/R-package---Meta-Analysis

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R-package---Meta-Analysis

R package for various meta analysis methods to combine p-values. A meta-analysis is a statistical technique used in research to combine and analyze data from multiple independent studies on a specific topic or research question. Meta-analysis methods typically do not directly combine p-values but instead combine effect sizes or other relevant statistical measures from individual studies.

Combine p-values

Fisher

The Fisher’s method sums up the logtransformed p-values obtained from individual studies. The combined Fisher’s statistic $X_{fisher}^2 = \sum\limits_{i=1}^{k}\ln(p_i)$ follows a $X^2$ distribution with 2k degrees of freedom under the null hypothesis (assuming null p-values are uniformly distributed).

Stouffer

Stouffer's method is used to combine the results from several independence tests bearing upon the same overall hypothesis (H0). The method sums the inverse normal transformed p-values. ${Z_{Stouffer} = \sum\limits_{i=1}^{k} Z_{i}/\sqrt{k}}$

Maximum p-value (maxP)

The maxP method takes maximum p-value as the test statistic. It follows a beta distribution with degrees of freedom ${\alpha = K}$ and ${\beta = 1}$ under the null hypothesis

Minimum p-value (minP)

The minP method takes the minimum p-vlaue among the K studies as the test statistic. It follows a beta distribution with degrees of freedom ${\alpha = 1}$ and ${\beta = k}$ under the null hypothesis.

Weighted Stouffer

weight is the square root of the sample size, wi ${Z_{weighted~Stouffer}} = \frac{\sum\limits_{i=1}^{k} w_i Z_i}{\sqrt{\sum\limits_{i=1}^{k} w_i^2}}$

Lancaster

Lancaster's method generalized Fisher's method by assignning different weights using the additivity of chi-squared distribution. ${T = \sum\limits_{i=1}^{k} [X_{n_i}^{2}]^{-1}(1-p_i)}$ where ${[X_{n_i}^{2}]^{-1}}$ is the inverse cumulative chi-square distributon function with ni degrees of freedom

Reference:

https://bmcbioinformatics.biomedcentral.com/articles/10.1186/1471-2105-14-368

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3135688/