Minimum MSE Weighted Estimator to Make Inferences for a Common Risk Ratio across Sparse Meta-Analysis Data

Chukiat Viwatwongkasem,Jutatip Sillabutra,Sutthisak Srisawad,Hathaikan Chootrakool,Pichitpong Soontornpipit,Pratana Satitvipawee,Prasong Kitidamrongsuk

doi:10.4236/ojs.2022.121004

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 , or are close together and they are the best when the sample sizes are moderate to large (and) while the study size is rather small.

Highlights

Biostatisticians would like to evaluate the effects of treatments or risk factors in terms of risk difference, relative risk, and/or odds ratio between two independent sample groups and binary outcomes in a 2 × 2 table
The main question rises which continuity correction values are the best choice for the adjusted relative risk estimator in a center study and multi-center study with sparse data
For estimation of fixing θ (θ = log risk ratio (RR) ) in a center ( k = 1 ), regardless of a true value of RR, the proposed estimator adjusted by c= c=1 c=2 1 3 performs the best with the smallest mean square error (MSE)

Summary

Introduction

Biostatisticians would like to evaluate the effects of treatments or risk factors in terms of risk difference, relative risk (risk ratio), and/or odds ratio between two independent sample groups (e.g., treatment or control, presence or absence of a risk factor) and binary outcomes (e.g., disease or non-disease, success or failure, dead or alive) in a 2 × 2 table. Yate [1] first used the continuity correction of 0.5 in the approximation of a discrete distribution to a continuous one in 1934 It seems that the correction value of 0.5 has been used extensively until now, for examples: Lane [2], Stijnen et al [3], White et al [4], Lui and Lin [5], Sankey et al [6], Gart and Zwefel [7], Walter [8], and Cox [9] used value 0.5 adjustment for zero observations in each cell of the 2 × 2 table. Another choice of c for this class such as 0.25, 0.5 and 1 had been suggested by Li and

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