Leave-one-out sensitivity analysis

Reruns the meta-analysis \(k\) times, each time excluding one study, to assess whether any single study drives the result (Cochrane Handbook, Section 10.14).

Usage

mx_sensitivity(
  de_results,
  method = c("random_effects", "fixed_effects", "fisher", "stouffer", "inverse_normal",
    "minp", "maxp", "rop", "awmeta"),
  padj_threshold = 0.05,
  ...
)

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.

method

Character scalar. One of:

"random_effects"

(default) Inverse-variance random-effects model; between-study variance \(\tau^2\) estimated by tau_method. Estimates the average effect across populations and reports a prediction interval.

"fixed_effects"

Inverse-variance common-effect model. Appropriate only when studies are near-replicates (low \(I^2\)).

"fisher"

Fisher's sum of \(-2\log p\). With directional = TRUE (default) the two one-sided Fisher tests are computed and combined as in Owen (2009), so evidence in opposite directions does not accumulate. Like all Fisher-type tests it can still be driven by one extreme study; check direction_consistency.

"stouffer"

Unweighted Stouffer Z on signed z-scores.

"inverse_normal"

Weighted inverse-normal (Stouffer) combination with weights \(\sqrt{n_s}\), as in Marot et al. (2009) and Rau et al. (2014).

"minp"

Tippett's minimum p: DE in at least one study. Non-directional.

"maxp"

Wilkinson's maximum p: DE in all studies. Non-directional.

"rop"

r-th ordered p-value (Song & Tseng 2014): DE in at least r studies. Non-directional.

"awmeta"

AWmeta (Hu et al. 2026). The p-value is the adaptively weighted Fisher statistic (AW-Fisher; Li & Tseng 2011), calibrated with the AWFisher package (Huo et al. 2020), which also returns binary per-study weights indicating which studies contribute. The effect size is an REML random-effects estimate over the selected studies only (AW-REM). Requires AWFisher and lfcSE. Non-directional, as in the original method; check direction_consistency. The selected studies are reported in aw_studies.

padj_threshold

Numeric. FDR threshold used to call genes in the robustness summary. Default: 0.05.

...

Further arguments passed to mx_meta (e.g. tau_method, hksj).

Value

A named list of metaXpressResult objects, one per excluded study. The attribute "robustness" holds a data.frame with, for every gene, the number and fraction of leave-one-out runs in which it remained significant (meta_padj <= padj_threshold) with the same direction as in the full analysis.

References

Higgins, J.P.T. et al. (eds.) (2019) Cochrane Handbook for Systematic Reviews of Interventions. 2nd edn. Chichester: John Wiley & Sons. doi:10.1002/9781119536604

See also

mx_meta

Examples

set.seed(1)
de <- lapply(1:4, function(s) {
  lfc <- rnorm(100, c(rep(1, 10), rep(0, 90)), 0.2); se <- rep(0.25, 100)
  p <- 2 * pnorm(-abs(lfc / se))
  data.frame(gene_id = paste0("G", 1:100), log2FC = lfc, lfcSE = se,
             pvalue = p, padj = p.adjust(p, "BH"))
})
names(de) <- paste0("S", 1:4)
loo <- mx_sensitivity(de, method = "random_effects")
#> Running leave-one-out sensitivity analysis...
#>   Excluding: S1
#>   Excluding: S2
#>   Excluding: S3
#>   Excluding: S4
head(attr(loo, "robustness"))
#>   gene_id    full_padj n_loo_sig frac_loo_sig
#> 1      G1 1.480181e-14         4            1
#> 2      G2 1.167633e-15         4            1
#> 3      G3 1.562896e-11         4            1
#> 4      G4 7.823927e-16         4            1
#> 5      G5 9.692259e-08         4            1
#> 6      G6 8.707619e-17         4            1