This study includes three issues about the dynamic of 30-days Taiwan Commercial Paper rate (CP2).The first issue focuses on the estimation of continuous-time short-term interest rate models. We discretize the continuous-time models by using two different approaches, and then use weekly and monthly data to estimate the parameters. The models are evaluated by data fit. We find that the estimated parameters are similar for different discretization approaches and would be more stable and efficient under quasi-maximum likelihood (QML) with weekly data. There exists mean reversion for Taiwan CP rate and the relationship between the volatility and the level of interest rates are less than 1 and smaller than that of American T-Bill rates reported by CKLS (1992) and Nowman (1997). We also find that CIR-SR model performs best for Taiwan CP rate. The second issue compares the continuous-time short-term interest rate models empirically both by predictive accuracy test and encompassing test. Having the estimated parameters of the models by discretization of Nowman(1997) and QML, we produce the forecasts on conditional mean and volatility for the interest rate over multiple-step-ahead horizons. The results indicate that the sophisticated models outperform the simpler models in the in-sample data fit, but have a distinct performance in the out-of-sample forecasting. The models equipped with mean reversion can produce better forecasts on conditional means during some period, and the heteroskedasticity variance model with outperform counterparts in volatility forecasting in some periods. The third issue concerns the persistent and massive volatility of short-term interest rates. This part inquires how the realizations on Taiwan short-term interest rates can be best described empirically. Various popular volatility specifications are estimated and tested. The empirical findings reveal that the mean reversion is an important characteristic for the Taiwan interest rates, and the level effect exists. Overall, the GARCH-L model fits well to Taiwan interest rates.

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Doctor of Philosophy(PhD) / This thesis employs survival analysis framework (Allison, 1984) and the Cox’s hazard model (Cox, 1972) to estimate the probability that a credit rating survives in its current grade at a certain forecast horizon. The Cox’s hazard model resolves some significant drawbacks of the conventional estimation approaches. It allows a rigorous testing of non-Markovian behaviours and time heterogeneity in rating dynamics. It accounts for the changes in risk factors over time, and features the time structure of probability survival estimates. The thesis estimates three stratified Cox’s hazard models, including a proportional hazard model, and two dynamic hazard models which account for the changes in macro-economic conditions, and the passage of survival time over rating durations. The estimation of these stratified Cox’s hazard models for downgrades and upgrades offers improved understanding of the impact of rating history in a static and a dynamic estimation framework. The thesis overcomes the computational challenges involved in forming dynamic probability estimates when the standard proportionality assumption of Cox’s model does not hold and when the data sample includes multiple strata. It is found that the probability of rating migrations is a function of rating history and that rating history is more important than the current rating in determining the probability of a rating change. Switching from a static estimation framework to a dynamic estimation framework does not alter the effect of rating history on the rating migration hazard. It is also found that rating history and the current rating interact with time. As the rating duration extends, the main effects of rating history and current rating variables decay. Accounting for this decay has a substantial impact on the risk of rating transitions. Downgrades are more affected by rating history and time interactions than upgrades. To evaluate the predictive performance of rating history, the Brier score (Brier, 1950) and its covariance decomposition (Yates, 1982) were employed. Tests of forecast accuracy suggest that rating history has some predictive power for future rating changes. The findings suggest that an accurate forecast framework is more likely to be constructed if non-Markovian behaviours and time heterogeneity are incorporated into credit risk models.

La prédiction d'un événement clinique à l'aide d'outils pronostiques est une question centrale en oncologie. L'émergence des biomarqueurs mesurés au cours du temps permet de proposer des outils incorporant les données répétées de ces biomarqueurs pour mieux guider le clinicien dans la prise en charge des patients. L'objectif de ce travail est de développer et valider des outils pronostiques dynamiques de rechute de cancer de la prostate, chez des patients traités initialement par radiothérapie externe, en prenant en compte les données répétées du PSA, l'antigène spécifique de la prostate, en plus des facteurs pronostiques standard. Ces outils sont dynamiques car ils peuvent être mis à jour à chaque nouvelle mesure disponible du biomarqueur. Ils sont construits à partir de modèles conjoints pour données longitudinales et de temps d'événement. Le principe de la modélisation conjointe est de décrire l'évolution du biomarqueur à travers un modèle linéaire mixte, décrire le risque d'événement à travers un modèle de survie et lier ces deux processus à travers une structure latente. Deux approches existent, les modèles conjoints à effets aléatoires partagés et les modèles conjoints à classes latentes. Dans un premier travail, nous avons tout d'abord comparé, en terme de qualité d'ajustement et de pouvoir prédictif, des modèles conjoints à effets aléatoires partagés différant par leur forme de dépendance entre le PSA et le risque de rechute clinique. Puis nous avons évalué et comparé ces deux approches de modélisation conjointe. Dans un deuxième travail, nous avons proposé un outil pronostique dynamique différentiel permettant d'évaluer le risque de rechute clinique suivant l'initiation ou non d'un second traitement (un traitement hormonal) au cours du suivi. Dans ces travaux, la validation de l'outil pronostique a été basée sur deux mesures de pouvoir prédictif: le score de Brier et l'entropie croisée pronostique. Dans un troisième travail, nous avons enfin décrit la dynamique des PSA après un second traitement de type hormonal chez des patients traités initialement par une radiothérapie seule. / The prediction of a clinical event with prognostic tools is a central issue in oncology. The emergence of biomarkers measured over time can provide tools incorporating repeated data of these biomarkers to better guide the clinician in the management of patients. The objective of this work is to develop and validate dynamic prognostic tools of recurrence of prostate cancer in patients initially treated by external beam radiation therapy, taking into account the repeated data of PSA, the Prostate-Specific Antigen, in addition to standard prognostic factors. These tools are dynamic because they can be updated at each available new measurement of the biomarker. They are built from joint models for longitudinal and time-to-event data. The principle of joint modelling is to describe the evolution of the biomarker through a linear mixed model, describe the risk of event through a survival model and link these two processes through a latent structure. Two approaches exist, shared random-effect models and joint latent class models. In a first study, we first compared in terms of goodness-of-fit and predictive accuracy shared random-effect models differing in the form of dependency between the PSA and the risk of clinical recurrence. Then we have evaluated and compared these two approaches of joint modelling. In a second study, we proposed a differential dynamic prognostic tool to evaluate the risk of clinical recurrence according to the initiation or not of a second treatment (an hormonal treatment) during the follow-up. In these works, validation of the prognostic tool was based on two measures of predictive accuracy: the Brier score and the prognostic cross-entropy. In a third study, we have described the PSA dynamics after a second treatment (hormonal) in patients initially treated by a radiation therapy alone.

Le nombre croissant d’essais cliniques pour le traitement du cancer a conduit à la standardisation de l’évaluation de la réponse tumorale. Dans les essais cliniques de phase III des cancers avancés, la survie sans progression est souvent appliquée comme un critère de substitution pour la survie globale. Pour les tumeurs solides, la progression est généralement définie par les critères RECIST qui utilisent l’information sur le changement de taille des lésions cibles et les progressions de la maladie non-cible. Malgré leurs limites, les critères RECIST restent l’outil standard pour l’évaluation des traitements. En particulier, la taille tumorale mesurée au cours de temps est utilisée comme variable ponctuelle catégorisée pour identifier l’état d’un patient. L’approche statistique de la modélisation conjointe permet une analyse plus précise des marqueurs de réponse tumorale et de la survie. En outre, les modèles conjoints sont utiles pour les prédictions dynamiques individuelles. Dans ce travail, nous avons proposé d’appliquer un modèle conjoint trivarié pour des données longitudinales (taille tumorale), des évènements récurrents (les progressions de la maladie non-cible) et la survie. En utilisant des mesures de capacité prédictive, nous avons comparé le modèle proposé avec un modèle pour les progressions tumorales, définies selon les critères standards et la survie. Pour un essai clinique randomisé porté sur le cancer colorectal, nous avons trouvé une meilleure capacité prédictive du modèle proposé. Dans la deuxième partie, nous avons développé un logiciel en libre accès pour l’application de l’approche de modélisation conjointe proposée et les prédictions. Enfin, nous avons étendu le modèle à une analyse plus sophistiquée de l’évolution tumorale à l’aide d’un modèle mécaniste. Une équation différentielle ordinaire a été mise en œuvre pour décrire la trajectoire du marqueur biologique en tenant compte les caractéristiques biologiques de la croissance tumorale. Cette nouvelle approche contribue à la recherche clinique sur l’évaluation d’un traitement dans les essais cliniques grâce à une meilleure compréhension de la relation entre la réponse tumorale et la survie. / The increasing number of clinical trials for cancer treatments has led to standardization of guidelines for evaluation of tumor response. In phase III clinical trials of advanced cancer, progression-free survival is often applied as a surrogate endpoint for overall survival (OS). For solid tumors, progression is usually defined using the RECIST criteria that use information on the change of size of target lesions and progressions of non-target disease. The criteria remain the standard tool for treatment evaluation despite their limitations. In particular, repeatedly measured tumor size is used as a pointwise categorized variable to identify a patient’s status. Statistical approach of joint modeling allows for more accurate analysis of the tumor response markers and survival. Moreover, joint models are useful for individual dynamic predictions of death using patient’s history. In this work, we proposed to apply a trivariate joint model for a longitudinal outcome (tumor size), recurrent events (progressions of non-target disease) and survival. Using adapted measures of predictive accuracy we compared the proposed joint model with a model that considered tumor progressions defined within standard criteria and OS. For a randomized clinical trial for colorectal cancer patients, we found better predictive accuracy of the proposed joint model. In the second part, we developed freely available software for application of the proposed joint modeling and dynamic predictions approach. Finally, we extended the model to a more sophisticated analysis of tumor size evolution using a mechanistic model. An ordinary differential equation was implemented to describe the trajectory of the biomarker regarding the biological characteristics of tumor size under a treatment. This new approach contributes to clinical research on treatment evaluation in clinical trials by better understanding of the relationship between the markers of tumor response with OS.

Indiana University-Purdue University Indianapolis (IUPUI) / Law enforcement agencies across the U.S. use maps of crime to inform their practice and make efforts to reduce crime. Hotspot maps using historic crime data can show practitioners concentrated areas of criminal offenses and the types of offenses that have occurred; however, not all of these hotspot crime mapping techniques produce the same results. This study compares three hotspot crime mapping techniques and four crime types using the Predictive Accuracy Index (PAI) to measure the predictive accuracy of these mapping techniques in Marion County, Indiana. Results show that the grid hotspot mapping technique and crimes of robbery are most predictive. Understanding the most effective crime mapping technique will allow law enforcement to better predict and therefore prevent crimes.