Interactive spatiotemporal modelling of health systems: the SEKS–GUI framework

Abstract

This paper describes the spatiotemporal epistematics knowledge synthesis and graphical user interface (SEKS–GUI) framework and its application in medical geography problems. Based on sound theoretical reasoning, the interactive software library of SEKS–GUI explores heterogeneous (spatially non-homogeneous and temporally non-stationary) health attribute distributions (disease incidence, mortality, human exposure, epidemic propagation etc.); expresses the health system’s dependence structure using (ordinary and generalized) spatiotemporal covariance models; synthesizes core knowledge bases, empirical evidence and multi-sourced system uncertainty; and generates a meaningful picture of the real-world system using space–time dependent probability functions and associated maps of health attributes. The implementation stages of the SEKS–GUI library are described in considerable detail using appropriate screens. The wide applicability of SEKS–GUI is demonstrated by reviewing a selection of real-world case studies.

Appendices

Appendix A: The case of co-located data at Phase 2

Because duplicate coordinates (co-located data) may result in covariance matrix singularities, an initial check for duplicates is performed. The same adverse effect may occur at the prediction phase when geographical data are very close to each other. Co-location is not necessary associated with common public health problems in which a common geocode is assigned to participants with missing/incomplete addresses or to those residing in a specified geographic region to assure confidentiality. The interface defines the degree of proximity with respect to the geographical extent of the dataset and treats data that are too close to each other as co-located. Many methods may be used to alleviate the co-location issue, among them value averaging, slight spatial data displacement, and choosing a datum as the representative value of the co-located dataset. Another possibility is to merge co-located hard data into a unique soft data interval ranging within the span of the co-located hard data values. To preserve the character of the user’s dataset, the SEKS–GUI performs a simple averaging of the co-located hard data values and deals with co-location of soft uncertain data with other soft or hard data by means of slight random displacements.

Appendix B: Transformation options at Phase 2

By way of a summary, SEKS–GUI offers the following transformation options:

• (a) No transformation. The detrended dataset is left unaltered and the user proceeds to the prediction phase with the data in their original space.

• (b) N-scores transformation (also known as normal scores or Gaussian anamorphosis; Olea 1999). The detrended dataset is transformed to a N(0, 1) Gaussian distribution and the resulting dataset (used in space–time prediction) lies in the N-score space. Back-transformation to the original space is possible by using the N-score matrix. Since some extreme values may not back-transform properly using the N-score matrix, the SEKS–GUI sets upper and lower transformation limits that depend on the data span of the particular study, thus providing a means for extreme predictions to be appropriately back-transformed. All the N-score transformation functions are automatic and seamless to the user.

• (c) Box-Cox transformation (Box et al. 1994). The detrended dataset is tested with a series of power transformations based on a λ-parameter typically ranging within ± 2. The transformation eventually uses the λ-value bringing the data distribution closest to a Gaussian one. The resulting data values to be used in prediction are in the Box-Cox space. The back-transformation depends on the optimal λ-value chosen for the specific dataset. Note that the Box-Cox transformation is defined for positive data values only, while the detrended data will likely feature negative or zero values. If negative values are present, a constant is added to the detrended set so that all transformed values are positive. After being back-transformed to the original space, the constant is removed. The interface also accounts for the possibility of zero values (which pose problems when calculating logarithms). The above functions are performed automatically and are seamless to the user.

Appendix C: The BME and GBME techniques

Some of the implementation differences between BME and GBME are briefly discussed below (for more information about the two theories and technical details, the interested reader is referred to the relevant literature).

The two techniques may use different modelling assumptions and emphasize distinct core knowledge bases. For practical reasons, BME studies heterogeneity in an indirect way: it assumes a decomposition of the original attribute distribution into a mean function and a residual attribute, and a transformation operator is applied to the residual before BME is implemented. GBME theory deals directly with attribute heterogeneity in terms of space–time increments of the original distribution. Accordingly, the numerical implementation of GBME requires fewer steps than BME and its implementation is intrinsic, to a considerable extent. On the other hand, the BME steps are explicit, often allowing an increased participation of the user. GBME provides information about the space–time dependence structure in terms of the heterogeneity orders, which are not available in BME. GBME correlation analysis focuses on a local space–time scale at each prediction point, whereas BME analysis applies at a larger geographical scale that includes several prediction points. Accordingly, the GBME should perform best when enough data points are available at each local scale. On the other hand, there are more data points available at the BME scale, often generating smoother maps. While BME uses ordinary covariance functions that need to be positive-definite, GBME uses generalized covariance functions that need to be only conditionally positive-definite. Under certain conditions, the user may consider the implementation of a combination of BME and GBME, i.e., a decision is made to apply the BME technique in some sub-regions of the study area and the GBME technique in some others.