Browsing by Subject "Survival Analysis"

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    Bayesian hierarchical modeling for adaptive incorporation of historical information In clinical trials.
    (2010-08) Hobbs, Brian Paul
    Bayesian clinical trial designs offer the possibility of a substantially reduced sample size, increased statistical power, and reductions in cost and ethical hazard. However when prior and current information conflict, Bayesian methods can lead to higher than expected Type I error, as well as the possibility of a costlier and lengthier trial. We develop several models that allow for the commensurability of the information in the historical and current data to determine how much historical information is used. First, we propose methods for univariate Gaussian data and provide an example analysis of data from two successive colon cancer trials that illustrates a linear models extension of our adaptive borrowing approach. Next, we extend the general method to linear and linear mixed models as well as generalized linear and generalized linear mixed models. We also provide two more sample analyses using the colon cancer data. Finally, we consider the effective historical sample size of our adaptive method for the case when historical data is available only for the concurrent control arm, and propose "optimal" use of new patients in the current trial using an adaptive randomization scheme that is balanced with respect to the amount of incorporated historical information. The approach is then demonstrated using data from a trial comparing antiretroviral strategies in HIV-1-infected persons. Throughout the thesis we present simulation studies that compare frequentist operating characteristics and highlight the advantages of our adaptive borrowing methods.
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    Hierarchical models for combining nonexchangeable sources of survival and functional data
    (2014-08) Murray, Thomas
    Conventional approaches to statistical inference preclude structures that facilitate incorporation of partially informative supplemental information acquired from similar circumstances. Borrowing strength from supplemental data promises to facilitate greater efficiency in the scientific investigative process, but neglecting to account for heterogeneity across the sources of information obscures understanding of the complex underlying mechanisms that produced the primary data, and may lead to biased inference. As such, inference should derive from flexible statistical models that account for inherent uncertainty while favoring the primary information as evidence for between-source heterogeneity arises. We extend existing flexible borrowing methods to settings where the estimation of a curve is of primary interest, and the amount of borrowing reflects congruence in curve shape across sources of information. First, we propose flexible borrowing methods for time-to-event data using a piecewise exponential model construction, wherein we borrow with respect to the a parameterized baseline hazard function. We apply these methods to data assessing time to cardiac revascularization in peritoneal dialysis patients who received a heart stent. Second, we develop a piecewise log-linear hazard model using low rank thin-plate splines to model the baseline hazard and functional covariate effects possibly subject to shape restrictions. We apply these methods to data from a colorectal cancer clinical trial assessing the comparative effectiveness of three treatment regimes. Third, we propose a general methodological framework for borrowing with respect to the shape of an unknown curve that is characterized by a set of parameters. We illustrate these methods with two applications, in liver imaging and colorectal cancer clinical trials. Throughout the thesis, we conduct simulation investigations that assess the properties and advantages of the proposed methods. Last, we summarize and suggest avenues for future work.