A parametric meta-analysis

Stat Med. 2019 Sep 20;38(21):4013-4025. doi: 10.1002/sim.8278. Epub 2019 Jun 17.


In a meta-analysis, we assemble a sample of independent, nonidentically distributed p-values. The Fisher's combination procedure provides a chi-squared test of whether the p-values were sampled from the null uniform distribution. After rejecting the null uniform hypothesis, we are faced with the problem of how to combine the assembled p-values. We first derive a distribution for the p-values. The distribution is parameterized by the standardized mean difference (SMD) and the sample size. It includes the uniform as a special case. The maximum likelihood estimate (MLE) of the SMD can then be obtained from the independent, nonidentically distributed p-values. The MLE can be interpreted as a weighted average of the study-specific estimate of the effect size with a shrinkage. The method is broadly applicable to p-values obtained in the maximum likelihood framework. Simulation studies show that our method can effectively estimate the effect size with as few as 6 p-values in the meta-analyses. We also present a Bayes estimator for SMD and a method to account for publication bias. We demonstrate our methods on several meta-analyses that assess the potential benefits of citicoline for patients with memory disorders or patients recovering from ischemic stroke.

Keywords: Bayesian estimator; citicoline; distribution of p-values; standardized mean difference.

Publication types

  • Research Support, N.I.H., Extramural
  • Research Support, U.S. Gov't, P.H.S.

MeSH terms

  • Bayes Theorem
  • Computer Simulation
  • Humans
  • Likelihood Functions*
  • Meta-Analysis as Topic*