Browsing by Subject "Bayesian hierarchical modeling"

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    Bayesian Dimension Reduction and Prediction with Multiple Datasets
    (2023-06) Samorodnitsky, Sarah
    Biomedical investigators are increasingly able to collect multiple sources of omics data in pursuit of the understanding of disease pathogenesis. Integrative factorization methods for multi-omic datasets have been developed to reveal latent biological patterns driving variation among the observations. However, few methods can accommodate prediction for clinical or biological outcomes within datasets having this complex structure. In Chapter 2, we propose a framework for dimension reduction and prediction in the context of multi-omic, multi-cohort (bidimensional) datasets. We also extend the oft-used Bayesian variable selection approach, the spike-and-slab prior, to accommodate hierarchical variable selection across multiple regression models. We applied this framework to multi-omic data from the Cancer Genome Atlas to predict overall survival across disparate cancer types. We identified multi-omic biological patterns related to survival that persist across multiple cancers. In Chapter 3, we proposed a Bayesian framework to perform either integrative factorization or simultaneous factorization and prediction, which we term Bayesian Simultaneous Factorization and Prediction (BSFP). BSFP concurrently estimates latent factors driving variation within and across omics datasets while estimating their effects on an outcome, providing a complete framework for uncertainty. We show via simulation the importance of accounting for uncertainty in the estimated factorization within the predictive model and the flexibility of this framework for multiple imputation. We also apply BSFP to metabolomic and proteomic data to predict lung function decline among individuals living with HIV. Finally, in Chapter 4, we extend the framework described in Chapter 3 to accommodate simultaneous factorization and prediction using bidimensional data, i.e. across multiple omics sources and multiple sample cohorts, which we term multi-cohort BSFP, or MCBSFP. We evaluate the performance of this framework in recovering latent variation structures via simulation and we use this model to reanalyze the proteomic and metabolomic data from the study considered in Chapter 3.
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    Bayesian Hierarchical Modeling based on Multi-Source Exchangeability
    (2017-07) Kaizer, Alexander
    Progress in medical practice traditionally takes place over a sequence of clinical studies which are designed to establish clinical efficacy, identify the safety profile, and seek regulatory approval for a novel treatment strategy. These trials in humans can be expensive and present numerous challenges in their implementation. While some challenges may be addressed by the development of innovative trial designs, it may also be advantageous to incorporate supplemental sources of information, which are typically ignored in traditional approaches to analysis. In this dissertation, we introduce Multi-Source Exchangeability Models (MEMs), a general Bayesian hierarchical approach that integrates supplemental data arising from multiple, possibly non-exchangeable, sources into the analysis of a primary source. We first describe the proposed framework and prove some desirable asymptotic properties that show the consistency of posterior estimation. Simulation results illustrate that MEMs incorporate more supplemental information in the presence of homogeneous supplemental sources and exhibit reduced bias in the presence of heterogeneous supplemental sources relative to competing Bayesian hierarchical modeling strategies. Next, we illustrate how MEMs can be used to design a more efficient sequential platform design for Ebola virus disease by sharing information across trial segments. When compared to the standard platform design, we demonstrate that MEMs with adaptive randomization improved power by as much as 51% with limited type-I error inflation. We conclude by extending our work with model averaging to the estimation of multiple mixture distributions in the presence of a hypothesized biological relationship between groups to identify non-compliance in a regulatory tobacco clinical trial. The results of this dissertation illustrate that MEMs yield favorable characteristics across a variety of scenarios and motivates further research to extend the MEM framework to other settings, as well.
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    Hierarchical Bayesian methods for multiple outcomes in mixed treatment comparisons
    (2013-08) Hong, Hwanhee
    Biomedical decision makers confronted with questions about the comparative effectiveness and safety of interventions often wish to combine all sources of data. Such multiple treatment comparisons (MTCs) may or may not include head-to-head randomized controlled trials of the treatments of primary interest, instead relying largely on indirect comparisons (say, trials that separately compare each treatment to placebo). In such settings, hierarchical Bayes-MCMC meta-analytic methods are becoming more popular due to their flexibility and interpretability. Compared to frequentist approaches, Bayesian methods cope better with complex data structures and models, and produce estimates and measures of uncertainty that are generally better at capturing all sources of uncertainty in the data. In addition, the Bayesian approach helps to make sound decisions based on probabilities that each treatment is best overall, through a weighted scoring rule that trades off efficacy and safety. Many randomized clinical trials report multiple outcomes with possible inherent correlations. Moreover, MTC data are typically sparse (though richer than standard meta-analysis data, comparing only two treatments) and researchers often choose study arms based on previous trials. In this dissertation, we summarize existing hierarchical Bayesian methods for MTCs with a single outcome, and introduce novel Bayesian approaches for analyzing multiple outcomes simultaneously, rather than in separate MTC analyses. We incorporate missing data and the correlation structure between outcomes through contrast- and arm-based parameterizations that consider any unobserved treatment arms as missing data to be imputed. We also extend the model to apply to all types of generalized linear model outcomes, such as count or continuous responses, and mixed-type outcomes, such as paired continuous efficacy and binary safety responses. Finally, availability of individual patient-level data (IPD) broadens the scope of MTCs, and enables us to incorporate patient-level clinical characteristics. We close the dissertation by developing arm-based IPD MTC models which offer more straightforward interpretation and application compared to the existing contrast-based IPD MTC models.