The primary goal of this project is to develop, test, and evaluate new statistical methodology for Bayesian meta-analysis; design, sample size, and power considerations for future studies using meta-analytic models; meta-analysis of diagnostic tests; meta-analysis for regression analysis of rare adverse events; and for identifying optimal individualized therapies. Specifically, we will examine the following five aims:
Aim 1. Develop methodology for Bayesian meta analysis
We will develop novel Bayesian parametric and semiparametric models for meta-analysis for aggregated data, time to event data, discrete data, and longitudinal data. Specifically, we will consider:
- Normal random effects models and develop novel Bayesian derivation of the Q-function for assessing heterogeneity across different studies for aggregated data;
- Random effects generalized linear models for continuous or discrete data;
- Mixed effects models for longitudinal data; and
- Random effects Cox models with gamma process priors for time-to-event data. We will incorporate missing covariates and/or responses in all these models for various data types.
Aim 2. Develop methodology for Bayesian trial design using meta-analytic models
We will develop a new Bayesian approach of sample size determination (SSD) for the design of non-inferiority clinical trials using the novel meta-analytic models developed in Subproject 1. First, we will extend the fitting and sampling priors of Wang and Gelfand (2002) to Bayesian SSD using meta-analytic models with a focus on controlling type I error, type II error, and power. Second, we will develop novel simulation-based Bayesian SSD using meta-analytic random effects generalized linear models, generalized linear mixed models, and random effects Cox models with gamma process priors.
Aim 3. Develop meta-analytic methodology of diagnostic tests without a gold standard
First, we will develop statistical methods for estimating accuracies of two and multiple (i.e. >= 3) diagnostic tests in a meta-analysis in the absence of a gold standard using maximum likelihood and full Bayesian methods. Second, we will reanalyze the meta-analysis data of 17 studies to evaluate the accuracy of microsatellite instability testing (MSI) and mutation analysis (Chen, Watson, and Parmigiani 2005), and a multi-center data set from NCI Colorectal Cancer Family Registry Study to evaluate the accuracy of 10 biomarkers in predicting Lynch syndrome and other data sets.
Aim 4. Develop methodology for regression analysis of rare adverse events for post-marketing safety evaluation
We will first develop semi-parametric methods of inference for evaluating drug and risk factor effects for rare time-to-event outcomes in clinical trials and epidemiological studies. Second, we will develop semi-parametric methods of inference for extremely rare time-to-event outcomes. Third, we will extend both of the results to the adjudicated endpoint setting. Fourth, we will extend these results to the meta-analytic setting involving collections of clinical studies, registry data and health insurance claims data.
Aim 5. Develop methodology for identifying optimal individualized therapies from existing clinical trial data using meta-analysis, utility functions, classification and regression
We will develop a general inferential tool for determining optimal individualized therapies. First, we will propose an multi-attribute utility function for accommodating complex survival information, as well as cost and quality of life considerations. Second, we will develop rigorous inferential procedures for optimal dosing which will be broadly applicable to individualized therapies based on subject specific characteristics, including genomic as well as demographic and disease severity predictors. Third, we will utilize machine learning and other high dimensional statistical learning and regression techniques in addition to more traditional approaches to statistical modeling.