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Phase II clinical trials aim to potentially screen out ineffective and identify effective therapies to move forward to randomized phase III trials. Single-arm studies remain the most utilized design in phase II oncology trials, especially in scenarios where a randomized design is simply not practical. Due to concerns regarding excessive toxicity or ineffective new treatment strategies, interim analyses are typically incorporated in the trial, and the choice of statistical methods mainly depends on the type of primary endpoints. For oncology trials, the most common primary objectives in phase II trials include tumor response rate (binary endpoint) and progression disease-free survival (time-to-event endpoint). Interim strategies are well-developed for both endpoints in single-arm phase II trials. The advent of molecular targeted therapies, often with lower toxicity profiles from traditional cytotoxic treatments, has shifted the drug development paradigm into establishing evidence of biological activity, target modulation and pharmacodynamics effects of these therapies in early phase trials. As such, these trials need to address simultaneous evaluation of safety as well as proof-of-concept of biological marker activity or changes in continuous tumor size instead of binary response rates. In this dissertation, we extend a predictive probability design for binary outcomes in the single-arm clinical trial setting and develop two interim designs for continuous endpoints, such as continuous tumor shrinkage or change in a biomarker over time. The two-stage design mainly focuses on the futility stopping strategies, while it also has the capacity of early stopping for efficacy. Both optimal and minimax designs are presented for this two-stage design. The multi-stage design has the flexibility of stopping the trial early either due to futility or efficacy. Due to the intense computation and searching strategy we adopt, only the minimax design is presented for this multi-stage design. The multi-stage design allows for up to 40 interim looks with continuous monitoring possible for large and moderate effect sizes, requiring an overall sample size less than 40. The stopping boundaries for both designs are based on predictive probability with normal likelihood and its conjugated prior distributions, while the design itself satisfies the pre-specified type I and type II error rate constraints. From simulation results, when compared with binary endpoints, both designs well preserve statistical properties across different effect sizes with reduced sample size. We also develop an R package, PPSC, and detail it in chapter four, so that both designs can be freely accessible for use in future phase II clinical trials with the collaborative efforts of biostatisticians. Clinical investigators and biostatisticians have the flexibility to specify the parameters from the hypothesis testing framework, searching ranges of the boundaries for predictive probabilities, the number of interim looks involved and if the continuous monitoring is preferred and so on.

Apresentamos duas abordagens para obter uma densidade de probabilidades para o preço futuro de um ativo: uma densidade preditiva, baseada em um modelo Bayesiano para série de tempo e uma densidade implícita, baseada na fórmula de precificação de opções de Black & Scholes. Considerando o modelo de Black & Scholes, derivamos as condições necessárias para obter a densidade implícita do preço do ativo na data de vencimento. Baseando-­se nas densidades de previsão, comparamos o modelo implícito com a abordagem histórica do modelo Bayesiano. A partir destas densidades, calculamos probabilidades de ordem e tomamos decisões de vender/comprar um ativo. Como exemplo, apresentamos como utilizar estas distribuições para construir uma fórmula de precificação. / We present two different approaches to obtain a probability density function for the stocks future price: a predictive distribution, based on a Bayesian time series model, and the implied distribution, based on Black & Scholes option pricing formula. Considering the Black & Scholes model, we derive the necessary conditions to obtain the implied distribution of the stock price on the exercise date. Based on predictive densities, we compare the market implied model (Black & Scholes) with a historical based approach (Bayesian time series model). After obtaining the density functions, it is simple to evaluate probabilities of one being bigger than the other and to make a decision of selling/buying a stock. Also, as an example, we present how to use these distributions to build an option pricing formula.

Submitted by Alison Vanceto (alison-vanceto@hotmail.com) on 2017-08-28T13:57:07Z No. of bitstreams: 1 DissNLO.pdf: 2139734 bytes, checksum: 9d9000013e5ab1fd3e860be06fc72737 (MD5) / Approved for entry into archive by Ronildo Prado (ronisp@ufscar.br) on 2017-09-06T13:18:03Z (GMT) No. of bitstreams: 1 DissNLO.pdf: 2139734 bytes, checksum: 9d9000013e5ab1fd3e860be06fc72737 (MD5) / Approved for entry into archive by Ronildo Prado (ronisp@ufscar.br) on 2017-09-06T13:18:12Z (GMT) No. of bitstreams: 1 DissNLO.pdf: 2139734 bytes, checksum: 9d9000013e5ab1fd3e860be06fc72737 (MD5) / Made available in DSpace on 2017-09-06T13:28:02Z (GMT). No. of bitstreams: 1 DissNLO.pdf: 2139734 bytes, checksum: 9d9000013e5ab1fd3e860be06fc72737 (MD5) Previous issue date: 2017-06-01 / Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) / We present two different approaches to obtain a probability density function for the stock?s future price: a predictive distribution, based on a Bayesian time series model, and the implied distribution, based on Black & Scholes option pricing formula. Considering the Black & Scholes model, we derive the necessary conditions to obtain the implied distribution of the stock price on the exercise date. Based on predictive densities, we compare the market implied model (Black & Scholes) with a historical based approach (Bayesian time series model). After obtaining the density functions, it is simple to evaluate probabilities of one being bigger than the other and to make a decision of selling/buying a stock. Also, as an example, we present how to use these distributions to build an option pricing formula. / Apresentamos duas abordagens para obter uma densidade de probabilidades para o preço futuro de um ativo: uma densidade preditiva, baseada em um modelo Bayesiano para série de tempo e uma densidade implícita, baseada na fórmula de precificação de opções de Black & Scholes. Considerando o modelo de Black & Scholes, derivamos as condições necessárias para obter a densidade implícita do preço do ativo na data de vencimento. Baseando-se nas densidades de previsão, comparamos o modelo implícito com a abordagem histórica do modelo Bayesiano. A partir destas densidades, calculamos probabilidades de ordem e tomamos decisões de vender/comprar um ativo. Como exemplo, apresentamos como utilizar estas distribuições para construir uma fórmula de precificação.

Apresentamos duas abordagens para obter uma densidade de probabilidades para o preço futuro de um ativo: uma densidade preditiva, baseada em um modelo Bayesiano para série de tempo e uma densidade implícita, baseada na fórmula de precificação de opções de Black & Scholes. Considerando o modelo de Black & Scholes, derivamos as condições necessárias para obter a densidade implícita do preço do ativo na data de vencimento. Baseando-­se nas densidades de previsão, comparamos o modelo implícito com a abordagem histórica do modelo Bayesiano. A partir destas densidades, calculamos probabilidades de ordem e tomamos decisões de vender/comprar um ativo. Como exemplo, apresentamos como utilizar estas distribuições para construir uma fórmula de precificação. / We present two different approaches to obtain a probability density function for the stocks future price: a predictive distribution, based on a Bayesian time series model, and the implied distribution, based on Black & Scholes option pricing formula. Considering the Black & Scholes model, we derive the necessary conditions to obtain the implied distribution of the stock price on the exercise date. Based on predictive densities, we compare the market implied model (Black & Scholes) with a historical based approach (Bayesian time series model). After obtaining the density functions, it is simple to evaluate probabilities of one being bigger than the other and to make a decision of selling/buying a stock. Also, as an example, we present how to use these distributions to build an option pricing formula.

Background: Shifting the healthcare payment system from a volume-based to a value-based model has been a significant effort to improve the quality of care and reduce healthcare costs in the US. In 2018, Massachusetts Medicaid launched Accountable Care Organizations (ACOs) as part of the effort. Constructing, assessing, and risk-adjusting quality measures are integral parts of the reform process. Methods: Using data from the MassHealth Data Warehouse (2016-2019), we assessed the loss of community tenure (CTloss) as a potential quality measure for patients with bipolar, schizophrenia, or other psychotic disorders (BSP). We evaluated various statistical models for predicting CTloss using deviance, Akaike information criterion, Vuong test, squared correlation and observed vs. expected (O/E) ratios. We also used logistic regression to investigate risk factors that impacted medication nonadherence, another quality measure for patients with bipolar disorders (BD). Results: Mean CTloss was 12.1 (±31.0 SD) days in the study population; it varied greatly across ACOs. For risk adjustment modeling, we recommended the zero-inflated Poisson or doubly augmented beta model. The O/E ratio ranged from 0.4 to 1.2, suggesting variation in quality, after adjusting for differences in patient characteristics for which ACOs served as reflected in E. Almost half (47.7%) of BD patients were nonadherent to second-generation antipsychotics. Patient demographics, medical and mental comorbidities, receiving institutional services like those from the Department of Mental Health, homelessness, and neighborhood socioeconomic stress impacted medication nonadherence. Conclusions: Valid quality measures are essential to value-based payment. Heterogeneity implies the need for risk adjustment. The search for a model type is driven by the non-standard distribution of CTloss.