Traditional multiple hypothesis testing procedures, such as that of Benjamini and Hochberg, fix an error rate and determine the corresponding rejection region. In 2002 Storey proposed a fixed rejection region procedure and showed numerically that it can gain more power than the fixed error rate procedure of Benjamini and Hochberg while controlling the same false discovery rate (FDR). In this thesis it is proved that when the number of alternatives is small compared to the total number of hypotheses, Storeys method can be less powerful than that of Benjamini and Hochberg. Moreover, the two procedures are compared by setting them to produce the same FDR. The difference in power between Storeys procedure and that of Benjamini and Hochberg is near zero when the distance between the null and alternative distributions is large, but Benjamini and Hochbergs procedure becomes more powerful as the distance decreases. It is shown that modifying the Benjamini and Hochberg procedure to incorporate an estimate of the proportion of true null hypotheses as proposed by Black gives a procedure with superior power.<p> Multiple hypothesis testing can also be applied to regression diagnostics. In this thesis, a Bayesian method is proposed to test multiple hypotheses, of which the i-th null and alternative hypotheses are that the i-th observation is not an outlier versus it is, for i=1,...,m. In the proposed Bayesian model, it is assumed that outliers have a mean shift, where the proportion of outliers and the mean shift respectively follow a Beta prior distribution and a normal prior distribution. It is proved in the thesis that for the proposed model, when there exists more than one outlier, the marginal distributions of the deletion residual of the i-th observation under both null and alternative hypotheses are doubly noncentral t distributions. The outlyingness of the i-th observation is measured by the marginal posterior probability that the i-th observation is an outlier given its deletion residual. An importance sampling method is proposed to calculate this probability. This method requires the computation of the density of the doubly noncentral F distribution and this is approximated using Patnaiks approximation. An algorithm is proposed in this thesis to examine the accuracy of Patnaiks approximation. The comparison of this algorithms output with Patnaiks approximation shows that the latter can save massive computation time without losing much accuracy.<p> The proposed Bayesian multiple outlier identification procedure is applied to some simulated data sets. Various simulation and prior parameters are used to study the sensitivity of the posteriors to the priors. The area under the ROC curves (AUC) is calculated for each combination of parameters. A factorial design analysis on AUC is carried out by choosing various simulation and prior parameters as factors. The resulting AUC values are high for various selected parameters, indicating that the proposed method can identify the majority of outliers within tolerable errors. The results of the factorial design show that the priors do not have much effect on the marginal posterior probability as long as the sample size is not too small.<p> In this thesis, the proposed Bayesian procedure is also applied to a real data set obtained by Kanduc et al. in 2008. The proteomes of thirty viruses examined by Kanduc et al. are found to share a high number of pentapeptide overlaps to the human proteome. In a linear regression analysis of the level of viral overlaps to the human proteome and the length of viral proteome, it is reported by Kanduc et al. that among the thirty viruses, human T-lymphotropic virus 1, Rubella virus, and hepatitis C virus, present relatively higher levels of overlaps with the human proteome than the predicted level of overlaps. The results obtained using the proposed procedure indicate that the four viruses with extremely large sizes (Human herpesvirus 4, Human herpesvirus 6, Variola virus, and Human herpesvirus 5) are more likely to be the outliers than the three reported viruses. The results with thefour extreme viruses deleted confirm the claim of Kanduc et al.

Understanding species-habitat relationships for endangered species is critical for their conservation. However, many studies have limited value for conservation because they fail to account for habitat associations at multiple spatial scales, anthropogenic variables, and imperfect detection. We addressed these three limitations by developing models for an endangered wetland bird, Yuma Ridgway's rail (Rallus obsoletus yumanensis), that examined how the spatial scale of environmental variables, inclusion of anthropogenic disturbance variables, and accounting for imperfect detection in validation data influenced model performance. These models identified associations between environmental variables and occupancy. We used bird survey and spatial environmental data at 2473 locations throughout the species' U.S. range to create and validate occupancy models and produce predictive maps of occupancy. We compared habitat-based models at three spatial scales (100, 224, and 500 m radii buffers) with and without anthropogenic disturbance variables using validation data adjusted for imperfect detection and an unadjusted validation dataset that ignored imperfect detection. The inclusion of anthropogenic disturbance variables improved the performance of habitat models at all three spatial scales, and the 224-m-scale model performed best. All models exhibited greater predictive ability when imperfect detection was incorporated into validation data. Yuma Ridgway's rail occupancy was negatively associated with ephemeral and slow-moving riverine features and high-intensity anthropogenic development, and positively associated with emergent vegetation, agriculture, and low-intensity development. Our modeling approach accounts for common limitations in modeling species-habitat relationships and creating predictive maps of occupancy probability and, therefore, provides a useful framework for other species.

Landslide susceptibility maps are useful for spatial decision-making to minimize the lossof lives and properties. There are many studies related to the development of landslidesusceptibility maps using various methods such as Analytic Hierarchy Process, Weight ofEvidence and Logistic Regression. Commonly, the geospatial data required for such analysis(such as land cover and soil type maps) are only locally available and pertinent to smallcase studies. Transferable and scalable approaches utilizing publicly available, large scaledatasets (ie., global or continental) are necessary to develop susceptibility maps in areaswhere local data is not available or when large-scale analysis is required. To develop suchapproaches, a systematic comparison between locally available, fine resolution, and largerscale, openly available but coarser resolution datasets is essential. The objective of this study isto investigate the efficiency of globally available public data for landslide susceptibility mappingby comparing it with the performance of the data provided from local institutions. For this purpose, the Göta river valley in Sweden and the country of Rwanda were selectedas study areas. Göta river valley was used for the comparison of local and open data.While Rwanda was used as a study area to ensure the efficiency of open data analysis andtransferability of the framework. The selected landslide impact factors for this study are;elevation, slope, soil type, land cover, precipitation, lithology, distance to roads, and distanceto drainage network. Landslide susceptibility maps were prepared by using the state-of-the-artFrequency Ratio method. The validation results using the prediction rate curve technique show92.9%, 90.2%, and 83.1% area under curve values for local and open data analyses of Göta rivervalley and open data analysis of Rwanda country, respectively. The results show that globallyavailable open data demonstrate strong potential for landslide susceptibility mapping whenhigh-resolution local data are not available.

The aim of this thesis was to investigate the use of effect sizes to report the results of statistical credit rating models in a more practical way. Rating systems in the form of statistical probability models like logistic regression models are used to forecast the behaviour of clients and guide business in rating clients as “high” or “low” risk borrowers. Therefore, model results were reported in terms of statistical significance as well as business language (practical significance), which business experts can understand and interpret. In this thesis, statistical results were expressed as effect sizes like Cohen‟s d that puts the results into standardised and measurable units, which can be reported practically. These effect sizes indicated strength of correlations between variables, contribution of variables to the odds of defaulting, the overall goodness-of-fit of the models and the models‟ discriminating ability between high and low risk customers. / Statistics / M. Sc. (Statistics)

Introdução: A administração de morfina através de bomba de infusão controlada pelo paciente (ACP) no tratamento da dor pós-cirurgica e traumática tem-se mostrado promissora e faz parte da rotina terapêutica de muitos hospitais. No entanto, doses altas ou repetidas deste opióide estão associadas a efeitos adversos dose dependentes, dentre eles, a depressão respiratória. No caso de pacientes submetidos a cirurgias de tórax, além da analgesia pós-operatória, devem também ser considerados como parâmetros relevantes a anestesia regional (intratecal) no intra-operatório, a qual pode contribuir para melhora da função pulmonar pós-operatória e extubação precoce no pós-operatório e a circulação extracorpórea (CEC), potencial fator de alteração na cinética de fármacos. Objetivos: Investigar a influência da morfina intratecal e da circulação extracorpórea (CEC) sobre o consumo de morfina ACP, área sob a curva e escores de dor no período pós-operatório, bem como propor modelo farmacocinético-farmacodinâmico (PK-PD) para correlação dessas variáveis. Adicionalmente, foi desenvolvido método analítico para quantificação da morfina plasmática. Métodos: 59 pacientes submetidos à cirurgia eletiva de revascularização com CEC e sem CEC, na presença ou não de morfina intratecal intra-operatória foram distribuídos em grupos com base na combinação das intervenções acima mencionadas. No período pós-operatório, todos os pacientes receberam bolus IV de 1mg de morfina, e então o dispositivo ACP foi instalado na unidade de terapia intensiva, através de cateter venoso após a extubação orotraqueal. A morfina ACP foi liberada através de livre demanda solicitada pelo paciente (bolus de 1 mg), lock-out de 5 min até 36 horas do pós-operatório. Coletaram-se amostras seriadas de sangue de cateter venoso no período (3,6,12,18,24,36 horas) e a morfina plasmática foi determinada através da cromatografia líquida - espectrometria de massas (LC-MS/MS ESI+) após a purificação das amostras de plasma. A intensidade da dor foi monitorada no mesmo período pela escala análoga visual (EAV). A modelagem PK-PD foi investigada pelo GraphPad Prism 5.0. Resultados: O consumo de morfina e a intensidade da dor diferiram entre os grupos. O modelo do EMAX e a curva de histerese foram propostos pela modelagem PK-PD. Conclusões: O método analítico mostrou-se adequado na determinação da morfina plasmática. O consumo de morfina os escores de dor EAV no pós-operatório diferiram pela comparação dos grupos de pacientes investigados. Menores doses de morfina ACP foram requeridas pelos pacientes que receberam morfina intratecal intra-operatória. Demonstrou-se através do modelo do EMAX correlação não linear entre os parâmetros consumo de morfina e AUC0-36, e curva de histerese foi obtida quando se plotou consumo de morfina versus escore de dor. / Introduction: Morphine administration using patient controlled analgesia (PCA) for treatment of post surgical and traumatic pain has been a current practice in many hospitals. However, large or repeated doses of this opioid are associated to dose dependent adverse events, including, respiratory depression. Considering patients submitted to thoracic surgery, in addition to the postoperatory analgesia, two other relevant parameters must be considered: regional anesthesia (intrathecal) in the intra-operatory period, which should contribute to the respiratory function improvement and decrease in the extubation time; and the cardiopulmonary bypass (OPCAB), that potentially alters the drugs\' kinetics. Objectives: To investigate the influence of intrathecal morphine administration and cardiopulmonary bypass (OPCAB) in the morphine PCA drug requirements, area under the curve of morphine plasma concentration versus time and pain scores in the postoperative period, and to choose a pharmacokinetic-pharmacodynamic model to correlate these variables. In addition, an analytical method was developed to quantify morphine in plasma. Methods: 59 patients submitted to elective coronary artery bypass grafting (CABG) with (CPB) and without cardiopulmonary bypass (OPCAB), with and without intrathecal morphine in the intra-operative period were distributed by the combination of the above mentioned interventions. In the postoperative period, all the patients were given an IV bolus of 1mg of morphine, and then PCA device was installed in the intensive care unit by a venous catheter after the orotracheal extubation. Morphine PCA was delivered on demand (boluses of 1 mg), lock-out of 5 min until 36 hours of the postoperative period. A serial of blood samples were collected from venous catheter of patients at the postoperative period (3,6,12,18,24,36 hrs) and morphine plasma concentrations were determined by Liquid Chromatography-Mass Spectrometry ((LC-MS/MS ESI+)) after the purification of plasma samples. Pain scores were monitored during the same period by a visual analogue scale, VAS or 1-2-3 pain scale. PK-PD modeling was investigated by applying the GraphPad Prism 5.0. Results: Drug dose requirements and analgesia were significant different in patients of groups investigated. EMAX model and the hysteresis curve were proposed by PK-PD modeling to correlate drug requirements and AUC 0-36 or VAS. Conclusions: LC-MS/MS (ESI+) method was adequate for drug measurements in plasma. Morphine dose requirements and analgesia were different by comparison of groups. Lower doses of morphine by PCA were required for the groups that have received intrathecal morphine intraoperatively. It was demonstrated a non linear correlation between parameters by EMAX model when drug requirements and AUC0-36 were plotted, and the hysteresis curve was obtained when analgesia dose requirements was plotted against pain score.

Introdução: A administração de morfina através de bomba de infusão controlada pelo paciente (ACP) no tratamento da dor pós-cirurgica e traumática tem-se mostrado promissora e faz parte da rotina terapêutica de muitos hospitais. No entanto, doses altas ou repetidas deste opióide estão associadas a efeitos adversos dose dependentes, dentre eles, a depressão respiratória. No caso de pacientes submetidos a cirurgias de tórax, além da analgesia pós-operatória, devem também ser considerados como parâmetros relevantes a anestesia regional (intratecal) no intra-operatório, a qual pode contribuir para melhora da função pulmonar pós-operatória e extubação precoce no pós-operatório e a circulação extracorpórea (CEC), potencial fator de alteração na cinética de fármacos. Objetivos: Investigar a influência da morfina intratecal e da circulação extracorpórea (CEC) sobre o consumo de morfina ACP, área sob a curva e escores de dor no período pós-operatório, bem como propor modelo farmacocinético-farmacodinâmico (PK-PD) para correlação dessas variáveis. Adicionalmente, foi desenvolvido método analítico para quantificação da morfina plasmática. Métodos: 59 pacientes submetidos à cirurgia eletiva de revascularização com CEC e sem CEC, na presença ou não de morfina intratecal intra-operatória foram distribuídos em grupos com base na combinação das intervenções acima mencionadas. No período pós-operatório, todos os pacientes receberam bolus IV de 1mg de morfina, e então o dispositivo ACP foi instalado na unidade de terapia intensiva, através de cateter venoso após a extubação orotraqueal. A morfina ACP foi liberada através de livre demanda solicitada pelo paciente (bolus de 1 mg), lock-out de 5 min até 36 horas do pós-operatório. Coletaram-se amostras seriadas de sangue de cateter venoso no período (3,6,12,18,24,36 horas) e a morfina plasmática foi determinada através da cromatografia líquida - espectrometria de massas (LC-MS/MS ESI+) após a purificação das amostras de plasma. A intensidade da dor foi monitorada no mesmo período pela escala análoga visual (EAV). A modelagem PK-PD foi investigada pelo GraphPad Prism 5.0. Resultados: O consumo de morfina e a intensidade da dor diferiram entre os grupos. O modelo do EMAX e a curva de histerese foram propostos pela modelagem PK-PD. Conclusões: O método analítico mostrou-se adequado na determinação da morfina plasmática. O consumo de morfina os escores de dor EAV no pós-operatório diferiram pela comparação dos grupos de pacientes investigados. Menores doses de morfina ACP foram requeridas pelos pacientes que receberam morfina intratecal intra-operatória. Demonstrou-se através do modelo do EMAX correlação não linear entre os parâmetros consumo de morfina e AUC0-36, e curva de histerese foi obtida quando se plotou consumo de morfina versus escore de dor. / Introduction: Morphine administration using patient controlled analgesia (PCA) for treatment of post surgical and traumatic pain has been a current practice in many hospitals. However, large or repeated doses of this opioid are associated to dose dependent adverse events, including, respiratory depression. Considering patients submitted to thoracic surgery, in addition to the postoperatory analgesia, two other relevant parameters must be considered: regional anesthesia (intrathecal) in the intra-operatory period, which should contribute to the respiratory function improvement and decrease in the extubation time; and the cardiopulmonary bypass (OPCAB), that potentially alters the drugs\' kinetics. Objectives: To investigate the influence of intrathecal morphine administration and cardiopulmonary bypass (OPCAB) in the morphine PCA drug requirements, area under the curve of morphine plasma concentration versus time and pain scores in the postoperative period, and to choose a pharmacokinetic-pharmacodynamic model to correlate these variables. In addition, an analytical method was developed to quantify morphine in plasma. Methods: 59 patients submitted to elective coronary artery bypass grafting (CABG) with (CPB) and without cardiopulmonary bypass (OPCAB), with and without intrathecal morphine in the intra-operative period were distributed by the combination of the above mentioned interventions. In the postoperative period, all the patients were given an IV bolus of 1mg of morphine, and then PCA device was installed in the intensive care unit by a venous catheter after the orotracheal extubation. Morphine PCA was delivered on demand (boluses of 1 mg), lock-out of 5 min until 36 hours of the postoperative period. A serial of blood samples were collected from venous catheter of patients at the postoperative period (3,6,12,18,24,36 hrs) and morphine plasma concentrations were determined by Liquid Chromatography-Mass Spectrometry ((LC-MS/MS ESI+)) after the purification of plasma samples. Pain scores were monitored during the same period by a visual analogue scale, VAS or 1-2-3 pain scale. PK-PD modeling was investigated by applying the GraphPad Prism 5.0. Results: Drug dose requirements and analgesia were significant different in patients of groups investigated. EMAX model and the hysteresis curve were proposed by PK-PD modeling to correlate drug requirements and AUC 0-36 or VAS. Conclusions: LC-MS/MS (ESI+) method was adequate for drug measurements in plasma. Morphine dose requirements and analgesia were different by comparison of groups. Lower doses of morphine by PCA were required for the groups that have received intrathecal morphine intraoperatively. It was demonstrated a non linear correlation between parameters by EMAX model when drug requirements and AUC0-36 were plotted, and the hysteresis curve was obtained when analgesia dose requirements was plotted against pain score.

The aim of this thesis was to investigate the use of effect sizes to report the results of statistical credit rating models in a more practical way. Rating systems in the form of statistical probability models like logistic regression models are used to forecast the behaviour of clients and guide business in rating clients as “high” or “low” risk borrowers. Therefore, model results were reported in terms of statistical significance as well as business language (practical significance), which business experts can understand and interpret. In this thesis, statistical results were expressed as effect sizes like Cohen‟s d that puts the results into standardised and measurable units, which can be reported practically. These effect sizes indicated strength of correlations between variables, contribution of variables to the odds of defaulting, the overall goodness-of-fit of the models and the models‟ discriminating ability between high and low risk customers. / Statistics / M. Sc. (Statistics)

This thesis focuses on (1) the statistical methodologies for the estimation of spatial data with outliers and (2) classification accuracy of disease diagnosis. Chapter I, Robust Estimation for Spatial Markov Random Field Models: Markov Random Field (MRF) models are useful in analyzing spatial lattice data collected from semiconductor device fabrication and printed circuit board manufacturing processes or agricultural field trials. When outliers are present in the data, classical parameter estimation techniques (e.g., least squares) can be inefficient and potentially mislead the analyst. This chapter extends the MRF model to accommodate outliers and proposes robust parameter estimation methods such as the robust M- and RA-estimates. Asymptotic distributions of the estimates with differentiable and non-differentiable robustifying function are derived. Extensive simulation studies explore robustness properties of the proposed methods in situations with various amounts of outliers in different patterns. Also provided are studies of analysis of grid data with and without the edge information. Three data sets taken from the literature illustrate advantages of the methods. Chapter II, Extending the Skill Test for Disease Diagnosis: For diagnostic tests, we present an extension to the skill plot introduced by Mozer and Briggs (2003). The method is motivated by diagnostic measures for osteoporosis in a study. By restricting the area under the ROC curve (AUC) according to the skill statistic, we have an improved diagnostic test for practical applications by considering the misclassification costs. We also construct relationships, using the Koziol-Green model and mean-shift model, between the diseased group and the healthy group for improving the skill statistic. Asymptotic properties of the skill statistic are provided. Simulation studies compare the theoretical results and the estimates under various disease rates and misclassification costs. We apply the proposed method in classification of osteoporosis data.

Magister Pharmaceuticae - MPharm / Many studies have investigated the pharmacokinetics of anti-tuberculosis drugs in patients infected with tuberculosis. However, little is known about the pharmacokinetics of the drugs that are used in the treatment of multi-drug resistant tuberculosis (MDRTB).Therefore, the objective of the present study was to investigate the steady state concentrations and the pharmacokinetics of ofloxacin, one of the drugs used in the treatment of MDR-TB in patients infected with MDR-TB and patients with MDR-TB co-infected with HIV Plasma samples were drawn at different times over 24 hours after ofloxacin oral administration. For the determination of ofloxacin plasma concentrations, the liquid chromatography coupled with mass spectrometry analysis method was used.The method was validated over a concentration range of 0.1-10 μg/ml. The lower limit of ofloxacin detection was 0.05μg/ml, while the lower limit of quantification was 0.1μg/ml. The response was linear over the range used with a mean recovery of 97.6%. Ofloxacin peak was well separated at a retention time of 9.6 minutes.The pharmacokinetic parameters obtained were presented as mean ± standard deviation(SD). The peak concentration of ofloxacin (Cmax) was 4.71± 2.27 μg/ml occurred at Tmax 3±1.29 hours after ofloxacin oral administration. The mean (±SD) for the area under the concentration-time curve (AUC0-24) and the area under the concentration-time curve(AUC0-∞) were 68.8±42.61 μg/ml.hr and 91.93±76.86 μg/ml.hr, respectively. Ofloxacin distributed widely with a mean (±SD) volume of distribution (Vd) 2.77±1.16 L/kg and it was eliminated with a mean (±SD) total clearance rate of 0.27±0.25 L/hr/kg. Ofloxacin mean (±SD) half-life was 9.55± 4.69 hours and mean (±SD) of the mean residence time (MRT) was 1512± 6.59 hours.In summary, compared with the previous findings in the literature, ofloxacin pharmacokinetic was altered in MDR-TB patients with or without HIV co-infection.The AUC and Cmax were reduced, while the half-life and the time to reach the peak concentration were prolonged. This suggests that, both the rate and the extent of ofloxacin absorption were decreased. Furthermore, ofloxacin was highly eliminated in patients, which may be related to the altered liver function in this group of patients.Further studies investigating the effect of HIV, liver and kidney dysfunctions on ofloxacin pharmacokinetics are recommended in large number of patients infected with MDR-TB.in addition to the therapeutic drug monitoring to maintain the desired concentration of ofloxacin in the patients.

本論文的研究目標是建構一個由多標記複合成的最佳疾病診斷工具，所考慮的評估準則為操作者特徵曲線在特定特異度範圍之線下面積(pAUC)。在常態分布假設下，我們推導多標記線性組合之pAUC以及最佳線性組合之必要條件。由於函數本身過於複雜使得計算困難。除此之外，我們也發現其最佳解可能不唯一，以及局部極值存在，這些情況使得現有演算法的運用受限，我們因此提出多重初始值演算法。當母體參數未知時，我們利用最大概似估計量以獲得樣本pAUC以及令其極大化之最佳線性組合，並證明樣本最佳線性組合將一致性地收斂到母體最佳線性組合。在進一步的研究中，我們針對單標記的邊際判別能力、多標記的複合判別能力以及個別標記的條件判別能力，分別提出相關統計檢定方法。這些統計檢定被運用至兩個標記選取的方法，分別是前進選擇法與後退淘汰法。我們運用這些方法以選取與疾病檢測有顯著相關的標記。本論文透過模擬研究來驗證所提出的演算法、統計檢定方法以及標記選取的方法。另外，也將這些方法運用在數組實際資料上。 / The aim of this work is to construct a composite diagnostic tool based on multiple biomarkers under the criterion of the partial area under a ROC curve (pAUC) for a predetermined specificity range. Recently several studies are interested in the optimal linear combination maximizing the whole area under a ROC curve (AUC). In this study, we focus on finding the optimal linear combination by a direct maximization of the pAUC under normal assumption. In order to find an analytic solution, the first derivative of the pAUC is derived. The form is so complicated, that a further validation on the Hessian matrix is difficult. In addition, we find that the pAUC maximizer may not be unique and sometimes, local maximizers exist. As a result, the existing algorithms, which depend on the initial-point, are inadequate to serve our needs. We propose a new algorithm by adopting several initial points at one time. In addition, when the population parameters are unknown and only a random sample data set is available, the maximizer of the sample version of the pAUC is shown to be a strong consistent estimator of its theoretical counterpart. We further focus on determining whether a biomarker set, or one specific biomarker has a significant contribution to the disease diagnosis. We propose three statistical tests for the identification of the discriminatory power. The proposed tests are applied to biomarker selection for reducing the variable number in advanced analysis. Numerical studies are performed to validate the proposed algorithm and the proposed statistical procedures.