Credit Line Analysis plays a very important role in the housing market, especially with the situation of large number of frozen loans during the current financial crisis. In this thesis, we apply the methods of kernel estimate and the Receiver Operating Characteristic (ROC) curve in the credit loan application process in order to help banks select the optimal threshold to differentiate good customers from bad customers. Better choice of the threshold is essential for banks to prevent loss and maximize profit from loans. One of the main advantages of our study is that the method does not require us to specify the distribution of the latent risk score. We apply bootstrap method to construct the confidence interval for the estimate.

The ongoing financial crisis has had major adverse impact on the credit market. As the financial crisis progresses, the skyrocketing unemployment rate puts more and more customers in such a position that they cannot pay back their credit debts. The deteriorating economic environment and growing pressures for revenue generation have led creditors to re-assess their existing portfolios. The credit re-assessment is to accurately estimate customers' behavior and distill information for credit decisions that differentiate bad customers from good customers. Lending institutions often need a specific rule for defining an optimal cut-off value to maximize revenue and minimize risk. In this dissertation research, I consider a problem in the broad area of credit risk management: the selection of critical thresholds, which comprises of the "optimal cut-off point" and an interval containing cut-off points near the optimal cut-off point (a "near-optimal interval"). These critical thresholds can be used in practice to adjust credit lines, to close accounts involuntarily, to re-price, etc. Better credit re-assessment practices are essential for banks to prevent loan loss in the future and restore the flow of credit to entrepreneurs and individuals. The Profit Function is introduced to estimate the optimal cut-off and the near-optimal interval, which are used to manage the credit risk in the financial industry. The credit scores of the good population and bad population are assumed from two distributions, with the same or different dispersion parameters. In a homoscedastic Normal-Normal model, a closed-form solution of optimal cut-off and some properties of optimal cut-off are provided for three possible shapes of the Profit Functions. The same methodology can be generalized to other distributions in the exponential family, including the heteroscedastic Normal-Normal Profit Function and the Gamma-Gamma Profit Function. It is shown that a Profit Function is a comprehensive tool in the selection of critical thresholds, and its solution can be found using easily implemented computing algorithms. The estimation of near-optimal interval is developed in three possible shapes of the bi-distributional Profit Function. The optimal cut-off has a closed-form formula, and the estimation results of near-optimal intervals can be simplified to this closed-form formula when the tolerance level is zero. Two nonparametric methods are introduced to estimate critical thresholds if the latent risk score is not from some known distribution. One method uses the Kernel density estimation method to derive a tabulated table, which is used to estimate the values of critical thresholds. A ROC Graphical method is also developed to estimate critical thresholds. In the theoretical portion of the dissertation, we use Taylor Series and the Delta method to develop the asymptotic distribution of the non-constrained optimal cut-off. We also use the Kernel density estimator to derive the asymptotic variance of the Profit function. / Statistics

Many continuous medical tests often rely on a threshold for diagnosis. There are two sequential testing strategies of interest: Believe the Positive (BP) and Believe the Negative (BN). BP classifies a patient positive if either the first test is greater than a threshold θ1 or negative on the first test and greater than θ2 on the second test. BN classifies a patient positive if the first test is greater than a threshold θ3 and greater than θ4 on the second test. Threshold pairs θ = (θ1, θ2) or (θ3, θ4), depending on strategy, are defined as optimal if they maximized GYI = Se + r(Sp – 1). Of interest is to determine if these optimal threshold, or optimal operating point (OOP), estimates are “good” when calculated from a sample. The methods proposed in this dissertation derive formulae to estimate θ assuming tests follow a binormal distribution, using the Newton-Raphson algorithm with ridging. A simulation study is performed assessing bias, root mean square error, percentage of over estimation of Se/Sp, and coverage of simultaneous confidence intervals and confidence regions for sets of population parameters and sample sizes. Additionally, OOPs are compared to the traditional empirical approach estimates. Bootstrapping is used to estimate the variance of each optimal threshold pair estimate. The study shows that parameters such as the area under the curve, ratio of standard deviations of disease classification groups within tests, correlation between tests within a disease classification, total sample size, and allocation of sample size to each disease classification group were all influential on OOP estimation. Additionally, the study shows that this method is an improvement over the empirical estimate. Equations for researchers to use in estimating total sample size and SCI width are also developed. Although the models did not produce high coefficients of determination, they are a good starting point for researchers when designing a study. A pancreatic cancer dataset is used to illustrate the OOP estimation methodology for sequential tests.

En France, la recherche contre le cancer est un enjeu majeur de santé publique. On estime notamment que le nombre de nouveaux cas de cancer a plus que doublé entre 1980 et 2012. L’hétérogénéité des caractéristiques tumorales, pour un même cancer, impose des défis complexes dans la recherche de traitements efficaces. Dans ce contexte, des espoirs importants sont placés dans la recherche de biomarqueurs prédictifs reflétant les caractéristiques des patients ainsi que de leur tumeur afin d’orienter le choix de la stratégie thérapeutique. Par exemple, pour les cancers colorectaux métastatiques, il est maintenant reconnu que l’ajout de cetuximab (un anti-EGFR) à la chimiothérapie classique (ici le FOLFOX4), n’apporte un bénéfice qu’aux patients dont le gène KRAS est non muté. Le gène KRAS est ici un biomarqueur prédictif binaire, mais de nombreux biomarqueurs sont le résultat d’une quantification ou d’un dosage. L’objectif de cette thèse est dans un premier temps, de quantifier la capacité globale d’un biomarqueur quantitatif à guider le choix du traitement. Après une revue de la littérature, une nouvelle méthode basée sur une extension des courbes ROC est proposée, et comparée aux méthodes existantes. Son principal avantage est d’être non paramétrique, et d’être indépendante de l’efficacité moyenne des traitements. Dans un second temps, lorsqu’un biomarqueur prédictif quantitatif est étudié, la définition d’un seuil de marqueur au-delà duquel la première option de traitement sera préférée, et en-deçà duquel la deuxième option de traitement sera préférée se pose. Une approche reposant sur la définition d’une fonction d’utilité est proposée permettant alors de tenir compte de l’efficacité des traitements ainsi que de leur impact sur la qualité de vie des patients. Une méthode Bayésienne d’estimation de ce seuil optimal est proposée / In France, the cancer research is a major public health issue. The number of new cancer cases nearly doubled between 1980 and 2012. The heterogeneity of the tumor characteristics, for a given cancer, presents a great challenge in the research of new effective treatments. In this context, much hope is placed in the research of predictive (or treatment selection) biomarkers that reflect the patients’ characteristics in order to guide treatment choice. For example, in the metastatic colorectal cancer setting, it is admitted that the addition of cetuximab (an anti-EGFR) to classical chemotherapy (the FOLFOX4), only improve the outcome of patients with KRAS wild-type tumors. In that context, the KRAS gene is a binary treatment selection marker, but plenty of biomarkers result from some quantifications or dosage measurements. The first aim of this thesis is to quantify the global treatment selection ability of a biomarker. After a review of the existing litterature, a method based on an extension of ROC curves is proposed and compared to existing methods. Its main advantage is that it is non-parametric, and that it does not depend on the mean risk of event in each treatment arm. In a second time, when a quantitative treatment selection biomarker is assessed, there is a need to estimate a marker thereshold value above which one treatment is preferred, and below which the other treatment is recommended. An approach that relies on the definition of a utility function is proposed in order to take into account both efficacy and toxicity of treatments when estimating the optimal threshold. A Bayesian method for the estimation of the optimal threshold is proposed