Statistical inference for inverse binomial proportion and dependent p-values

Meta-analysis is a statistical method to combine multiple studies for decision making, which has been widely applied in psychology, medicine, social science and other areas for several decades. Evidences from meta-analysis are nowadays regarded as the strongest evidences in evidence-based medicine. In this three-year research plan, we propose to tackle some emerging and challenging issues for modern meta-analysis, in particular in
developing new models and methods for meta-analysis with rare-event studies or nonindependent studies. To accomplish the research projects, there are 4 main objectives as follows. The first objective is to construct new confidence intervals for the inverse
binomial proportion, as well as perform theoretical and numerical studies to evaluate their statistical properties and finite sample performance. The second objective is to investigate whether, or to what extent, the statistical inference derived from the inverse
binomial proportion will further advance the existing literature on meta-analysis with rare-event studies. The third objective is to derive the joint distribution of the multivariate p-values, and study its statistical properties under some general settings. And the last objective is to apply the statistical inference derived from the multivariate p-value distribution to meta-analysis with non-independent studies. Extensive simulations will also be carried out that compare the new methods with the classic meta-analysis for independent studies, together with real applications to interesting
problems raised from the real-world study. Our proposed studies are also fundamental and significant for medical statistics, and upon a successful completion, the research outputs from this proposal will largely enhance the existing literature on meta-analysis with rare-event studies and non-independent studies. Lastly, to cater for the demands of the application, we will also develop online calculators and freely available R packages
for implementing our newly developed models and methods for both meta-analysis and medical statistics.