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 thenumber 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
References
[1]
Yates, F. (1934) Contingency Tables Involving Small Numbers and the Chi-Squared Test. Supplement to the Journal of the Royal Statistical Society, 1, 217-235.
https://doi.org/10.2307/2983604
[2]
Lane, P.W. (2013) Meta-Analysis of Incidence of Rare Events. Statistical Methods in Medical Research, 22, 117-132. https://doi.org/10.1177/0962280211432218
[3]
Stijnen, T., Hamza, T.H. and Özdemir, P. (2010) Random Effects Meta-Analysis of Event Outcome in the Framework of the Generalized Linear Mixed Model with Applications in Sparse Data. Statistics in Medicine, 29, 3046-3067.
https://doi.org/10.1002/sim.4040
[4]
White, I.R., Daniel, R. and Royston, P. (2010) Avoiding Bias Due to Perfect Prediction in Multiple Imputation of Incomplete Categorical Variables. Computational Statistics and Data Analysis, 54, 2267-2275.
https://doi.org/10.1016/j.csda.2010.04.005
[5]
Lui, K.J. and Lin, C.D. (2003) A Revisit on Comparing the Asymptotic Interval Estimators of Odds Ratio in a Single 2 × 2 Table. Biometrical Journal, 45, 226-237.
https://doi.org/10.1002/bimj.200390008
[6]
Sankey, S.S., Weissfeld, L.A., Fine, M.J. and Kapoor, W. (1996) An Assessment of the Use of the Continuity Correction for Sparse Data in Meta-Analysis. Communications in Statistics—Simulation and Computation, 25, 1031-1056.
https://doi.org/10.1080/03610919608813357
[7]
Gart, J.J. and Zweifel, J.R. (1967) On the Bias of Various Estimators of the Logit and Its Variance with Application to Quantal Bioassay. Biometrika, 54, 181-187.
https://doi.org/10.1093/biomet/54.1-2.181
[8]
Walter, S.D. (1975) The Distribution of Levin’s Measure of Attributable Risk. Biometrika, 62, 371-372. https://doi.org/10.1093/biomet/62.2.371
[9]
Cox, D.R. (1970) The Continuity Correction. Biometrika, 57, 217-219.
https://doi.org/10.1093/biomet/57.1.217
[10]
Li, L. and Wang, X. (2017) Meta-Analysis of Rare Binary Events in Treatment Groups with Unequal Variability. Statistical Methods in Medical Research, 28, 263-274. https://doi.org/10.1177/0962280217721246
[11]
Tukey, J.W. (1977) Exploratory Data Analysis. Addison-Wesley Publishing Company, Boston.
[12]
Sánchez-Meca, J. and Marín-Martínez, F. (2000) Testing the Significance of a Common Risk Difference in Meta-Analysis. Computational Statistics and Data Analysis, 33, 299-313. https://doi.org/10.1016/S0167-9473(99)00055-9
[13]
Böhning, D. and Viwatwongkasem, C. (2005) Revisiting Proportion Estimators. Statistical Methods in Medical Research, 14, 147-169.
https://doi.org/10.1191/0962280205sm393oa
[14]
Agresti, A. and Caffo, B. (2000) Simple and Effective Confidence Intervals for Proportions and Differences of Proportions Result from Adding Two Successes and Two Failures. The American Statistician, 54, 280-288.
https://doi.org/10.1080/00031305.2000.10474560
[15]
McClave, J.T. and Sincich, T.T. (2012) Statistics. Pearson Education, London.
[16]
Pettigrew, H.M., Gart, J.J. and Thomas, D.G. (1986) The Bias and Higher Cumulants of the Logarithm of a Binomial Variate. Biometrika, 73, 425-435.
https://doi.org/10.1093/biomet/73.2.425
[17]
Lipsitz, S.R., Dear, K.B.G., Laird, N.M. and Molenberghs, G. (1998) Tests for Homogeneity of the Risk Difference When Data Are Sparse. Biometrics, 54, 148-160.
[18]
Cooper, M.R., Dear, K.B.G., McIntyre, O.R., Ozer, H., Ellerton, J.Cannellos, G., Duggan, B. and Schiffer, C. (1993) A Randomized Clinical Trial Comparing Melphalan/Prednisone with and without α-2b Interferon in Newly-Diagnosed Patients with Multiple Myeloma: A Cancer and Leukemia Group B Study. Journal of Clinical Oncology, 11, 155-160. https://doi.org/10.1200/JCO.1993.11.1.155
[19]
Viwatwongkasem, C., Jitthavech, J., Böhning, D. and Lorchirachoonkul, V. (2012) Minimum MSE Weights of Adjusted Summary Estimator of Risk Difference in Multi-Center Studies. Open Journal of Statistics, 2, 48-59.
https://doi.org/10.4236/ojs.2012.21006
[20]
Greenland, S. and Robin, J.M. (1985) Estimation of a Common Effect Parameter from Sparse Follow-up Data. Biometrics, 45, 55-68.
[21]
Soulakova, J.N. and Bright, B.C. (2013) Applications of Asymptotic Confidence Intervals with Continuity Corrections for Asymmetric Comparisons in Noninferiority Trials. Pharmaceutical Statistics, 12, 147-155. https://doi.org/10.1002/pst.1566
![\"\"](\"Edit_1cfd6af9-9943-4e4e-a60b-b3701c145d66.png\")
![\"\"](\"Edit_83bbc97f-19ba-47c9-b719-a5bbc6d1be3e.png\")
![\"\"](\"Edit_a389f341-ea7b-4385-aa05-b9c32ee4d358.png\")
![\"\"](\"Edit_a7d34aaa-b76f-4199-afb1-d8a0c6c666f4.png\")
![\"\"](\"Edit_ffdfa7ec-b72a-4811-a71b-1ad2a63501ad.png\")
![\"\"](\"Edit_8d6380b3-2e8c-4602-a2e5-0b52d08f2cc6.png\")
![\"\"](\"Edit_ba50e079-9912-46e6-ac67-2ca770636e16.png\")
![\"\"](\"Edit_069d7550-e6ca-4797-80a5-7240fc6904b1.png\")
