Compute per-gene heterogeneity statistics

Returns Cochran's Q, degrees of freedom, \(I^2\), the between-study variance \(\tau^2\) and the p-value of the Q test for each gene measured in at least two studies.

Usage

mx_heterogeneity(de_results, tau_method = c("REML", "PM", "DL"))

Arguments

de_results

A named list of data.frame objects (the de_result slots produced by mx_de), or a named list of metaXpressStudy objects after mx_de_all. Required columns: gene_id, log2FC, pvalue, padj; effect-size methods also need lfcSE.

tau_method

Estimator of the between-study variance for "random_effects": "REML" (default; restricted maximum likelihood), "PM" (Paule-Mandel) or "DL" (DerSimonian-Laird). REML and PM are preferred over DL, which underestimates \(\tau^2\) (Veroniki et al. 2016; Langan et al. 2019).

Value

A data.frame with columns gene_id, Q, df, I_sq, tau_sq, p_heterogeneity.

Details

\(I^2 = \max(0, (Q - df)/Q)\) describes the proportion of variability due to between-study differences rather than sampling error (Higgins & Thompson 2002). With few studies the Q test has low power and \(I^2\) is imprecise, so heterogeneity should be interpreted alongside \(\tau^2\) and the prediction interval from mx_meta.

References

Cochran, W.G. (1954) The combination of estimates from different experiments. Biometrics, 10(1), 101–129. doi:10.2307/3001666

Higgins, J.P.T. & Thompson, S.G. (2002) Quantifying heterogeneity in a meta-analysis. Statistics in Medicine, 21(11), 1539–1558. doi:10.1002/sim.1186

See also

mx_meta, mx_heterogeneity_plot

Examples

set.seed(1)
de <- lapply(1:3, function(s) {
  lfc <- rnorm(50, s * 0.3, 0.2); se <- rep(0.2, 50)
  p <- 2 * pnorm(-abs(lfc / se))
  data.frame(gene_id = paste0("G", 1:50), log2FC = lfc, lfcSE = se,
             pvalue = p, padj = p.adjust(p, "BH"))
})
het <- mx_heterogeneity(de)
summary(het$I_sq)
#>    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
#>    0.00   23.13   50.66   47.10   70.70   88.32