Ce travail a eu pour objectif de proposer des méthodes statistiques pour évaluer et comparer les capacités prédictives de divers outils pronostiques. Le Brier score et principalement les courbes ROC dépendant du temps ont été étudiés. Tous deux dépendent d'un temps t, représentant un horizon de prédiction. Motivé par les applications à la prédiction de la démence et des données de cohortes de personnes âgées, ce travail s'est spécifiquement intéressé à des procédures d'inférence en présence de données censurées et de risques concurrents. Le risque concurrent de décès sans démence est en effet important lorsque l'on s'intéresse à prédire une démence chez des sujets âgés. Pour obtenir des estimateurs consistants, nous avons utilisé une méthode appelée “Inverse Probability of Censoring Weighting” (IPCW). Dans un premier travail, nous montrons qu'elle permet d'étendre simplement les estimateurs pour données non censurées et de prendre en compte une censure éventuellement dépendante de l'outil pronostique étudié. Dans un second travail, nous proposons des adaptations pour les situations de risques concurrents. Quelques résultats asymptotiques sont donnés et permettent de dériver des régions de confiance et des tests de comparaison d'outils pronostiques. Enfin, un troisième travail s'intéresse à la comparaison d'outils pronostiques dynamiques, basés sur des marqueurs longitudinaux. Les mesures de capacités pronostiques dépendent ici à la fois du temps s auquel on fait la prédiction et de l'horizon de prédiction t. Des courbes de capacités pronostiques selon s sont proposées pour leur évaluation et quelques procédures d'inférence sont développées, permettant de construire des régions de confiance et des tests de comparaison de ces courbes. L'application des méthodes proposées a permis de montrer que des outils prédictifs de la démence basés sur des tests cognitifs ou des mesures répétées de ces tests ont de bonnes capacités pronostiques. / The objective of this work is to develop statistical methods that can be used to evaluate and compare the prognostic ability of different prognostic tools. To measure prognostic ability, mainly the time-dependent ROC curve is studied and also the Brier score for a prediction horizon t. Motivated by applications where the aim is to predict the risk of dementia in cohort data of elderly people, this work focuses on inference procedures in the presence of right censoring and competing risks. In elderly populations death is a highly prevalent competing risk. To define consistent estimators of the prediction ability measures, we use the inverse probability of censoring weighting (IPCW) approach. In our first work, we show that the IPCW approach provides consistent estimators of prediction ability based on right censored data, even when the censoring distribution is marker-dependent. In our second work, we adapt the estimators to settings with competing risks. Asymptotic results are provided and we derive confidence regions and tests for comparing different prognostic tools. Finally, in a third work we focus on comparing dynamic prognostic tools which use information from repeated marker measurements to predict future events. The prognostic ability measures now depend on both the time s at which predictions are made and on the prediction horizon t. Curves of the prognostic ability as a function of s are developed for the evaluation of dynamic risk predictions. Inference procedures are adapted and so are confidence regions and tests to compare the curves. The applications of the proposed methods to cohort data show that the prognostic tools that use cognitive tests, or repeated measurements of cognitive tests, have high prognostic abilities.

No description available.

Measures of epistemic utility are used by formal epistemologists to make determinations of epistemic betterness among cognitive states. The Brier rule is the most popular choice (by far) among formal epistemologists for such a measure. In this paper, however, we show that the Brier rule is sometimes seriously wrong about whether one cognitive state is epistemically better than another. In particular, there are cases where an agent gets evidence that definitively eliminates a false hypothesis (and the probabilities assigned to the other hypotheses stay in the same ratios), but where the Brier rule says that things have become epistemically worse. Along the way to this 'elimination experiment' counter-example to the Brier rule as a measure of epistemic utility, we identify several useful monotonicity principles for epistemic betterness. We also reply to several potential objections to this counter-example.

There are many different types of non-alcoholic beverages (NAB) available in the United States today compared to a decade ago. Additionally, the needs of beverage consumers have evolved over the years centering attention on functionality and health dimensions. These trends in volume of consumption are a testament to the growth in the NAB industry. Our study pertains to ten NAB categories. We developed and employed a unique cross-sectional and time-series data set based on Nielsen Homescan data associated with household purchases of NAB from 1998 through 2003. First, we considered demographic and economic profiling of the consumption of NAB in a two-stage model. Race, region, age and presence of children and gender of household head were the most important factors affecting the choice and level of consumption. Second, we used expectation-prediction success tables, calibration, resolution, the Brier score and the Yates partition of the Brier score to measure the accuracy of predictions generated from qualitative choice models used to model the purchase decision of NAB by U.S. households. The Yates partition of the Brier score outperformed all other measures. Third, we modeled demand interrelationships, dynamics and habits of NAB consumption estimating own-price, cross-price and expenditure elasticities. The Quadratic Almost Ideal Demand System, the synthetic Barten model and the State Adjustment Model were used. Soft drinks were substitutes and fruit juices were complements for most of non-alcoholic beverages. Investigation of a proposed tax on sugar-sweetened beverages revealed the importance of centering attention not only to direct effects but also to indirect effects of taxes on beverage consumption. Finally, we investigated factors affecting nutritional contributions derived from consumption of NAB. Also, we ascertained the impact of the USDA year 2000 Dietary Guidelines for Americans associated with the consumption of NAB. Significant factors affecting caloric and nutrient intake from NAB were price, employment status of household head, region, race, presence of children and the gender of household food manager. Furthermore, we found that USDA nutrition intervention program was successful in reducing caloric and caffeine intake from consumption of NAB. The away-from-home intake of beverages and potential impacts of NAB advertising are not captured in our work. In future work, we plan to address these limitations.

This dissertation addresses: 1) the reliability of El Niño Southern Oscillation (ENSO) forecasts generated by the International Research Institute for Climate and Society (IRI) of Columbia University; 2) estimation of parameters of Mexican crop demand; and 3) the potential impacts of climate change on Mexican agriculture. The IRI ENSO forecasts were evaluated using prequential analysis, with calibration and scoring rules. Calibration tests and the Yates’ decomposition measures of the Brier score suggest that the IRI ENSO forecasts are improving in reliability and skill, showing a learning by doing behavior, i.e., these IRI ENSO forecasts show improved ability to predict the ENSO phases that really happen. In terms of estimation of the parameters of Mexican crop demand, an LA/AIDS model was used but the results were not very satisfactory with statistical tests rejecting homogeneity and symmetry. Furthermore, the estimated uncompensated price and income elasticities were found to be located in the tail regions of the Monte Carlo simulated density functions, showing poor validation of the initial estimates under similar economic (price and consumption) circumstances. Finally, in terms of the potential impacts that climate change has on Mexican agriculture, two 2050 climate change scenarios were examined. The central result indicates that Mexico benefits from climate change under the IPCC ensemble results for the B1 scenario and would experience welfare losses under the ensemble results for the A2 scenario. Moreover, dryland hectareage would decrease and would be replaced by irrigated areas. Finally, producer’s net income was found to decrease at the national level under both climate change scenarios. The results were generated using a mathematical programming sector model that was updated for the study.

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.