Escalonamento com controle de overdose (EWOC-PH, escalation with overdose control proporcional hazards) é um método bayesiano com controle de overdose que estima a dose máxima tolerada (MTD, maximum tolerated dose) assumindo que o tempo que um paciente leva para apresentar toxicidade segue o modelo de riscos proporcionais. Neste trabalho analisamos quais são as consequências em adotarmos um método que se baseia no modelo de riscos proporcionais quando o tempo até toxicidade segue o modelo de chances de sobrevivência proporcionais. A fim de buscar responder se teríamos uma superestimativa ou uma subestimativa da MTD foram feitas simulações em que consideramos dados de chances de sobrevivência proporcionais e aplicação do método EWOC-PH para analisarmos a MTD. Como uma extensão do método EWOC-PH, propomos o método EWOC-POS que assume que os tempos seguem o modelo de chances de sobrevivência proporcionais. / Escalation with overdose control proportional hazards is a Bayesian method with overdose control that estimates the maximum tolerated dose (MTD) assuming that the time a patient takes to show toxicity follows the proportional hazards model. In this work, we analyse the consequences of adopting a method based on the proportional hazard model when the time until toxicity follows the proportional survival model. In order to seek to answer if we would have an overestimate or an underestimate of MTD, simulations were performed in which we considered proportional odds survival data and application of the EWOC-PH method. As an extension of the EWOC-PH method, we propose the EWOC-POS method which assumes that time until toxicity follows the proportional odds survival model.

<p>In drug development clinical trials are designed to investigate whether a new treatment is safe and has the desired effect on the disease in the target patient population. Categorical endpoints, for example different ranking scales or grading of adverse events, are commonly used to measure effects in the trials. </p><p>Pharmacokinetic/Pharmacodynamic (PK/PD) models are used to describe the plasma concentration of a drug over time and its relationship to the effect studied. The models are utilized both in drug development and in discussions with drug regulating authorities. Methods for incorporation of ordered categorical data in PK/PD models were studied using a non-linear mixed effects modelling approach as implemented in the software NONMEM. The traditionally used proportional odds model was used for analysis of a 6-grade sedation scale in acute stroke patients and for analysis of a T-cell receptor expression in patients with Multiple Sclerosis, where the results also were compared with an analysis of the data on a continuous scale. Modifications of the proportional odds model were developed to enable analysis of a spontaneously reported side-effect and to analyze situations where the scale used is heterogeneous or where the drug affects the different scores in the scale in a non-proportional way. The new models were compared with the proportional odds model and were shown to give better predictive performances in the analyzed situations. </p><p>The results in this thesis show that categorical data obtained in clinical trials with different design and different categorical endpoints successfully can be incorporated in PK/PD models. The models developed can also be applied to analyses of other ordered categorical scales than those presented.</p>

Effects of drugs are in clinical trials often measured on categorical scales. These measurements are increasingly being analyzed using mixed-effects logistic regression. However, the experience with such analyzes is limited and only a few models are used. The aim of this thesis was to investigate the performance and improve the use of models and methods for mixed-effects categorical data analysis. The Laplacian method was shown to produce biased parameter estimates if (i) the data variability is large or (ii) the distribution of the responses is skewed. Two solutions are suggested; the Gaussian quadrature method and the back-step method. Two assumptions made with the proportional odds model have also been investigated. The assumption with proportional odds for all categories was shown to be unsuitable for analysis of data arising from a ranking scale of effects with several underlying causes. An alternative model, the differential odds model, was developed and shown to be an improvement, in regard to statistical significance as well as predictive performance, over the proportional odds model for such data. The appropriateness of the likelihood ratio test was investigated for an analysis where dependence between observations is ignored, i.e. performing the analysis using the proportional odds model. The type I error was found to be affected; thus assessing the actual critical value is prudent in order to verify the statistical significance level. An alternative approach is to use a Markov model, in which dependence between observations is incorporated. In the case of polychotomous data such model may involve considerable complexity and thus, a strategy for the reduction of the time-consuming model building with the Markov model and sleep data is presented. This thesis will hopefully contribute to a more confident use of models for categorical data analysis within the area of pharmacokinetic and pharmacodynamic modelling in the future.

In drug development clinical trials are designed to investigate whether a new treatment is safe and has the desired effect on the disease in the target patient population. Categorical endpoints, for example different ranking scales or grading of adverse events, are commonly used to measure effects in the trials. Pharmacokinetic/Pharmacodynamic (PK/PD) models are used to describe the plasma concentration of a drug over time and its relationship to the effect studied. The models are utilized both in drug development and in discussions with drug regulating authorities. Methods for incorporation of ordered categorical data in PK/PD models were studied using a non-linear mixed effects modelling approach as implemented in the software NONMEM. The traditionally used proportional odds model was used for analysis of a 6-grade sedation scale in acute stroke patients and for analysis of a T-cell receptor expression in patients with Multiple Sclerosis, where the results also were compared with an analysis of the data on a continuous scale. Modifications of the proportional odds model were developed to enable analysis of a spontaneously reported side-effect and to analyze situations where the scale used is heterogeneous or where the drug affects the different scores in the scale in a non-proportional way. The new models were compared with the proportional odds model and were shown to give better predictive performances in the analyzed situations. The results in this thesis show that categorical data obtained in clinical trials with different design and different categorical endpoints successfully can be incorporated in PK/PD models. The models developed can also be applied to analyses of other ordered categorical scales than those presented.

<p>This dissertation investigates whether dual credit students' academic performance in subsequent university courses is comparable to that of non-dual-credit students. The study uses data from a Midwest regional public university over a ten-year period and employs propensity score matching and proportional odds ordinal logistic regression to create balanced comparison groups and analyze the results. The findings indicate that students who completed the prerequisite course as dual credit have similar grades in subsequent university courses as those who completed the prerequisite course as a university student. The study also identifies significant predictors of academic performance in subsequent university courses, such as sex, historically underserved groups status, high school GPA, and course subject, regardless of dual credit status. However, first-generation status, SAT scores, and the time between courses are not statistically significant predictors. These results suggest that dual credit students are as prepared for subsequent university courses as non-dual-credit students. Nevertheless, academic outcomes differ based on certain factors, which should be considered when designing student success initiatives and allocating resources.</p>

L’objectif des essais de phase I en oncologie est d’identifier la dose maximale tolérée (DMT). Le schéma « 3+3 » nécessite d’interrompre les inclusions en attendant l’évaluation d’une cohorte de trois patients pour définir la dose à attribuer aux patients suivants. Les investigateurs d’oncologie pédiatrique ont proposé l’adaptation Rolling 6 pour éviter cette suspension temporaire des inclusions. Dans une étude de simulation, nous avons montré qu’un schéma adaptatif avec attribution des doses basées sur un modèle statistique permettait de pallier ce problème, et identifiait plus fréquemment la DMT. Néanmoins ces trois schémas restent limités pour identifier la DMT, notamment du fait que le critère de jugement est un critère binaire, la survenue de toxicité dose-limitante sur un cycle de traitement. Nous avons proposé un nouveau schéma adaptatif utilisant les données ordinales répétées de toxicité sur l’ensemble des cycles de traitement. La dose à identifier est celle associée au taux de toxicité grave maximal par cycle que l’on juge tolérable. Le grade maximal de toxicité par cycle de traitement, en 3 catégories (grave / modéré / nul), a été modélisé par le modèle mixte à cotes proportionnelles. Le modèle est performant à la fois pour détecter un effet cumulé dans le temps et améliore l’identification de la dose cible, sans risque majoré de toxicité, et sans rallonger la durée des essais. Nous avons aussi étudié l’intérêt de ce modèle ordinal par rapport à un modèle logistique mixte plus parcimonieux. Ces modèles pour données longitudinales devraient être plus souvent utilisés pour l’analyse des essais de phase I étant donné leur pertinence et la faisabilité de leur implémentation. / Phase I dose-finding trials aim at identifying the maximum tolerated dose (MTD). The “3+3” design requires an interruption of enrolment while the evaluation of the previous three patients is pending. In pediatric oncology, investigators proposed the Rolling 6 design to allow for a more continuous enrollment. In a simulation study, we showed that an adaptive dose-finding design, with dose allocation guided by a statistical model not only minimizes accrual suspension as with the rolling 6, and but also led to identify more frequently the MTD. However, the performance of these designs in terms of correct identification of the MTD is limited by the binomial variability of the main outcome: the occurrence of dose-limiting toxicity over the first cycle of treatment. We have then proposed a new adaptive design using repeated ordinal data of toxicities experienced during all the cycles of treatment. We aim at identifying the dose associated with a specified tolerable probability of severe toxicity per cycle. The outcome was expressed as the worst toxicity experienced, in three categories (severe / moderate / no toxicity), repeated at each treatment cycle. It was modeled through a proportional odds mixed model. This model enables to seek for cumulated toxicity with time, and to increase the ability to identify the targeted dose, with no increased risk of toxicity, and without delaying study completion. We also compared this ordinal model to a more parsimonious logistic mixed model.Because of their applicability and efficiency, those models for longitudinal data should be more often used in phase I dose-finding trials.

No description available.

Cure rate models, introduced by Boag (1949), are very commonly used while modelling lifetime data involving long time survivors. Applications of cure rate models can be seen in biomedical science, industrial reliability, finance, manufacturing, demography and criminology. In this thesis, cure rate models are discussed under a competing cause scenario, with the assumption of proportional odds (PO) lifetime distributions for the susceptibles, and statistical inferential methods are then developed based on right-censored data. In Chapter 2, a flexible cure rate model is discussed by assuming the number of competing causes for the event of interest following the Conway-Maxwell (COM) Poisson distribution, and their corresponding lifetimes of non-cured or susceptible individuals can be described by PO model. This provides a natural extension of the work of Gu et al. (2011) who had considered a geometric number of competing causes. Under right censoring, maximum likelihood estimators (MLEs) are obtained by the use of expectation-maximization (EM) algorithm. An extensive Monte Carlo simulation study is carried out for various scenarios, and model discrimination between some well-known cure models like geometric, Poisson and Bernoulli is also examined. The goodness-of-fit and model diagnostics of the model are also discussed. A cutaneous melanoma dataset example is used to illustrate the models as well as the inferential methods. Next, in Chapter 3, the destructive cure rate models, introduced by Rodrigues et al. (2011), are discussed under the PO assumption. Here, the initial number of competing causes is modelled by a weighted Poisson distribution with special focus on exponentially weighted Poisson, length-biased Poisson and negative binomial distributions. Then, a damage distribution is introduced for the number of initial causes which do not get destroyed. An EM-type algorithm for computing the MLEs is developed. An extensive simulation study is carried out for various scenarios, and model discrimination between the three weighted Poisson distributions is also examined. All the models and methods of estimation are evaluated through a simulation study. A cutaneous melanoma dataset example is used to illustrate the models as well as the inferential methods. In Chapter 4, frailty cure rate models are discussed under a gamma frailty wherein the initial number of competing causes is described by a Conway-Maxwell (COM) Poisson distribution in which the lifetimes of non-cured individuals can be described by PO model. The detailed steps of the EM algorithm are then developed for this model and an extensive simulation study is carried out to evaluate the performance of the proposed model and the estimation method. A cutaneous melanoma dataset as well as a simulated data are used for illustrative purposes. Finally, Chapter 5 outlines the work carried out in the thesis and also suggests some problems of further research interest. / Thesis / Doctor of Philosophy (PhD)

近來地理資訊系統(GIS)之資料庫受到不同領域的統計學家廣泛的研究，以期建立及分析可描述空間聚集效應及變異之模型，而描述空間相關存活資料之統計模式為公共衛生及流行病學上新興的研究議題。本文擬建立多維度半參數的貝氏階層模型，並結合空間及非空間隨機效應以描述存活資料中的空間變異。此模式將利用多變量條件自回歸(MCAR)模型以檢驗在不同地理區域中是否存有空間聚集效應。而基準風險函數之生成為分析貝氏半參數階層模型的重要步驟，本研究將利用混合Polya樹之方式生成基準風險函數。美國國家癌症研究院之「流行病監測及最終結果」(Surveillance Epidemiology and End Results, SEER)資料庫為目前美國最完整的癌症病人長期追蹤資料，包含癌症病人存活狀況、多重癌症史、居住地區及其他分析所需之個人資料。本文將自此資料庫擷取美國愛荷華州之癌症病人資料為例作實證分析，並以貝氏統計分析中常用之模型比較標準如條件預測指標(CPO)、平均對數擬邊際概似函數值(ALMPL)、離差訊息準則(DIC)分別測試其可靠度。 / The databases of Geographic Information System (GIS) have gained attention among different fields of statisticians to develop and analyze models which account for spatial clustering and variation. There is an emerging interest in modeling spatially correlated survival data in public health and epidemiologic studies. In this article, we develop Bayesian multivariate semiparametric hierarchical models to incorporate both spatially correlated and uncorrelated frailties to answer the question of spatial variation in the survival patterns, and we use multivariate conditionally autoregressive (MCAR) model to detect that whether there exists the spatial cluster across different areas. The baseline hazard function will be modeled semiparametrically using mixtures of finite Polya trees. The SEER (Surveillance Epidemiology and End Results) database from the National Cancer Institute (NCI) provides comprehensive cancer data about patient’s survival time, regional information, and others demographic information. We implement our Bayesian hierarchical spatial models on Iowa cancer data extracted from SEER database. We illustrate how to compute the conditional predictive ordinate (CPO), the average log-marginal pseudo-likelihood (ALMPL), and deviance information criterion (DIC), which are Bayesian criterions for model checking and comparison among competing models.