RANGE ADAPTIVE PROTON THERAPY FOR PROSTATE CANCER

Purpose: The rapid distal falloff of a proton beam allows for sparing of normal tissues distal to the target. However proton beams that aim directly towards critical structures are avoided due to concerns of range uncertainties, such as CT number conversion and anatomy variations. We propose to eliminate range uncertainty and enable prostate treatment with a single anterior beam by detecting the proton’s range at the prostate-rectal interface and adaptively adjusting the range in vivo and in real-time. Materials and Methods: A prototype device, consisting of an endorectal liquid scintillation detector and dual-inverted Lucite wedges for range compensation, was designed to test the feasibility and accuracy of the technique. Liquid scintillation filled volume was fitted with optical fiber and placed inside the rectum of an anthropomorphic pelvic phantom. Photodiode-generated current signal was generated as a function of proton beam distal depth, and the spatial resolution of this technique was calculated by relating the variance in detecting proton spills to its maximum penetration depth. The relative water-equivalent thickness of the wedges was measured in a water phantom and prospectively tested to determine the accuracy of range corrections. Treatment simulation studies were performed to test the potential dosimetric benefit in sparing the rectum. Results: The spatial resolution of the detector in phantom measurement was 0.5 mm. The precision of the range correction was 0.04 mm. The residual margin to ensure CTV coverage was 1.1 mm. The composite distal margin for 95% treatment confidence was 2.4 mm. Planning studies based on a previously estimated 2mm margin (90% treatment confidence) for 27 patients showed a rectal sparing up to 51% at 70 Gy and 57% at 40 Gy relative to IMRT and bilateral proton treatment. Conclusion: We demonstrated the feasibility of our design. Use of this technique allows for proton treatment using a single anterior beam, significantly reducing the rectal dose.

Outcome-based adaptive randomization for binary data in clinical trials---Compare and contrast

Monte Carlo simulation has been conducted to investigate parameter estimation and hypothesis testing in some well known adaptive randomization procedures. The four urn models studied are Randomized Play-the-Winner (RPW), Randomized Pôlya Urn (RPU), Birth and Death Urn with Immigration (BDUI), and Drop-the-Loses Urn (DL). Two sequential estimation methods, the sequential maximum likelihood estimation (SMLE) and the doubly adaptive biased coin design (DABC), are simulated at three optimal allocation targets that minimize the expected number of failures under the assumption of constant variance of simple difference (RSIHR), relative risk (ORR), and odds ratio (OOR) respectively. Log likelihood ratio test and three Wald-type tests (simple difference, log of relative risk, log of odds ratio) are compared in different adaptive procedures. ^ Simulation results indicates that although RPW is slightly better in assigning more patients to the superior treatment, the DL method is considerably less variable and the test statistics have better normality. When compared with SMLE, DABC has slightly higher overall response rate with lower variance, but has larger bias and variance in parameter estimation. Additionally, the test statistics in SMLE have better normality and lower type I error rate, and the power of hypothesis testing is more comparable with the equal randomization. Usually, RSIHR has the highest power among the 3 optimal allocation ratios. However, the ORR allocation has better power and lower type I error rate when the log of relative risk is the test statistics. The number of expected failures in ORR is smaller than RSIHR. It is also shown that the simple difference of response rates has the worst normality among all 4 test statistics. The power of hypothesis test is always inflated when simple difference is used. On the other hand, the normality of the log likelihood ratio test statistics is robust against the change of adaptive randomization procedures. ^

Apply response adaptive randomization to group sequential with early stopping

Group sequential methods and response adaptive randomization (RAR) procedures have been applied in clinical trials due to economical and ethical considerations. Group sequential methods are able to reduce the average sample size by inducing early stopping, but patients are equally allocated with half of chance to inferior arm. RAR procedures incline to allocate more patients to better arm; however it requires more sample size to obtain a certain power. This study intended to combine these two procedures. We applied the Bayesian decision theory approach to define our group sequential stopping rules and evaluated the operating characteristics under RAR setting. The results showed that Bayesian decision theory method was able to preserve the type I error rate as well as achieve a favorable power; further by comparing with the error spending function method, we concluded that Bayesian decision theory approach was more effective on reducing average sample size.^

Adaptive clinical trial design for targeted therapy development

The development of targeted therapy involve many challenges. Our study will address some of the key issues involved in biomarker identification and clinical trial design. In our study, we propose two biomarker selection methods, and then apply them in two different clinical trial designs for targeted therapy development. In particular, we propose a Bayesian two-step lasso procedure for biomarker selection in the proportional hazards model in Chapter 2. In the first step of this strategy, we use the Bayesian group lasso to identify the important marker groups, wherein each group contains the main effect of a single marker and its interactions with treatments. In the second step, we zoom in to select each individual marker and the interactions between markers and treatments in order to identify prognostic or predictive markers using the Bayesian adaptive lasso. In Chapter 3, we propose a Bayesian two-stage adaptive design for targeted therapy development while implementing the variable selection method given in Chapter 2. In Chapter 4, we proposed an alternate frequentist adaptive randomization strategy for situations where a large number of biomarkers need to be incorporated in the study design. We also propose a new adaptive randomization rule, which takes into account the variations associated with the point estimates of survival times. In all of our designs, we seek to identify the key markers that are either prognostic or predictive with respect to treatment. We are going to use extensive simulation to evaluate the operating characteristics of our methods.^

BAYESIAN STATISTICAL METHODS IN GENE-ENVIRONMENT AND GENE-GENE INTERACTION STUDIES

Complex diseases such as cancer result from multiple genetic changes and environmental exposures. Due to the rapid development of genotyping and sequencing technologies, we are now able to more accurately assess causal effects of many genetic and environmental factors. Genome-wide association studies have been able to localize many causal genetic variants predisposing to certain diseases. However, these studies only explain a small portion of variations in the heritability of diseases. More advanced statistical models are urgently needed to identify and characterize some additional genetic and environmental factors and their interactions, which will enable us to better understand the causes of complex diseases. In the past decade, thanks to the increasing computational capabilities and novel statistical developments, Bayesian methods have been widely applied in the genetics/genomics researches and demonstrating superiority over some regular approaches in certain research areas. Gene-environment and gene-gene interaction studies are among the areas where Bayesian methods may fully exert its functionalities and advantages. This dissertation focuses on developing new Bayesian statistical methods for data analysis with complex gene-environment and gene-gene interactions, as well as extending some existing methods for gene-environment interactions to other related areas. It includes three sections: (1) Deriving the Bayesian variable selection framework for the hierarchical gene-environment and gene-gene interactions; (2) Developing the Bayesian Natural and Orthogonal Interaction (NOIA) models for gene-environment interactions; and (3) extending the applications of two Bayesian statistical methods which were developed for gene-environment interaction studies, to other related types of studies such as adaptive borrowing historical data. We propose a Bayesian hierarchical mixture model framework that allows us to investigate the genetic and environmental effects, gene by gene interactions (epistasis) and gene by environment interactions in the same model. It is well known that, in many practical situations, there exists a natural hierarchical structure between the main effects and interactions in the linear model. Here we propose a model that incorporates this hierarchical structure into the Bayesian mixture model, such that the irrelevant interaction effects can be removed more efficiently, resulting in more robust, parsimonious and powerful models. We evaluate both of the 'strong hierarchical' and 'weak hierarchical' models, which specify that both or one of the main effects between interacting factors must be present for the interactions to be included in the model. The extensive simulation results show that the proposed strong and weak hierarchical mixture models control the proportion of false positive discoveries and yield a powerful approach to identify the predisposing main effects and interactions in the studies with complex gene-environment and gene-gene interactions. We also compare these two models with the 'independent' model that does not impose this hierarchical constraint and observe their superior performances in most of the considered situations. The proposed models are implemented in the real data analysis of gene and environment interactions in the cases of lung cancer and cutaneous melanoma case-control studies. The Bayesian statistical models enjoy the properties of being allowed to incorporate useful prior information in the modeling process. Moreover, the Bayesian mixture model outperforms the multivariate logistic model in terms of the performances on the parameter estimation and variable selection in most cases. Our proposed models hold the hierarchical constraints, that further improve the Bayesian mixture model by reducing the proportion of false positive findings among the identified interactions and successfully identifying the reported associations. This is practically appealing for the study of investigating the causal factors from a moderate number of candidate genetic and environmental factors along with a relatively large number of interactions. The natural and orthogonal interaction (NOIA) models of genetic effects have previously been developed to provide an analysis framework, by which the estimates of effects for a quantitative trait are statistically orthogonal regardless of the existence of Hardy-Weinberg Equilibrium (HWE) within loci. Ma et al. (2012) recently developed a NOIA model for the gene-environment interaction studies and have shown the advantages of using the model for detecting the true main effects and interactions, compared with the usual functional model. In this project, we propose a novel Bayesian statistical model that combines the Bayesian hierarchical mixture model with the NOIA statistical model and the usual functional model. The proposed Bayesian NOIA model demonstrates more power at detecting the non-null effects with higher marginal posterior probabilities. Also, we review two Bayesian statistical models (Bayesian empirical shrinkage-type estimator and Bayesian model averaging), which were developed for the gene-environment interaction studies. Inspired by these Bayesian models, we develop two novel statistical methods that are able to handle the related problems such as borrowing data from historical studies. The proposed methods are analogous to the methods for the gene-environment interactions on behalf of the success on balancing the statistical efficiency and bias in a unified model. By extensive simulation studies, we compare the operating characteristics of the proposed models with the existing models including the hierarchical meta-analysis model. The results show that the proposed approaches adaptively borrow the historical data in a data-driven way. These novel models may have a broad range of statistical applications in both of genetic/genomic and clinical studies.