Quantifying uncertainty in cost effectiveness analyses

This study compared four alternative approaches (Taylor, Fieller, percentile bootstrap, and bias-corrected bootstrap methods) to estimating confidence intervals (CIs) around cost-effectiveness (CE) ratio. The study consisted of two components: (1) Monte Carlo simulation was conducted to identify characteristics of hypothetical cost-effectiveness data sets which might lead one CI estimation technique to outperform another. These results were matched to the characteristics of an (2) extant data set derived from the National AIDS Demonstration Research (NADR) project. The methods were used to calculate (CIs) for data set. These results were then compared. The main performance criterion in the simulation study was the percentage of times the estimated (CIs) contained the “true” CE. A secondary criterion was the average width of the confidence intervals. For the bootstrap methods, bias was estimated. ^ Simulation results for Taylor and Fieller methods indicated that the CIs estimated using the Taylor series method contained the true CE more often than did those obtained using the Fieller method, but the opposite was true when the correlation was positive and the CV of effectiveness was high for each value of CV of costs. Similarly, the CIs obtained by applying the Taylor series method to the NADR data set were wider than those obtained using the Fieller method for positive correlation values and for values for which the CV of effectiveness were not equal to 30% for each value of the CV of costs. ^ The general trend for the bootstrap methods was that the percentage of times the true CE ratio was contained in CIs was higher for the percentile method for higher values of the CV of effectiveness, given the correlation between average costs and effects and the CV of effectiveness. The results for the data set indicated that the bias corrected CIs were wider than the percentile method CIs. This result was in accordance with the prediction derived from the simulation experiment. ^ Generally, the bootstrap methods are more favorable for parameter specifications investigated in this study. However, the Taylor method is preferred for low CV of effect, and the percentile method is more favorable for higher CV of effect. ^

Application of stellar photometry to the analysis of microarray images

Improvements in the analysis of microarray images are critical for accurately quantifying gene expression levels. The acquisition of accurate spot intensities directly influences the results and interpretation of statistical analyses. This dissertation discusses the implementation of a novel approach to the analysis of cDNA microarray images. We use a stellar photometric model, the Moffat function, to quantify microarray spots from nylon microarray images. The inherent flexibility of the Moffat shape model makes it ideal for quantifying microarray spots. We apply our novel approach to a Wilms' tumor microarray study and compare our results with a fixed-circle segmentation approach for spot quantification. Our results suggest that different spot feature extraction methods can have an impact on the ability of statistical methods to identify differentially expressed genes. We also used the Moffat function to simulate a series of microarray images under various experimental conditions. These simulations were used to validate the performance of various statistical methods for identifying differentially expressed genes. Our simulation results indicate that tests taking into account the dependency between mean spot intensity and variance estimation, such as the smoothened t-test, can better identify differentially expressed genes, especially when the number of replicates and mean fold change are low. The analysis of the simulations also showed that overall, a rank sum test (Mann-Whitney) performed well at identifying differentially expressed genes. Previous work has suggested the strengths of nonparametric approaches for identifying differentially expressed genes. We also show that multivariate approaches, such as hierarchical and k-means cluster analysis along with principal components analysis, are only effective at classifying samples when replicate numbers and mean fold change are high. Finally, we show how our stellar shape model approach can be extended to the analysis of 2D-gel images by adapting the Moffat function to take into account the elliptical nature of spots in such images. Our results indicate that stellar shape models offer a previously unexplored approach for the quantification of 2D-gel spots. ^

Bayesian doubly optimal group sequential designs for randomized clinical trials

When conducting a randomized comparative clinical trial, ethical, scientific or economic considerations often motivate the use of interim decision rules after successive groups of patients have been treated. These decisions may pertain to the comparative efficacy or safety of the treatments under study, cost considerations, the desire to accelerate the drug evaluation process, or the likelihood of therapeutic benefit for future patients. At the time of each interim decision, an important question is whether patient enrollment should continue or be terminated; either due to a high probability that one treatment is superior to the other, or a low probability that the experimental treatment will ultimately prove to be superior. The use of frequentist group sequential decision rules has become routine in the conduct of phase III clinical trials. In this dissertation, we will present a new Bayesian decision-theoretic approach to the problem of designing a randomized group sequential clinical trial, focusing on two-arm trials with time-to-failure outcomes. Forward simulation is used to obtain optimal decision boundaries for each of a set of possible models. At each interim analysis, we use Bayesian model selection to adaptively choose the model having the largest posterior probability of being correct, and we then make the interim decision based on the boundaries that are optimal under the chosen model. We provide a simulation study to compare this method, which we call Bayesian Doubly Optimal Group Sequential (BDOGS), to corresponding frequentist designs using either O'Brien-Fleming (OF) or Pocock boundaries, as obtained from EaSt 2000. Our simulation results show that, over a wide variety of different cases, BDOGS either performs at least as well as both OF and Pocock, or on average provides a much smaller trial. ^

A coalescent analysis for modeling the mutation process in colorectal cancer

Colorectal cancer is the forth most common diagnosed cancer in the United States. Every year about a hundred forty-seven thousand people will be diagnosed with colorectal cancer and fifty-six thousand people lose their lives due to this disease. Most of the hereditary nonpolyposis colorectal cancer (HNPCC) and 12% of the sporadic colorectal cancer show microsatellite instability. Colorectal cancer is a multistep progressive disease. It starts from a mutation in a normal colorectal cell and grows into a clone of cells that further accumulates mutations and finally develops into a malignant tumor. In terms of molecular evolution, the process of colorectal tumor progression represents the acquisition of sequential mutations. ^ Clinical studies use biomarkers such as microsatellite or single nucleotide polymorphisms (SNPs) to study mutation frequencies in colorectal cancer. Microsatellite data obtained from single genome equivalent PCR or small pool PCR can be used to infer tumor progression. Since tumor progression is similar to population evolution, we used an approach known as coalescent, which is well established in population genetics, to analyze this type of data. Coalescent theory has been known to infer the sample's evolutionary path through the analysis of microsatellite data. ^ The simulation results indicate that the constant population size pattern and the rapid tumor growth pattern have different genetic polymorphic patterns. The simulation results were compared with experimental data collected from HNPCC patients. The preliminary result shows the mutation rate in 6 HNPCC patients range from 0.001 to 0.01. The patients' polymorphic patterns are similar to the constant population size pattern which implies the tumor progression is through multilineage persistence instead of clonal sequential evolution. The results should be further verified using a larger dataset. ^

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. ^

On Bayesian seamless phase I-II designs

Early phase clinical trial designs have long been the focus of interest for clinicians and statisticians working in oncology field. There are several standard phse I and phase II designs that have been widely-implemented in medical practice. For phase I design, the most commonly used methods are 3+3 and CRM. A newly-developed Bayesian model-based mTPI design has now been used by an increasing number of hospitals and pharmaceutical companies. The advantages and disadvantages of these three top phase I designs have been discussed in my work here and their performances were compared using simulated data. It was shown that mTPI design exhibited superior performance in most scenarios in comparison with 3+3 and CRM designs. ^ The next major part of my work is proposing an innovative seamless phase I/II design that allows clinicians to conduct phase I and phase II clinical trials simultaneously. Bayesian framework was implemented throughout the whole design. The phase I portion of the design adopts mTPI method, with the addition of futility rule which monitors the efficacy performance of the tested drugs. Dose graduation rules were proposed in this design to allow doses move forward from phase I portion of the study to phase II portion without interrupting the ongoing phase I dose-finding schema. Once a dose graduated to phase II, adaptive randomization was used to randomly allocated patients into different treatment arms, with the intention of more patients being assigned to receive more promising dose(s). Again simulations were performed to compare the performance of this innovative phase I/II design with a recently published phase I/II design, together with the conventional phase I and phase II designs. The simulation results indicated that the seamless phase I/II design outperform the other two competing methods in most scenarios, with superior trial power and the fact that it requires smaller sample size. It also significantly reduces the overall study time. ^ Similar to other early phase clinical trial designs, the proposed seamless phase I/II design requires that the efficacy and safety outcomes being able to be observed in a short time frame. This limitation can be overcome by using validated surrogate marker for the efficacy and safety endpoints.^

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.