relative risk: $exp({\varphi}_{t}+{\gamma}_{t})$ with 95% credible interval, year 2019.

Type | Cases | Sample | Domain | Freq | Covariates |
---|---|---|---|---|---|

Routine | 39,936 | Sector (416) | Daily/Month | Gender, location | |

DHS | 99 | 3665 | District (30) | Cross-sectional | Gender, HHD, location |

Shapefile | Sector (416) | ||||

Population size | Sector (416) |

Models | M1 | M3 | ||||
---|---|---|---|---|---|---|

Parameters | Est (sd) | LL | UL | Est (sd) | LL | UL |

Fixed Effect | ||||||

${\mu}_{0}$ | −2.584 (1.069) | −4.796 | $-0.588$ | |||

${\mu}_{Male}$ | −5.892 (0.047) | $-5.984$ | $-5.800$ | |||

${\mu}_{Female}$ | −5.865 (0.047) | $-5.957$ | $-5.773$ | |||

${\beta}_{1Altitude}$ | −0.002 (0.001) | $-0.003$ | $0.001$ | |||

Random Effect | ||||||

${u}_{r}$ | −4.62 (0.268) | $-5.14$ | $-4.62$ | 0.584 (0.124) | $0.380$ | $0.866$ |

${v}_{r}$ | 2.69 (0.186) | 2.33 | 3.06 | 1.242 (0.192) | 0.905 | 1.658 |

${\phi}_{j}$ | 15.59 (4.72) | 8.025 | 26.420 | |||

$varf\left({\widehat{P}}_{r}\right)$ | 3.072 (0.975) | 1.538 | 5.336 |

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**MDPI and ACS Style**

Semakula, M.; Niragire, F.; Faes, C.
Spatio-Temporal Bayesian Models for Malaria Risk Using Survey and Health Facility Routine Data in Rwanda. *Int. J. Environ. Res. Public Health* **2023**, *20*, 4283.
https://doi.org/10.3390/ijerph20054283

**AMA Style**

Semakula M, Niragire F, Faes C.
Spatio-Temporal Bayesian Models for Malaria Risk Using Survey and Health Facility Routine Data in Rwanda. *International Journal of Environmental Research and Public Health*. 2023; 20(5):4283.
https://doi.org/10.3390/ijerph20054283

**Chicago/Turabian Style**

Semakula, Muhammed, François Niragire, and Christel Faes.
2023. "Spatio-Temporal Bayesian Models for Malaria Risk Using Survey and Health Facility Routine Data in Rwanda" *International Journal of Environmental Research and Public Health* 20, no. 5: 4283.
https://doi.org/10.3390/ijerph20054283