Cases, clusters, densities: Modeling the nonlinear dynamics of complex health trajectories

Abstract

In the health informatics era, modeling longitudinal data remains problematic. The issue is method: health data are highly nonlinear and dynamic, multilevel and multidimensional, comprised of multiple major/minor trends, and causally complex -making curve fitting, modeling and prediction difficult. The current study is fourth in a series exploring a case-based density (CBD) approach for modeling complex trajectories; which has the following advantages: it can (1) convert databases into sets of cases (k dimensional vectors) based on a set of bio-social variables, called traces; (2) compute the trajectory (velocity vector) for each case, based on (3) key traces from the k dimensional profile; (4) construct a theoretical map to explain these traces; (5) use vector quantization (i.e., k-means, topographical neural nets) to longitudinally cluster case trajectories into major/minor trends; (6) employ genetic algorithms and ordinary differential equations to create a microscopic (vector field) model (the inverse problem) of these trajectories; (7) look for complex steady-state behaviors (e.g., spiraling sources, etc) in the microscopic model; (8) draw from thermodynamics, synergetics and transport theory to translate the vector field (microscopic model) into the linear movement of macroscopic densities; (9) use the macroscopic model to simulate known and novel case-based scenarios (the forward problem); and (10) construct multiple accounts of the data by linking the theoretical map and k dimensional profile with the macroscopic, microscopic and cluster models. Given the utility of this approach, our purpose here is to organize our method (as applied to recent research) so it can be employed by others.

Measurement of Symptom Change Following Web-Based Psychotherapy: Statistical Characteristics and Analytical Methods for Measuring and Interpreting Change (Preprint)

“…Second, the current findings support a well-established statistical idea posing that the selection of a statistical analysis must match the characteristics of the dataset in order to arrive at valid and accurate statistical measurement, interpretation and conclusions (Flay et al, 2005;Field & Wilcox, 2017 (Castellani et al, 2016;Panagiotakopoulos et al, 2010).…”

“…For example, under circumstances where change is proportional in nature, the selection of a proportional statistical analysis can greatly increase the accuracy and validity of estimating longitudinal clinical change (Fitzmaurice & Laird, 2012;Liang and Zenger, 1986), the detection of moderators of symptom change (Castellani, Rajaram, Gunn, & Griffiths, 2016), the classification of subgroups, such as remitters or non-responders (Panagiotakopoulos, Lyras, Livaditis, Sgarbas, Anastassopoulos & Lymberopoulos, 2010), as well as the ability to research other objectives (Pocock, Clayton & Stone, 2015). For this reason, the function of symptom change must be researched, and more clearly understood.…”

High-Definition Medicine

“…However, due to their incomplete nature, many of these models have been found to grossly overestimate risk and lead to unnecessary therapy initiation (Rana et al, 2016). More comprehensive representation of patient characteristics with high definition medicine technologies will allow for a more accurate definition of genetic, environmental, and behavioral risks, link those risks to clinical health parameters measured by high definition prevention technologies, individualize the interpretation of those health parameters via various data-mining techniques, and ultimately allow for the definition of highly complex models of health trajectories leading to a truly predictive and preventative health care system (Castellani et al, 2016). …”

A MapReduce‐Based Parallel Frequent Pattern Growth Algorithm for Spatiotemporal Association Analysis of Mobile Trajectory Big Data

“…delete top element in HP; (8) insert V + sup(v) into HP; (9) end if (10) end if (11) end for (12) return ⟨ , V ⟩ pairs; Algorithm 6: Reduce( , V ).…”

“…Actually, big data usually consists of massive small files in various practical applications such as mobile trajectory data, financial and investment data, business transaction data, and health trajectory data [8]. Recently, mobile trajectory big data analytics has been a research hotspot of urban computing and smart cities, which attracts great attention from the industry, academia, and government [9][10][11].…”