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.

Survival analysis of adult tuberculosis disease

Background: We conducted a survival analysis of all the confirmed cases of Adult Tuberculosis (TB) patients treated in Cork-City, Ireland. The aim of this study was to estimate Survival time (ST), including median time of survival and to assess the association and impact of covariates (TB risk factors) to event status and ST. The outcome of the survival analysis is reported in this paper. Methods: We used a retrospective cohort study research design to review data of 647 bacteriologically confirmed TB patients from the medical record of two teaching hospitals. Mean age 49 years (Range 18–112). We collected information on potential risk factors of all confirmed cases of TB treated between 2008–2012. For the survival analysis, the outcome of interest was ‘treatment failure’ or ‘death’ (whichever came first). A univariate descriptive statistics analysis was conducted using a non- parametric procedure, Kaplan -Meier (KM) method to estimate overall survival (OS), while the Cox proportional hazard model was used for the multivariate analysis to determine possible association of predictor variables and to obtain adjusted hazard ratio. P value was set at <0.05, log likelihood ratio test at >0.10. Data were analysed using SPSS version 15.0. Results: There was no significant difference in the survival curves of male and female patients. (Log rank statistic = 0.194, df = 1, p = 0.66) and among different age group (Log rank statistic = 1.337, df = 3, p = 0.72). The mean overall survival (OS) was 209 days (95%CI: 92–346) while the median was 51 days (95% CI: 35.7–66). The mean ST for women was 385 days (95%CI: 76.6–694) and for men was 69 days (95%CI: 48.8–88.5). Multivariate Cox regression showed that patient who had history of drug misuse had 2.2 times hazard than those who do not have drug misuse. Smokers and alcohol drinkers had hazard of 1.8 while patients born in country of high endemicity (BICHE) had hazard of 6.3 and HIV co-infection hazard was 1.2. Conclusion: There was no significant difference in survival curves of male and female and among age group. Women had a higher ST compared to men. But men had a higher hazard rate compared to women. Anti-TNF, immunosuppressive medication and diabetes were found to be associated with longer ST, while alcohol, smoking, RICHE, BICHE was associated with shorter ST.

Sectoral impacts on the diversity of carabid beetles (Coleoptera: Carabidae) and their associated ecosystem service of biocontrol

This thesis aimed to provide an understanding of how human-induced changes in the economic sectors of agriculture and transport affect carabid diversity, potential carabidmediated biocontrol and predator-pest interactions. The research involved both observational and manipulative laboratory and field-based studies. Observational research consisted of two large-scale investigations of (1) the impact of Miscanthus and oilseed rape production (n=45) and (2) the impact of horticultural and ecological based landscaping of roadside verges (n=64). This research is the first record of carabid diversity, potential biocontrol and community assemblage with respect to bioenergy crop production and roadside landscaping in an Irish context and it is also an important addition to the limited knowledge of carabid populations in these ecosystems internationally. Manipulative work involved the examination of the role predator identity, diversity and biomass play in the suppression of pollen beetle larvae (an economically damaging insect pest of oilseed rape in Europe), using a novel experimental design called ‘simplex’. To complement this research, an additional field study on the impact of low and high oilseed rape pesticide management on carabid species richness and abundance, and crop yield, was also conducted. This research is a great contribution to the existing understanding of what constitutes the important components of predator biodiversity and expands the knowledge of the usefulness of carabid predators in the context of pollen beetle larvae control. In particular, the work shows that the abundance or biomass of beetles has an effect that is far larger than the effect of diversity on the capacity of beetles to consume prey. In turn, the field study showed that pesticide applications had little impact on yield, or carabid richness, but that carabid abundance/biomass declined drastically. The work provides compelling evidence that management practices erode the useful components of biodiversity that are essential for the delivery of biocontrol services.