Trees and tracking

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 RN, classical ODT-algorithms use evolutionary procedures or heuristics. We have developed an optimal ODT-algorithm in R2, 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.

Growth tracks in pre-pubertal children

The present investigation characterizes common growth tracks in pre-pubertal children. Growth tracks denominate areas of probability within which subsequent measurements of the body height (or body height SDS) of a healthy individual will predominantly be found. Growth tracks are defined over several years and they are insensitive to the timing of measurements. The concept of growth tracks was developed to improve separating aberrant patterns from normal growth. Longitudinal data on height were obtained from six large national growth studies, performed at Berkeley, USA, Jena, Germany, Lublin, Poland, Paris, France, Prague, Czech Republic and Zurich, Switzerland with a total of 515 healthy boys and 532 healthy girls. Four hundred and two series of annual height measurements were available in pre-pubertal boys (aged 3-11 years), 416 series in pre-pubertal girls (aged 3-10). Body height was converted into height SDS. Thereafter, average personal height SDS was determined, and subtracted from height SDS, resulting in individual series of residual height SDS. These were sorted by cluster analysis and distributed into groups (clusters) according to similarity or dissimilarity (squared difference). We identified similar clusters, and named them 'growth tracks'. We found five pre-pubertal male growth tracks, each containing between 4 and 37% of the boys. Twenty boys could not be assigned to either one of the five tracks. Very similar results were obtained in girls, with five pre-pubertal growth tracks also, each containing between 3 and 50%. Twenty-three individuals grew irregularly and could not be assigned. Growth tracks are narrow, with an average width between 12.1 and 14.8% of the SD of body height. Most children exhibited almost horizontal height SDS patterns. Others showed linearly declining, rising, or intersection -shaped patterns. None of the patterns were predominantly found in particularly short or tall children. Preliminary data support the practical advantages of the concept of growth tracks.