Allometric and fluctuation scaling in health, well-being and mortality

Sutton, J. ORCID: 0000-0002-7635-6578, 2022. Allometric and fluctuation scaling in health, well-being and mortality. PhD, Nottingham Trent University.

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In the urban scaling hypothesis, it has been noted that cities exhibit self-similar behaviour. Much of the scaling literature focuses on cities, whilst not including rural regions. Initially, rural-urban population density scaling was investigated using a diverse set of indicators (crime, property, mortality and age) in England and Wales. These were fitted using either a single or segmented powerlaw (PL) model where preference was chosen using a Davies test and confirmed using both Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC). In this study, it was found that most indicators exhibited a change point between rural-urban regions typically around 27 people per hectare. Mortality, for example, declined above the change point showing that urban regions have a ‘protective’ effect influenced by age demographics. Residuals obtained from the preferred PL model were analysed using methods such as hierarchical clustering and self-organising maps (SOM) displaying regional clusters, strong extensive correlations and disparities. The most interesting finding was that age demographics break the self-similarity behaviour that is a fundamental and underlying part of the urban scaling hypothesis. Scaling is usually cumulatively data over a large timeframe. Finer granularity of data is not easily accessible, although the COVID-19 pandemic was a unique opportunity to obtain and explore the scaling of daily data. It is thought that scaling exponent is slow changing and exhibited little fluctuation. However, it was found that COVID-19 cases revealed that the scaling exponents along with residual variance and skew varied with considerable complexity. Scaling exponents continually evolved and reversed where preference of propagation between ruralurban regions switched 6 times. Regional homogeneity occurred in periods with low variance where regions are located close to the PL. Contrary, regional heterogeneity occurred in periods with high variance where regions are located further away from the PL. Skew also exhibited both positive and 4 negative skew; both important features of propagation where the latter is not appreciated in the modelling of community propagation. Positive skew indicates a long tail of ‘hotspots’ and ‘superspreading’ events whilst negative skew indicates a long tail of ‘cold spots’ and ‘super-isolators’. In contrast, COVID-19 deaths exhibit near constant scale, variance and skew despite the extended studied timeframe, government intervention, different testing regimes and the national vaccination programme. This was also evident in the regions position relative to the PL where it remained either below or above the expectation throughout the pandemic. In the initial study of COVID-19, residual variance did not meet the conditions of standard linear regression. The variance expanded and contracted over time and residual distributions included both positive and negative skew, thus, normality and homoscedasticity assumptions of standard linear regression were not always met. This investigation stimulated the development of the generalised logistic distribution (GLD) within a Bayesian framework to model expectation and dispersion using Markov chain Monte Carlo (MCMC) methods. The advantage of the GLD is its flexibility when looking at skewed or otherwise nonnormally distributed data. The GLD regression model and its key features are demonstrated using COVID-19 data. However, the proposed framework will benefit a range of systems with linear structure. The additional dispersion regression coefficients account for heteroscedasticity together with the parameters of the GLD to provide more realistic shapes (e.g., skew). The normal regression model assumes a normally distributed homoscedastic system, producing relatively large model bias, relative to the improved GLD regression model. Gelman-Rubin diagnostics and deviance information criterion (DIC) was included in the proposed framework showing good convergence and data were explained well by the fitted GLD regression model.

Item Type: Thesis
Creators: Sutton, J.
Shahtahmassebi, G.Thesis
Hanley, Q.Thesis
Date: July 2022
Rights: The copyright in this work is held by the author. You may copy up to 5% of this work for private study, or personal, non-commercial research. Any re-use of the information contained within this document should be fully referenced, quoting the author, title, university, degree level and pagination. Queries or requests for any other use, or if a more substantial copy is required, should be directed to the author.
Divisions: Schools > School of Science and Technology
Record created by: Linda Sullivan
Date Added: 07 Nov 2023 14:30
Last Modified: 07 Nov 2023 14:37

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