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HAL Id: hal-02866666 https://hal-amu.archives-ouvertes.fr/hal-02866666 Submitted on 15 Jun 2020 HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés. Distributed under a Creative Commons Attribution| 4.0 International License Application of Functional Data Analysis to Identify Patterns of Malaria Incidence, to Guide Targeted Control Strategies Sokhna Dieng, Pierre Michel, Abdoulaye Guindo, Kankoé Sallah, El-Hadj Ba, Badara Cisse, Maria Patrizia Carrieri, Cheikh Sokhna, Paul Milligan, Jean Gaudart To cite this version: Sokhna Dieng, Pierre Michel, Abdoulaye Guindo, Kankoé Sallah, El-Hadj Ba, et al.. Application of Functional Data Analysis to Identify Patterns of Malaria Incidence, to Guide Targeted Control Strategies. International Journal of Environmental Research and Public Health, MDPI, 2020, 17 (11), pp.4168. ￿10.3390/ijerph17114168￿. ￿hal-02866666￿ Int. J. Environ. Res. Public Health 2020, 17, 4168; doi:10.3390/ijerph17114168 www.mdpi.com/journal/ijerph Article Application of Functional Data Analysis to Identify Patterns of Malaria Incidence, to Guide Targeted Control Strategies Sokhna Dieng 1,*, Pierre Michel 2, Abdoulaye Guindo 1,3, Kankoe Sallah 1,4, El-Hadj Ba 5, Badara Cissé 6, Maria Patrizia Carrieri 1, Cheikh Sokhna 5, Paul Milligan 7 and Jean Gaudart 8 1 Sciences Economiques et Sociales de la Santé et Traitement de de l’Information Médicale (SESSTIM), Institut de Recherche pour le Développement (IRD), Institut national de la santé et de la recherche médicale (INSERM), Aix Marseille Université, 13005 Marseille, France; aguindo15@yahoo.fr (A.G.); levisallah@gmail.com (K.S.); pmcarrieri@aol.com (M.P.C.) 2 Aix Marseille School of Economics (AMSE), Centrale Marseille, Ecoles des Hautes Etudes en Sciences Sociales (EHESS), Centre National de la Recherche Scientifique (CNRS), Aix Marseille Université, 13001 Marseille, France; pierre.michel@univ-amu.fr (P.M) 3 Mère et Enfant face aux Infections Tropicales (MERIT), Institut de Recherche pour le Développement (IRD), Université Paris 5, 75006 Paris, France; aguindo15@yahoo.fr 4 Unité de Recherche Clinique Paris Nord Val de Seine (PNVS), Hôpital Bichat, Assistance Publique— Hôpitaux de Paris (AP-HP), 75018 Paris, France; levisallah@gmail.com 5 Unité Mixte de Recherche (UMR), Vecteurs-Infections Tropicales et Méditerranéennes (VITROME), Campus International Institut de Recherche pour le Développement-Université Cheikh Anta Diop (IRD- UCAD) de l’IRD, CP 18524 Dakar, Sénégal; el-hadj.ba@ird.fr (E.-H.B.); cheikh.sokhna@ird.fr (C.S.) 6 Institut de Recherche en Santé, de Surveillance Épidémiologique et de Formation (IRESSEF) Diamniadio, BP 7325 Dakar, Sénégal; badara.cisse@iressef.org 7 London School of Hygiene and Tropical Medicine, WC1E 7HT London, UK; Paul.Milligan@lshtm.ac.uk 8 Aix Marseille Université, Assistance Publique - Hôpitaux de Marseille(APHM), INSERM, IRD, SESSTIM, Hop Timone, BioSTIC, Biostatistic and ICT, 13005 Marseille, France; jean.gaudart@univ-amu.fr * Correspondence: sokhna.dieng@etu.univ-amu.fr Received: 29 April 2020; Accepted: 6 June 2020; Published: 11 June 2020 Abstract: We introduce an approach based on functional data analysis to identify patterns of malaria incidence to guide effective targeting of malaria control in a seasonal transmission area. Using functional data method, a smooth function (functional data or curve) was fitted from the time series of observed malaria incidence for each of 575 villages in west-central Senegal from 2008 to 2012. These 575 smooth functions were classified using hierarchical clustering (Ward’s method), and several different dissimilarity measures. Validity indices were used to determine the number of distinct temporal patterns of malaria incidence. Epidemiological indicators characterizing the resulting malaria incidence patterns were determined from the velocity and acceleration of their incidences over time. We identified three distinct patterns of malaria incidence: high-, intermediate- , and low-incidence patterns in respectively 2% (12/575), 17% (97/575), and 81% (466/575) of villages. Epidemiological indicators characterizing the fluctuations in malaria incidence showed that seasonal outbreaks started later, and ended earlier, in the low-incidence pattern. Functional data analysis can be used to identify patterns of malaria incidence, by considering their temporal dynamics. Epidemiological indicators derived from their velocities and accelerations, may guide to target control measures according to patterns. Keywords: functional data analysis; time series clustering; malaria patterns; malaria dynamic Int. J. Environ. Res. Public Health 2020, 17, 4168 2 of 23 1. Introduction The development of technology has increasingly enabled the use of sophisticated tools to collect and store large amounts of complex data, particularly in scientific fields. These data are often continuous but observed over a finite number of points (discretization points) [1–3]. This is the case for meteorological data, electrocardiogram, time series, growth curves, for example. A functional data approach would be better adapted to handle these data by taking into account some of their particularities. Indeed, this approach is useful to handle a large sample of spatial units (villages) allowing comparison between them and to reduce data dimensions (number of observations) for long time series. In addition, the number of observations may be higher than the size of the sample making statistical analysis difficult. The observations are not always made at a regular time lag (every hour, every day etc.) and this latter may differ from one place to another [1,3]. Moreover, the use of functional data also allows the estimation of the velocity and acceleration of the time series. As a result, a considerable amount of research has been dedicated to the development of statistical methods and tools for analysis of functional data [1,2,4–6]. The works by Ramsay et al. have made these approaches popular, and R and MATLAB programs (The R Foundation for Statistical Computing, Vienna, Austria) have made the methods available to a wider group of researchers [5]. Applications in public health and biomedical sciences have been reviewed by Ullah and Finch (2013) [7]. In areas with low malaria transmission, because of the spatial heterogeneity of malaria incidence, World Health Organization (WHO) recommends the development of targeted control strategies adapted to the local epidemiological context [8]. Effective targeting requires identification of transmission foci or hotspots based on epidemiological data. Existing approaches used, to target malaria risk areas are based on aggregated incidence or prevalence rate, [9–15] in large discrete time sub-periods [16–20]. Thus, malaria risk areas were identified every rainy season or every year or another large sub-period and sometimes the status at malaria risk of areas between sub-periods can change. These approaches do not provide information about the trend or temporal dynamic of malaria and continuous time approaches are useful for dynamic analysis. Using the functional data approach, the observed malaria incidences can be described by estimated smooth functions (curves) in order to understand the underlying temporal trends of malaria. These smooth functions can be obtained for each of a large number of spatial units (villages), clustering algorithms can then be used to identify broad types of temporal patterns according to the characteristics of their dynamics (temporal trends). This would help to guide the development and implementation of targeted control strategies in the local context. In addition, for further understanding of malaria incidence dynamics, the velocity and the acceleration (velocity variation) are useful. Indeed, the velocity is the first derivative function which gives information over time about when the malaria incidence increases (growth phase period) or decreases (decline phase period). The acceleration, i.e., the variation of epidemic speed (velocity) is the second derivative function. This indicates how malaria incidence increases or decreases over time: quickly or slowly [21,22]. Thus, temporal variations of velocity and acceleration together provide information about the malaria dynamic. Moreover, key features of the malaria dynamic derived from velocity and acceleration functions as onsets, peaks, ends, and their lags between patterns are useful to refine targeted intervention schedules. In this paper, we introduced an approach based on functional data analysis to identify patterns of malaria incidence over a five-year period at village scale, in west-central Senegal. In addition, with the epidemiological indicators determined from the velocity and the acceleration of the resulting patterns, we investigated the spatiotemporal variation and features of malaria incidence in local context, in order to guide the targeted malaria control measures in a low transmission area and local context. Int. J. Environ. Res. Public Health 2020, 17, 4168 3 of 23 2. Methods 2.1. Study Area and Dataset The data used for this study were collected between January 2008 and December 2012 during a field trial of Seasonal Malaria Chemoprevention (SMC) among children from 575 villages in west- central Senegal [23,24]. This area is a part of the two national rural health districts, Bambey and Fatick, where the national malaria control program estimated the incidence under 5 cases/1000 person-years in 2018 [25]. The protocols for the field studies were approved by Senegal’s Conseil National pour la Recherche en Santé and the ethics committee of the London School of Hygiene and Tropical Medicine. The SMC trial [23] was registered number NCT00712374. The datasets analyzed during the current study are available from the corresponding author on reasonable request. Malaria surveillance was maintained in 38 health facilities serving a population of about 500,000 living in 575 villages (single villages or groups of adjacent hamlets). Malaria cases were patients examined at health facilities with fever or history uploads/Science et Technologie/ijerph-17-04168.pdf

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