TITLE:
Minimum MSE Weighted Estimator to Make Inferences for a Common Risk Ratio across Sparse Meta-Analysis Data
AUTHORS:
Chukiat Viwatwongkasem, Sutthisak Srisawad, Pichitpong Soontornpipit, Jutatip Sillabutra, Pratana Satitvipawee, Prasong Kitidamrongsuk, Hathaikan Chootrakool
KEYWORDS:
Minimum MSE Weights, Adjusted Log-Risk Ratio Estimator, Sparse Meta-Analysis Data, Continuity Correction
JOURNAL NAME:
Open Journal of Statistics,
Vol.12 No.1,
February
14,
2022
ABSTRACT: The paper aims to discuss three interesting issues of statistical
inferences for a common risk ratio (RR) in
sparse meta-analysis data. Firstly, the conventional log-risk ratio estimator
encounters a number of problems when the number of events in
the experimental or control group is zero in sparse data of a 2 × 2 table. The
adjusted log-risk ratio estimator with the continuity correction points based upon the minimum Bayes risk with respect to
the uniform prior density over (0, 1) and the Euclidean loss function is
proposed. Secondly, the interest is to find the optimal weights of the pooled estimate that minimize the mean square error (MSE) of subject to the constraint on where , , . Finally, the performance
of this minimum MSE weighted estimator adjusted with various values of points is investigated to compare with other popular estimators, such as the
Mantel-Haenszel (MH) estimator and the weighted least squares (WLS) estimator
(also equivalently known as the inverse-variance weighted estimator) in senses of point estimation and hypothesis
testing via simulation studies. The results of estimation illustrate that
regardless of the true values of RR, the MH estimator achieves
the best performance with the smallest MSE when the study size is rather large and the sample sizes within
each study are small. The MSE of WLS estimator and the proposed-weight
estimator adjusted by , or , orare close together and
they are the best when the sample sizes are moderate to large (and) while
the study size is rather small.