Interval Estimation of Diagnostic Odds Ratio in Meta-analysis by Means of Profile Likelihoods

Abstract

© 2016 The Authors. The objectives of this paper are to (1) derive the profile maximum likelihood estimator (PMLE) for a true diagnostic odds ratio over across k studies in meta-analysis, (2) build the confidence intervals by replacing PMLE into the variance of logarithm of each diagnostic odds ratio, leading to two profile likelihood intervals (WPLF, WPLR), (3) create bootstrapping confidence interval (BOOT) from PMLE distribution by using the percentile, (4) compare the interval performance between all profile intervals with the conventional intervals, such as Mantel-Haenszel method (MH) and Weighted least squares method (WLS) in terms of the coverage probability and the width of interval. The results under a simulation plan indicated that for moderated study size (k = 8, 16) and small sample size, there were only three proposed interval estimates (WPLF, WPLR, and BOOT) that could be calibrated the coverage probability at 95% and the interval widths of WPLF and WPLR are narrower than the BOOT. Hence, we recommend to use WPLF and WPLR rather than the conventional intervals in such situations.