A parametric meta-analysis.

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.

A parametric model to estimate the proportion from true null using a distribution for p-values.

Microarray studies generate a large number of p-values from many gene expression comparisons. The estimate of the proportion of the p-values sampled from the null hypothesis draws broad interest. The two-component mixture model is often used to estimate this proportion. If the data are generated under the null hypothesis, the p-values follow the uniform distribution. What is the distribution of p-values when data are sampled from the alternative hypothesis? The distribution is derived for the chi-squared test. Then this distribution is used to estimate the proportion of p-values sampled from the null hypothesis in a parametric framework. Simulation studies are conducted to evaluate its performance in comparison with five recent methods. Even in scenarios with clusters of correlated p-values and a multicomponent mixture or a continuous mixture in the alternative, the new method performs robustly. The methods are demonstrated through an analysis of a real microarray dataset.