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theses

In recent years, a new information combining method that combines confidence distributions has been demonstrated as a powerful statistical inferential tool. One can draw most types of frequentist inference based on confidence distributions (Singh et al., 2007). The fact that a confidence distribution contains a wealth of information can be leveraged for synthesizing information from multiple studies (Singh et al., 2005). Xie et al. (2012) showed that by applying appropriate recipes when combining data, the confidence distribution approach (hereinafter referred to as the CD approach) can subsume most of the classical meta-analysis methods within a unified meta-analysis framework. For a comprehensive review of the CD approach and recent developments, see Xie and Singh (2013). This dissertation extends the existing meta-analysis methods via combining confidence distributions to overcome two challenges. First, most of the existing data situations for which the CD approach has been examined have been to combine continuous data. Therefore, we demonstrate a new CD method for discrete data and apply it to combine 2 x 2 tables from disparate sources. Second, as a major extension of the recent efforts on drawing joint inference for multiple related parameters from di recent studies through combining multivariate confidence distributions (Liu et al., 2015; Yang et al., 2014), we propose a CD based three-stage synthesis method to combine 13 parameters from individual participant level data of 14 clinical studies. The rest part of this dissertation focuses on how to apply the CD approach to make exact inferences on 2 x 2 tables that may involve rare events. While most conventional methods rely on large sample approximations, many 2 x 2 tables derived in medical fields may have very limited total sample sizes, in which case the use of asymptotic based approaches may lead to misleading conclusions. In addition, we also consider the situations where study total sample size is large, but with zero observed events in one or both treatment arms in a 2 x 2 table. This can happen in drug safety studies where zero or rare cases of adverse effects are observed in large samples of patients. The new CD method provides an exact inference and does not rely on large sample approximations. In addition, by incorporating prior information, the proposed CD approach can deal with zero events more systematically in contrast to a typical approach adding a small constant (e.g., 0.5) to empty cells. This new approach accounts for various data sampling schemes and can readily be generalized to most of the risk metrics used for 2x2 tables. The second part of this dissertation focuses on how to synthesize multiple parameters from various studies with heterogeneous designs and partial information. Such a data situation is quite typical for synthesis of clinical studies. For instance, in our motivating data example, individual participant data from Project INTEGRATE were obtained from 24 clinical trials aimed at examining the efficacy of brief alcohol interventions to reduce excessive alcohol use and to prevent harm among college students. Despite having similar objectives among these trials, they differed in terms of the interventions evaluated, covariates assessed, follow-up schedules, among others. With the existing methods, one may have to limit the analysis to a subset of trials with all covariates or to a subset of covariates for a reduced model, either of which excludes partially available data, resulting in an important loss of information. The new CD-based method can efficiently combine all studies with all the covariates, thus minimizing the information loss that would have occurred under the existing synthesis methods. Moreover, compared to the existing multivariate CD approach proposed by Yang et al. (2014), the current work extends it to random-effects meta-analysis models and to a complex model requiring synthesis of a large number of parameters.

ETD_7830

Ph.D.

Includes bibliographical references

by Yang Jiao

doi:10.7282/T3Q81GH8

ETD doctoral

The author owns the copyright to this work.