Oblique decision trees for spatial pattern detection: optimal algorithm and application to malaria risk

BACKGROUND: In order to detect potential disease clusters where a putative source cannot be specified, classical procedures scan the geographical area with circular windows through a specified grid imposed to the map. However, the choice of the windows' shapes, sizes and centers is critical and different choices may not provide exactly the same results. The aim of our work was to use an Oblique Decision Tree model (ODT) which provides potential clusters without pre-specifying shapes, sizes or centers. For this purpose, we have developed an ODT-algorithm to find an oblique partition of the space defined by the geographic coordinates. METHODS: ODT is based on the classification and regression tree (CART). As CART finds out rectangular partitions of the covariate space, ODT provides oblique partitions maximizing the interclass variance of the independent variable. Since it is a NP-Hard problem in R(N), classical ODT-algorithms use evolutionary procedures or heuristics. We have developed an optimal ODT-algorithm in R(2), based on the directions defined by each couple of point locations. This partition provided potential clusters which can be tested with Monte-Carlo inference. We applied the ODT-model to a dataset in order to identify potential high risk clusters of malaria in a village in Western Africa during the dry season. The ODT results were compared with those of the Kulldorff' s SaTScan™. RESULTS: The ODT procedure provided four classes of risk of infection. In the first high risk class 60%, 95% confidence interval (CI95%) [52.22–67.55], of the children was infected. Monte-Carlo inference showed that the spatial pattern issued from the ODT-model was significant (p < 0.0001). Satscan results yielded one significant cluster where the risk of disease was high with an infectious rate of 54.21%, CI95% [47.51–60.75]. Obviously, his center was located within the first high risk ODT class. Both procedures provided similar results identifying a high risk cluster in the western part of the village where a mosquito breeding point was located. CONCLUSION: ODT-models improve the classical scanning procedures by detecting potential disease clusters independently of any specification of the shapes, sizes or centers of the clusters

Adverse Drug Reactions in Children—A Systematic Review

Adverse drug reactions in children are an important public health problem. We have undertaken a systematic review of observational studies in children in three settings: causing admission to hospital, occurring during hospital stay and occurring in the community. We were particularly interested in understanding how ADRs might be better detected, assessed and avoided

Magnetic Properties of Layer-Type Compounds TlGdS2\text{}_{2} and TlGdSe2\text{}_{2}

Ternary thallium lanthanide dichalcogenides TlLnX$\text{}_{2}$ (X = S, Se, or Te; Ln = lanthanide, except Ce and Pr) crystallize in the rhombohedral structure of α-NaFeO$\text{}_{2}$ type ($R\overline{3}m$). Their crystal lattice consists of the layers of Ln$\text{}^{3+}$ ions separated by three layers of the non-magnetic ions (-Ln-X-Tl-X-Ln-). The magnetization was measured in the field range 0-14 T. The molecular field constants λ$\text{}_{m}$ were estimated by fitting the Brillouin function to the experimental magnetization plots. The difference between the λ$\text{}_{m}$ values for the thallium gadolinium sulphide and the selenide corresponds to the different character of Gd-S and Gd-Se bonds and gives rise to the different J$\text{}_{1}$ and J$\text{}_{2}$ exchange integrals

Magnetic Properties of DyTe

Dysprosium monotelluride is a metallic substance with one valence electron per formula unit belonging to the conduction band. It crystallizes in the defected NaCl-type structure (a= 0.6070 nm) with cation deficiency in the metal sublattice. AC and DC susceptibilities exhibit a maximum at 15 K and a second maximum at higher temperatures which position is field dependent

Universidade Federal de Minas Gerais

This paper will be concentrated on the estimation of the optimal bandwidth, h opt . Before starting the study of the problem, we cite some properties of F n . More details can be seen in Nadaraya (1964) and Bessegato (2002). The expectance and the variance of F n are given by E = F (x) + h C 2 + o , and F (x)[1 F (x)] C 1 + o (h/n) respectively where C 1 = 2 F # (x) zW (z) w(z)dz and C 2 = We note that the estimator is biased and the bias does not depend directly on the sample size n, but depend on