Review Articles

Meta-analysis of independent datasets using constrained generalised method of moments

Menghao Xu ,

a KLATASDS-MOE, School of Statistics, East China Normal University, Shanghai, People's Republic of China

jason_xmh@163.com

Jun Shao

a KLATASDS-MOE, School of Statistics, East China Normal University, Shanghai, People's Republic of China;b Department of Statistics, University of Wisconsin-Madison, Madison, WI, USA

Pages 109-116 | Received 03 Feb. 2019, Accepted 07 Jun. 2019, Published online: 18 Jun. 2019,
  • Abstract
  • Full Article
  • References
  • Citations

Abstract

We propose a constrained generalised method of moments (CGMM) for enhancing the efficiency of estimators in meta-analysis in which some studies do not measure all covariates associated with the response or outcome. Under some assumptions, we show that the proposed CGMM estimators have good asymptotic properties. We also demonstrate the effectiveness of the proposed method through simulation studies with fixed sample sizes.

References

  1. Breslow, N. E., & Holubkov, R. (1997). Maximum likelihood estimation of logistic regression parameters under two-phase, outcome-dependent sampling. Journal of the Royal Statistical Society, Series B59(2), 447–461. doi: 10.1111/1467-9868.00078 [Crossref], [Google Scholar]
  2. Chatterjee, N., Chen, Y.-H., Maas, P., & Carroll, R. J. (2016). Constrained maximum likelihood estimation for model calibration using summary-level information from external big data sources. Journal of the American Statistical Association111, 107–117. doi: 10.1080/01621459.2015.1123157 [Taylor & Francis Online][Web of Science ®], [Google Scholar]
  3. Chen, Y.-H., & Chen, H. (2000). A unified approach to regression analysis under double sampling design. Journal of the Royal Statistical Society, Series B62, 449–460. doi: 10.1111/1467-9868.00243 [Crossref], [Google Scholar]
  4. Deville, J. C., & Sarndal, C. E. (1992). Calibration estimators in survey sampling. Journal of the American Statistical Association87, 376–382. doi: 10.1080/01621459.1992.10475217 [Taylor & Francis Online][Web of Science ®], [Google Scholar]
  5. Engle, R. F., & McFadden, D. L. (1994). Handbook of econometrics (Vol. 4). Amsterdam: Elsevier Science, North Holland. [Google Scholar]
  6. Hansen, L. P. (1982). Large sample properties of generalized method of moments estimators. Econometrica50, 1029–1054. doi: 10.2307/1912775 [Crossref][Web of Science ®], [Google Scholar]
  7. Hartung, J., Knapp, G., & Sinha, K. B. (2008). Statistical meta-analysis with applications. New York, NY: Wiley. [Crossref], [Google Scholar]
  8. Higgins, J. P. T., & Thompson, S. G. (2002). Quantifying heterogeneity in a meta-analysis. Statistics in Medicine21, 1539–1558. doi: 10.1002/sim.1186 [Crossref][Web of Science ®], [Google Scholar]
  9. Higgins, J. P. T., Thompson, S. G., Deeks, J. J., & Altman, D. G. (2003). Measuring inconsistency in meta-analyses. British Medical Journal327, 557–560. doi: 10.1136/bmj.327.7414.557 [Crossref][Web of Science ®], [Google Scholar]
  10. Lawless, J. F., Wild, C. J., & Kalbfleisch, J. D. (1999). Semiparametric methods for response-selective and missing data problems in regression. Journal of the Royal Statistical Society, Series B61, 413–438. doi: 10.1111/1467-9868.00185 [Crossref], [Google Scholar]
  11. Lu, T. T., & Shiou, S. H. (2002). Inverses of 2×22×2 block matrices. Computers and Mathematics with Applications43, 119–129. doi: 10.1016/S0898-1221(01)00278-4 [Crossref][Web of Science ®], [Google Scholar]
  12. Lumley, T., Shaw, P. A., & Dai, J. Y. (2011). Connections between survey calibration estimators and semiparametric models for incomplete data. International Statistical Review79, 200–220. doi: 10.1111/j.1751-5823.2011.00138.x [Crossref][Web of Science ®], [Google Scholar]
  13. Qin, J., Zhang, H., Li, P., Albanes, D., & Yu, K. (2015). Using covariate-specific disease prevalence information to increase the power of case- control studies. Biometrika102, 169–180. doi: 10.1093/biomet/asu048 [Crossref][Web of Science ®], [Google Scholar]
  14. Rao, J. N. K., & Molina, I. (2015). Small area estimation. New York, NY: Wiley. [Crossref], [Google Scholar]
  15. Robins, J. M., Rotnitzky, A., & Zhao, L. P. (1994). Estimation of regression coefficients when some regressors are not always observed. Journal of the American Statistical Association89, 846–866. doi: 10.1080/01621459.1994.10476818 [Taylor & Francis Online][Web of Science ®], [Google Scholar]
  16. Schmidt, F. L., & Hunter, J. E. (2014). Methods of meta-analysis: Correcting error and bias in research findings. Newbury Park, CA: Sage Publications. [Google Scholar]
  17. Scott, A. J., & Wild, C. J.. (1997). Fitting regression models to case-control data by maximum likelihood. Biometrika84, 57–71. doi: 10.1093/biomet/84.1.57 [Crossref][Web of Science ®], [Google Scholar]
  18. Simonian, R. D., & Laird, N. (1986). Meta-analysis in clinical trials. Controlled Clinical Trials7, 177–188. doi: 10.1016/0197-2456(86)90046-2 [Crossref], [Google Scholar]
  19. Slud, E., & DeMissie, D. (2011). Validity of regression meta-analyses versus pooled analyses of mixed linear models. Mathematics in Engineering, Science and Aerospace2, 251–265. [Google Scholar]
  20. Wu, C. (2003). Optimal calibration estimators in survey sampling. Biometrika90, 937–951. doi: 10.1093/biomet/90.4.937 [Crossref][Web of Science ®], [Google Scholar]
  21. Wu, C., & Sitter, R. R. (2001). A model-calibration approach to using complete auxiliary information from survey data. Journal of the American Statistical Association96, 185–193. doi: 10.1198/016214501750333054 [Taylor & Francis Online][Web of Science ®], [Google Scholar]