Nonparametric Inference for Meta-Analysis with Fixed Unknown, Study-Specific Parameters

• Activity Number: 515
• Type: Topic Contributed
• Date/Time: Wednesday, August 7, 2013 : 10:30 AM to 12:20 PM
• Sponsor: Health Policy Statistics Section
• Author(s): Brian Claggett*+ and Tian Lu and Min-ge Xie
• Companies: Harvard School of Public Health and Stanford University School of Medicine and Rutgers University
• Keywords: bootstrap ; confidence distribution ; extrema ; meta analysis ; robust methods ; ties

Abstract

Meta-analysis is a valuable tool for combining information from independent studies. However, meta-analysis techniques often rely on distributional assumptions that are difficult, if not impossible, to verify. In fixed-effects and random-effects models, we must assume that the study parameters are either constant across studies or that they are realizations of a random sample from a population, often under a parametric distributional assumption. In this paper, we present a new framework for summarizing information obtained from multiple studies and make inference that is not dependent on any distributional assumption for the study-level unknown, fixed parameters. Specifically, we draw inferences about the quantiles of this set of parameters using study-level summary statistics. To construct confidence intervals, we employ a novel resampling method via the confidence distributions of the study parameters. We justify the validity of the interval estimation procedure asymptotically and compare the new procedure with standard bootstrapping. We illustrate our proposal with data from a meta analysis of the effect of an antioxidant on the prevention of contrast-induced nephropathy.