On classical and other methods of discriminant analysis and estimation of log-odds

For two multinormal populations with equal covariance matrices the likelihood ratio discriminant function, an alternative allocation rule to the sample linear discriminant function when n1 ≠ n2 ,is studied analytically. With the assumption of a known covariance matrix its distribution is derived and the expectation of its actual and apparent error rates evaluated and compared with those of the sample linear discriminant function. This comparison indicates that the likelihood ratio allocation rule is robust to unequal sample sizes. The quadratic discriminant function is studied, its distribution reviewed and evaluation of its probabilities of misclassification discussed. For known covariance matrices the distribution of the sample quadratic discriminant function is derived. When the known covariance matrices are proportional exact expressions for the expectation of its actual and apparent error rates are obtained and evaluated. The effectiveness of the sample linear discriminant function for this case is also considered. Estimation of true log-odds for two multinormal populations with equal or unequal covariance matrices is studied. The estimative, Bayesian predictive and a kernel method are compared by evaluating their biases and mean square errors. Some algebraic expressions for these quantities are derived. With equal covariance matrices the predictive method is preferable. Where it derives this superiority is investigated by considering its performance for various levels of fixed true log-odds. It is also shown that the predictive method is sensitive to n1 ≠ n2. For unequal but proportional covariance matrices the unbiased estimative method is preferred. Product Normal kernel density estimates are used to give a kernel estimator of true log-odds. The effect of correlation in the variables with product kernels is considered. With equal covariance matrices the kernel and parametric estimators are compared by simulation. For moderately correlated variables and large dimension sizes the product kernel method is a good estimator of true log-odds.

Molecular analysis of evolutionary relationships of Phaseolus dumosus with the gene pool of common bean

Valuable genetic variation for bean breeding programs is held within the common bean secondary gene pool which consists of Phaseolus albescens, P. coccineus, P. costaricensis, and P. dumosus. However, the use of close relatives for bean improvement is limited due to the lack of knowledge about genetic variation and genetic plasticity of many of these species. Characterisation and analysis of the genetic diversity is necessary among beans' wild relatives; in addition, conflicting phylogenies and relationships need to be understood and a hypothesis of a hybrid origin of P. dumosus needs to be tested. This thesis research was orientated to generate information about the patterns of relationships among the common bean secondary gene pool, with particular focus on the species Phaseolus dumosus. This species displays a set of characteristics of agronomic interest, not only for the direct improvement of common bean but also as a source of valuable genes for adaptation to climate change. Here I undertake the first comprehensive study of the genetic diversity of P. dumosus as ascertained from both nuclear and chloroplast genome markers. A germplasm collection of the ancestral forms of P. dumosus together with wild, landrace and cultivar representatives of all other species of the common bean secondary gene pool, were used to analyse genetic diversity, phylogenetic relationships and structure of P. dumosus. Data on molecular variation was generated from sequences of cpDNA loci accD-psaI spacer, trnT-trnL spacer, trnL intron and rps14-psaB spacer and from the nrDNA the ITS region. A whole genome DArT array was developed and used for the genotyping of P. dumosus and its closes relatives. 4208 polymorphic markers were generated in the DArT array and from those, 742 markers presented a call rate >95% and zero discordance. DArT markers revealed a moderate genetic polymorphism among P. dumosus samples (13% of polymorphic loci), while P. coccineus presented the highest level of polymorphism (88% of polymorphic loci). At the cpDNA one ancestral haplotype was detected among all samples of all species in the secondary genepool. The ITS region of P. dumosus revealed high homogeneity and polymorphism bias to P. coccineus genome. Phylogenetic reconstructions made with Maximum likelihood and Bayesian methods confirmed previously reported discrepancies among the nuclear and chloroplast genomes of P. dumosus. The outline of relationships by hybridization networks displayed a considerable number of interactions within and between species. This research provides compelling evidence that P. dumosus arose from hybridisation between P. vulgaris and P. coccineus and confirms that P. costaricensis has likely been involved in the genesis or backcrossing events (or both) in the history of P. dumosus. The classification of the specie P. persistentus was analysed based on cpDNA and ITS sequences, the results found this species to be highly related to P. vulgaris but not too similar to P. leptostachyus as previously proposed. This research demonstrates that wild types of the secondary genepool carry a significant genetic variation which makes this a valuable genetic resource for common bean improvement. The DArT array generated in this research is a valuable resource for breeding programs since it has the potential to be used in several approaches including genotyping, discovery of novel traits, mapping and marker-trait associations. Efforts should be made to search for potential populations of P. persistentus and to increase the collection of new populations of P. dumosus, P. albescens and P. costaricensis that may provide valuable traits for introgression into common bean and other Phaseolus crops.

Worldwide trends in blood pressure from 1975 to 2015: a pooled analysis of 1479 population-based measurement studies with 19·1 million participants

Background: Raised blood pressure is an important risk factor for cardiovascular diseases and chronic kidney disease. We estimated worldwide trends in mean systolic and mean diastolic blood pressure, and the prevalence of, and number of people with, raised blood pressure, defined as systolic blood pressure of 140 mm Hg or higher or diastolic blood pressure of 90 mm Hg or higher. Methods: For this analysis, we pooled national, subnational, or community population-based studies that had measured blood pressure in adults aged 18 years and older. We used a Bayesian hierarchical model to estimate trends from 1975 to 2015 in mean systolic and mean diastolic blood pressure, and the prevalence of raised blood pressure for 200 countries. We calculated the contributions of changes in prevalence versus population growth and ageing to the increase in the number of adults with raised blood pressure. Findings: We pooled 1479 studies that had measured the blood pressures of 19·1 million adults. Global age-standardised mean systolic blood pressure in 2015 was 127·0 mm Hg (95% credible interval 125·7–128·3) in men and 122·3 mm Hg (121·0–123·6) in women; age-standardised mean diastolic blood pressure was 78·7 mm Hg (77·9–79·5) for men and 76·7 mm Hg (75·9–77·6) for women. Global age-standardised prevalence of raised blood pressure was 24·1% (21·4–27·1) in men and 20·1% (17·8–22·5) in women in 2015. Mean systolic and mean diastolic blood pressure decreased substantially from 1975 to 2015 in high-income western and Asia Pacific countries, moving these countries from having some of the highest worldwide blood pressure in 1975 to the lowest in 2015. Mean blood pressure also decreased in women in central and eastern Europe, Latin America and the Caribbean, and, more recently, central Asia, Middle East, and north Africa, but the estimated trends in these super-regions had larger uncertainty than in high-income super-regions. By contrast, mean blood pressure might have increased in east and southeast Asia, south Asia, Oceania, and sub-Saharan Africa. In 2015, central and eastern Europe, sub-Saharan Africa, and south Asia had the highest blood pressure levels. Prevalence of raised blood pressure decreased in high-income and some middle-income countries; it remained unchanged elsewhere. The number of adults with raised blood pressure increased from 594 million in 1975 to 1·13 billion in 2015, with the increase largely in low-income and middle-income countries. The global increase in the number of adults with raised blood pressure is a net effect of increase due to population growth and ageing, and decrease due to declining age-specific prevalence. Interpretation: During the past four decades, the highest worldwide blood pressure levels have shifted from high-income countries to low-income countries in south Asia and sub-Saharan Africa due to opposite trends, while blood pressure has been persistently high in central and eastern Europe.

Worldwide trends in diabetes since 1980: a pooled analysis of 751 population-based studies with 4·4 million participants

Background: One of the global targets for non-communicable diseases is to halt, by 2025, the rise in the age-standardised adult prevalence of diabetes at its 2010 levels. We aimed to estimate worldwide trends in diabetes, how likely it is for countries to achieve the global target, and how changes in prevalence, together with population growth and ageing, are affecting the number of adults with diabetes. Methods: We pooled data from population-based studies that had collected data on diabetes through measurement of its biomarkers. We used a Bayesian hierarchical model to estimate trends in diabetes prevalence - defined as fasting plasma glucose of 7·0 mmol/L or higher, or history of diagnosis with diabetes, or use of insulin or oral hypoglycaemic drugs - in 200 countries and territories in 21 regions, by sex and from 1980 to 2014. We also calculated the posterior probability of meeting the global diabetes target if post-2000 trends continue. Findings: We used data from 751 studies including 4 372 000 adults from 146 of the 200 countries we make estimates for Global age-standardised diabetes prevalence increased from 4·3% (95% credible interval 2·4-7·0) in 1980 to 9·0% (7·2-11·1) in 2014 in men, and from 5·0% (2·9-7·9) to 7·9% (6·4-9·7) in women. The number of adults with diabetes in the world increased from 108 million in 1980 to 422 million in 2014 (28·5% due to the rise in prevalence, 39·7% due to population growth and ageing, and 31·8% due to interaction of these two factors). Age-standardised adult diabetes prevalence in 2014 was lowest in northwestern Europe, and highest in Polynesia and Micronesia, at nearly 25%, followed by Melanesia and the Middle East and north Africa. Between 1980 and 2014 there was little change in age-standardised diabetes prevalence in adult women in continental western Europe, although crude prevalence rose because of ageing of the population. By contrast, age-standardised adult prevalence rose by 15 percentage points in men and women in Polynesia and Micronesia. In 2014, American Samoa had the highest national prevalence of diabetes (>30% in both sexes), with age-standardised adult prevalence also higher than 25% in some other islands in Polynesia and Micronesia. If post-2000 trends continue, the probability of meeting the global target of halting the rise in the prevalence of diabetes by 2025 at the 2010 level worldwide is lower than 1% for men and is 1% for women. Only nine countries for men and 29 countries for women, mostly in western Europe, have a 50% or higher probability of meeting the global target. Interpretation Since 1980, age-standardised diabetes prevalence in adults has increased, or at best remained unchanged, in every country. Together with population growth and ageing, this rise has led to a near quadrupling of the number of adults with diabetes worldwide. The burden of diabetes, both in terms of prevalence and number of adults aff ected, has increased faster in low-income and middle-income countries than in high-income countries.