Browsing by Subject "Bayesian method"

Now showing 1 - 4 of 4
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    A Bayesian adaptive marker‐stratified design for molecularly targeted agents with customized hierarchical modeling
    (Wiley, 2019-07) Zang, Yong; Guo, Beibei; Han, Yan; Cao, Sha; Zhang, Chi; Biostatistics, School of Public Health
    It is well known that the treatment effect of a molecularly targeted agent (MTA) may vary dramatically, depending on each patient's biomarker profile. Therefore, for a clinical trial evaluating MTA, it is more reasonable to evaluate its treatment effect within different marker subgroups rather than evaluating the average treatment effect for the overall population. The marker‐stratified design (MSD) provides a useful tool to evaluate the subgroup treatment effects of MTAs. Under the Bayesian framework, the beta‐binomial model is conventionally used under the MSD to estimate the response rate and test the hypothesis. However, this conventional model ignores the fact that the biomarker used in the MSD is, in general, predictive only for the MTA. The response rates for the standard treatment can be approximately consistent across different subgroups stratified by the biomarker. In this paper, we proposed a Bayesian hierarchical model incorporating this biomarker information into consideration. The proposed model uses a hierarchical prior to borrow strength across different subgroups of patients receiving the standard treatment and, therefore, improve the efficiency of the design. Prior informativeness is determined by solving a “customized” equation reflecting the physician's professional opinion. We developed a Bayesian adaptive design based on the proposed hierarchical model to guide the treatment allocation and test the subgroup treatment effect as well as the predictive marker effect. Simulation studies and a real trial application demonstrate that the proposed design yields desirable operating characteristics and outperforms the existing designs.
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    A Bayesian Approach to Recovering Missing Component Dependence for System Reliability Prediction via Synergy Between Physics and Data
    (ASME, 2021-11) Li, Huiru; Du, Xiaoping; Mechanical and Energy Engineering, School of Engineering and Technology
    Predicting system reliability is often a core task in systems design. System reliability depends on component reliability and dependence of components. Component reliability can be predicted with a physics-based approach if the associated physical models are available. If the models do not exist, component reliability may be estimated from data. When both types of components coexist, their dependence is often unknown, and the component states are therefore assumed independent by the traditional method, which can result in a large error. This work proposes a new system reliability method to recover the missing component dependence, thereby leading to a more accurate estimate of the joint probability density (PDF) of all the component states. The method works for series systems whose load is shared by its components that may fail due to excessive loading. For components without physical models available, the load data are recorded upon failure, and equivalent physical models are created; the model parameters are estimated by the proposed Bayesian approach. Then models of all component states become available, and the dependence of component states, as well as their joint PDF, can be estimated. Four examples are used to evaluate the proposed method, and the results indicate that the proposed method can produce more accurate predictions of system reliability than the traditional method that assumes independent component states.
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    Joint models for longitudinal and survival data
    (2014-07-11) Yang, Lili; Gao, Sujuan; Yu, Menggang; Tu, Wanzhu; Callahan, Christopher M.; Zollinger, Terrell
    Epidemiologic and clinical studies routinely collect longitudinal measures of multiple outcomes. These longitudinal outcomes can be used to establish the temporal order of relevant biological processes and their association with the onset of clinical symptoms. In the first part of this thesis, we proposed to use bivariate change point models for two longitudinal outcomes with a focus on estimating the correlation between the two change points. We adopted a Bayesian approach for parameter estimation and inference. In the second part, we considered the situation when time-to-event outcome is also collected along with multiple longitudinal biomarkers measured until the occurrence of the event or censoring. Joint models for longitudinal and time-to-event data can be used to estimate the association between the characteristics of the longitudinal measures over time and survival time. We developed a maximum-likelihood method to joint model multiple longitudinal biomarkers and a time-to-event outcome. In addition, we focused on predicting conditional survival probabilities and evaluating the predictive accuracy of multiple longitudinal biomarkers in the joint modeling framework. We assessed the performance of the proposed methods in simulation studies and applied the new methods to data sets from two cohort studies.
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    Recovering Missing Component Dependence for System Reliability Prediction via Synergy between Physics and Data
    (American Society of Mechanical Engineers, 2021) Li, Huiru; Du, Xiaoping; Mechanical and Energy Engineering, Purdue School of Engineering and Technology
    Predicting system reliability is often a core task in systems design. System reliability depends on component reliability and dependence of components. Component reliability can be predicted with a physics-based approach if the associated physical models are available. If the models do not exist, component reliability may be estimated from data. When both types of components coexist, their dependence is often unknown, and therefore, the component states are assumed independent by the traditional method, which can result in a large error. This study proposes a new system reliability method to recover the missing component dependence, thereby leading to a more accurate estimate of the joint probability density function (PDF) of all the component states. The method works for series systems whose load is shared by its components that may fail due to excessive loading. For components without physical models available, the load data are recorded upon failure, and equivalent physical models are created; the model parameters are estimated by the proposed Bayesian approach. Then models of all component states become available, and the dependence of component states, as well as their joint PDF, can be estimated. Four examples are used to evaluate the proposed method, and the results indicate that the method can produce more accurate predictions of system reliability than the traditional method that assumes independent component states.