Identifying Structural Breaks in Stochastic Mortality Models

In recent years, the issue of life expectancy has become of utmost importance to pension providers, insurance companies, and government bodies in the developed world. Significant and consistent improvements in mortality rates and hence life expectancy have led to unprecedented increases in the cost of providing for older ages. This has resulted in an explosion of stochastic mortality models forecasting trends in mortality data to anticipate future life expectancy and hence quantify the costs of providing for future aging populations. Many stochastic models of mortality rates identify linear trends in mortality rates by time, age, and cohort and forecast these trends into the future by using standard statistical methods. These approaches rely on the assumption that structural breaks in the trend do not exist or do not have a significant impact on the mortality forecasts. Recent literature has started to question this assumption. In this paper, we carry out a comprehensive investigation of the presence or of structural breaks in a selection of leading mortality models. We find that structural breaks are present in the majority of cases. In particular, we find that allowing for structural break, where present, improves the forecast result significantly.

Sediment changes upstream and downstream of the Altnahinch Dam in the River Bush in Northern Ireland: A preliminary study

The River Bush must reach a standard of good ecological potential (GEP) by 2015 due to the requirements of the water framework directive. The role of sediments within a water body is extremely important to all aspects of a river's regime. The aim of this research is to investigate the effects of Altnahinch Dam on sediment distribution in the River Bush (a heavily modified water body) with comparison made against the Glendun River (an unmodified water body). Samples collected from the rivers were analysed by physical (pebble count, sieve analysis) and statistical methods (ANOVA, GRADISTAT). An increase in fine sediments upstream of the dam provides evidence that the dam is impacting sediment distribution. Downstream effects are not shown to be significant. The output of this study also implies similar impacts at other drinking water storage impoundments. This research recommends that a sediment management plan be put in place for Altnahinch Dam and that further studies be carried-out concentrating on fine sediment distribution upstream of the dam. 

Any versus long-term prescribing of high risk medications in older people using 2012 Beers Criteria: results from three cross-sectional samples of primary care records for 2003/4, 2007/8 and 2011/12

Background: High risk medications are commonly prescribed to older US patients. Currently, less is known about high risk medication prescribing in other Western Countries, including the UK. We measured trends and correlates of high risk medication prescribing in a subset of the older UK population (community/institutionalized) to inform harm minimization efforts. Methods: Three cross-sectional samples from primary care electronic clinical records (UK Clinical Practice Research Datalink, CPRD) in fiscal years 2003/04, 2007/08 and 2011/12 were taken. This yielded a sample of 13,900 people aged 65 years or over from 504 UK general practices. High risk medications were defined by 2012 Beers Criteria adapted for the UK. Using descriptive statistical methods and regression modelling, prevalence of ‘any’ (drugs prescribed at least once per year) and ‘long-term’ (drugs prescribed all quarters of year) high risk medication prescribing and correlates were determined. Results: While polypharmacy rates have risen sharply, high risk medication prevalence has remained stable across a decade. A third of older (65+) people are exposed to high risk medications, but only half of the total prevalence was long-term (any = 38.4 % [95 % CI: 36.3, 40.5]; long-term = 17.4 % [15.9, 19.9] in 2011/12). Long-term but not any high risk medication exposure was associated with older ages (85 years or over). Women and people with higher polypharmacy burden were at greater risk of exposure; lower socio-economic status was not associated. Ten drugs/drug classes accounted for most of high risk medication prescribing in 2011/12. Conclusions: High risk medication prescribing has not increased over time against a background of increasing polypharmacy in the UK. Half of patients receiving high risk medications do so for less than a year. Reducing or optimising the use of a limited number of drugs could dramatically reduce high risk medications in older people. Further research is needed to investigate why the oldest old and women are at greater risk. Interventions to reduce high risk medications may need to target shorter and long-term use separately.

The single component geochemical map: Fact or fiction?

Single component geochemical maps are the most basic representation of spatial elemental distributions and commonly used in environmental and exploration geochemistry. However, the compositional nature of geochemical data imposes several limitations on how the data should be presented. The problems relate to the constant sum problem (closure), and the inherently multivariate relative information conveyed by compositional data. Well known is, for instance, the tendency of all heavy metals to show lower values in soils with significant contributions of diluting elements (e.g., the quartz dilution effect); or the contrary effect, apparent enrichment in many elements due to removal of potassium during weathering. The validity of classical single component maps is thus investigated, and reasonable alternatives that honour the compositional character of geochemical concentrations are presented. The first recommended such method relies on knowledge-driven log-ratios, chosen to highlight certain geochemical relations or to filter known artefacts (e.g. dilution with SiO2 or volatiles). This is similar to the classical normalisation approach to a single element. The second approach uses the (so called) log-contrasts, that employ suitable statistical methods (such as classification techniques, regression analysis, principal component analysis, clustering of variables, etc.) to extract potentially interesting geochemical summaries. The caution from this work is that if a compositional approach is not used, it becomes difficult to guarantee that any identified pattern, trend or anomaly is not an artefact of the constant sum constraint. In summary the authors recommend a chain of enquiry that involves searching for the appropriate statistical method that can answer the required geological or geochemical question whilst maintaining the integrity of the compositional nature of the data. The required log-ratio transformations should be applied followed by the chosen statistical method. Interpreting the results may require a closer working relationship between statisticians, data analysts and geochemists.

Compositional data-driven alternatives to single geochemical component maps

Conventional practice in Regional Geochemistry includes as a final step of any geochemical campaign the generation of a series of maps, to show the spatial distribution of each of the components considered. Such maps, though necessary, do not comply with the compositional, relative nature of the data, which unfortunately make any conclusion based on them sensitive
to spurious correlation problems. This is one of the reasons why these maps are never interpreted isolated. This contribution aims at gathering a series of statistical methods to produce individual maps of multiplicative combinations of components (logcontrasts), much in the flavor of equilibrium constants, which are designed on purpose to capture certain aspects of the data.
We distinguish between supervised and unsupervised methods, where the first require an external, non-compositional variable (besides the compositional geochemical information) available in an analogous training set. This external variable can be a quantity (soil density, collocated magnetics, collocated ratio of Th/U spectral gamma counts, proportion of clay particle fraction, etc) or a category (rock type, land use type, etc). In the supervised methods, a regression-like model between the external variable and the geochemical composition is derived in the training set, and then this model is mapped on the whole region. This case is illustrated with the Tellus dataset, covering Northern Ireland at a density of 1 soil sample per 2 square km, where we map the presence of blanket peat and the underlying geology. The unsupervised methods considered include principal components and principal balances
(Pawlowsky-Glahn et al., CoDaWork2013), i.e. logcontrasts of the data that are devised to capture very large variability or else be quasi-constant. Using the Tellus dataset again, it is found that geological features are highlighted by the quasi-constant ratios Hf/Nb and their ratio against SiO2; Rb/K2O and Zr/Na2O and the balance between these two groups of two variables; the balance of Al2O3 and TiO2 vs. MgO; or the balance of Cr, Ni and Co vs. V and Fe2O3. The largest variability appears to be related to the presence/absence of peat.

Exploring the joint compositional variability of major components and trace elements in the Tellus soil geochemistry survey (Northern Ireland)

The complexity of modern geochemical data sets is increasing in several aspects (number of available samples, number of elements measured, number of matrices analysed, geological-environmental variability covered, etc), hence it is becoming increasingly necessary to apply statistical methods to elucidate their structure. This paper presents an exploratory analysis of one such complex data set, the Tellus geochemical soil survey of Northern Ireland (NI). This exploratory analysis is based on one of the most fundamental exploratory tools, principal component analysis (PCA) and its graphical representation as a biplot, albeit in several variations: the set of elements included (only major oxides vs. all observed elements), the prior transformation applied to the data (none, a standardization or a logratio transformation) and the way the covariance matrix between components is estimated (classical estimation vs. robust estimation). Results show that a log-ratio PCA (robust or classical) of all available elements is the most powerful exploratory setting, providing the following insights: the first two processes controlling the whole geochemical variation in NI soils are peat coverage and a contrast between “mafic” and “felsic” background lithologies; peat covered areas are detected as outliers by a robust analysis, and can be then filtered out if required for further modelling; and peat coverage intensity can be quantified with the %Br in the subcomposition (Br, Rb, Ni).

Compositional data analysis of Holocene sediments from the West Bengal Sundarbans, India: Geochemical proxies for grain-size variability in a delta environment

This paper is part of a special issue of Applied Geochemistry focusing on reliable applications of compositional multivariate statistical methods. This study outlines the application of compositional data analysis (CoDa) to calibration of geochemical data and multivariate statistical modelling of geochemistry and grain-size data from a set of Holocene sedimentary cores from the Ganges-Brahmaputra (G-B) delta. Over the last two decades, understanding near-continuous records of sedimentary sequences has required the use of core-scanning X-ray fluorescence (XRF) spectrometry, for both terrestrial and marine sedimentary sequences. Initial XRF data are generally unusable in ‘raw-format’, requiring data processing in order to remove instrument bias, as well as informed sequence interpretation. The applicability of these conventional calibration equations to core-scanning XRF data are further limited by the constraints posed by unknown measurement geometry and specimen homogeneity, as well as matrix effects. Log-ratio based calibration schemes have been developed and applied to clastic sedimentary sequences focusing mainly on energy dispersive-XRF (ED-XRF) core-scanning. This study has applied high resolution core-scanning XRF to Holocene sedimentary sequences from the tidal-dominated Indian Sundarbans, (Ganges-Brahmaputra delta plain). The Log-Ratio Calibration Equation (LRCE) was applied to a sub-set of core-scan and conventional ED-XRF data to quantify elemental composition. This provides a robust calibration scheme using reduced major axis regression of log-ratio transformed geochemical data. Through partial least squares (PLS) modelling of geochemical and grain-size data, it is possible to derive robust proxy information for the Sundarbans depositional environment. The application of these techniques to Holocene sedimentary data offers an improved methodological framework for unravelling Holocene sedimentation patterns.

Statistical modelling of cement slurries for self compacting SIFCON containing silica fume

This paper reports a study carried out to develop a self-compacting fibre reinforced concrete containing a high fibre content with slurry infiltrated fibre concrete (SIFCON). The SIFCON was developed with 10% of steel fibres which are infiltrated by self-compacting cement slurry without any vibration. Traditionally, the infiltration of the slurry into the layer of fibres is carried out under intensive vibration. A two-level fractional factorial design was used to optimise the properties of cement-based slurries with four independent variables, such as dosage of silica fume, dosage of superplasticiser, sand content, and water/cement ratio (W/C). Rheometer, mini-slump test, Lombardi plate cohesion meter, J-fibre penetration test, and induced bleeding were used to assess the behaviour of fresh cement slurries. The compressive strengths at 7 and 28 days were also measured. The statistical models are valid for slurries made with W/C of 0.40 to 0.50, 50 to 100% of sand by mass of cement, 5 to 10% of silica fume by mass of cement, and SP dosage of 0.6 to 1.2% by mass of cement. This model makes it possible to evaluate the effect of individual variables on measured parameters of fresh cement slurries. The proposed models offered useful information to understand trade-offs between mix variables and compare the responses obtained from various test methods in order to optimise self-compacting SIFCON.

Statistical Monitoring of Dynamic Multivariate Processes: Part II: Identifying Fault Magnitude and Signature

This paper builds on work presented in the first paper, Part 1 [1] and is of equal significance. The paper proposes a novel compensation method to preserve the integrity of step-fault signatures prevalent in various processes that can be masked during the removal of both auto- and cross correlation. Using industrial data, the paper demonstrates the benefit of the proposed method, which is applicable to chemical, electrical, and mechanical process monitoring. This paper, (and Part 1 [1]), has led to further work supported by EPSRC grant GR/S84354/01 involving kernel PCA methods.

Development of sampling methods for Raman analysis of solid dosage forms of therapeutic and illicit drugs

The results of a study aimed at determining the most important experimental parameters for automated, quantitative analysis of solid dosage form pharmaceuticals (seized and model 'ecstasy' tablets) are reported. Data obtained with a macro-Raman spectrometer were complemented by micro-Raman measurements, which gave information on particle size and provided excellent data for developing statistical models of the sampling errors associated with collecting data as a series of grid points on the tablets' surface. Spectra recorded at single points on the surface of seized MDMA-caffeine-lactose tablets with a Raman microscope (lambda(ex) = 785 nm, 3 mum diameter spot) were typically dominated by one or other of the three components, consistent with Raman mapping data which showed the drug and caffeine microcrystals were ca 40 mum in diameter. Spectra collected with a microscope from eight points on a 200 mum grid were combined and in the resultant spectra the average value of the Raman band intensity ratio used to quantify the MDMA: caffeine ratio, mu(r), was 1.19 with an unacceptably high standard deviation, sigma(r), of 1.20. In contrast, with a conventional macro-Raman system (150 mum spot diameter), combined eight grid point data gave mu(r) = 1.47 with sigma(r) = 0.16. A simple statistical model which could be used to predict sigma(r) under the various conditions used was developed. The model showed that the decrease in sigma(r) on moving to a 150 mum spot was too large to be due entirely to the increased spot diameter but was consistent with the increased sampling volume that arose from a combination of the larger spot size and depth of focus in the macroscopic system. With the macro-Raman system, combining 64 grid points (0.5 mm spacing and 1-2 s accumulation per point) to give a single averaged spectrum for a tablet was found to be a practical balance between minimizing sampling errors and keeping overhead times at an acceptable level. The effectiveness of this sampling strategy was also tested by quantitative analysis of a set of model ecstasy tablets prepared from MDEA-sorbitol (0-30% by mass MDEA). A simple univariate calibration model of averaged 64 point data had R-2 = 0.998 and an r.m.s. standard error of prediction of 1.1% whereas data obtained by sampling just four points on the same tablet showed deviations from the calibration of up to 5%.

Performing meta-analysis with incomplete statistical information in clinical trials

Background: Results from clinical trials are usually summarized in the form of sampling distributions. When full information (mean, SEM) about these distributions is given, performing meta-analysis is straightforward. However, when some of the sampling distributions only have mean values, a challenging issue is to decide how to use such distributions in meta-analysis. Currently, the most common approaches are either ignoring such trials or for each trial with a missing SEM, finding a similar trial and taking its SEM value as the missing SEM. Both approaches have drawbacks. As an alternative, this paper develops and tests two new methods, the first being the prognostic method and the second being the interval method, to estimate any missing SEMs from a set of sampling distributions with full information. A merging method is also proposed to handle clinical trials with partial information to simulate meta-analysis.