Small-study effects and publication bias tests

Tests, gene by gene, whether smaller (less precise) studies report systematically larger effects, the pattern produced by publication bias or by other small-study effects. Two standard tests are provided: Egger's regression test and Begg and Mazumdar's rank correlation test.

Usage

mx_small_study(
  de_results,
  genes = NULL,
  method = c("egger", "begg", "both"),
  min_studies = 3
)

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.
genes: Optional character vector of genes to test (e.g. the significant genes of mx_meta). Default: all genes measured in at least min_studies studies.
method: "egger" (default), "begg" or "both".
min_studies: Minimum number of studies with a standard error for a gene to be tested. Default 3 (the minimum for Egger's test).

Value

A data.frame with gene_id, n_studies and, for Egger, egger_intercept, egger_se, egger_pvalue; for Begg, begg_tau, begg_pvalue. BH-adjusted columns (*_padj) are added across the genes tested.

Details

Egger's test regresses the standardized effect \(y_i / s_i\) on precision \(1/s_i\) by ordinary least squares; an intercept different from zero indicates funnel-plot asymmetry (t-test with \(k - 2\) df). Begg's test computes Kendall's \(\tau\) between the standardized deviates from the fixed-effect estimate and their variances.

Both tests have low power with few studies. The Cochrane Handbook advises against them with fewer than 10 studies, and a warning is issued in that case; a non-significant result then is not evidence of absence of bias. In transcriptomic meta-analyses of public data, genome-wide summary statistics are reported for all genes, so classical publication bias (selective reporting of genes) does not apply; asymmetry instead points to small-study differences in design, tissue or platform.

References

Egger, M., Davey Smith, G., Schneider, M. & Minder, C. (1997) Bias in meta-analysis detected by a simple, graphical test. BMJ, 315(7109), 629–634. doi:10.1136/bmj.315.7109.629

Begg, C.B. & Mazumdar, M. (1994) Operating characteristics of a rank correlation test for publication bias. Biometrics, 50(4), 1088–1101. doi:10.2307/2533446

Sterne, J.A.C. et al. (2011) Recommendations for examining and interpreting funnel plot asymmetry in meta-analyses of randomised controlled trials. BMJ, 343, d4002. doi:10.1136/bmj.d4002

Examples

ad <- readRDS(system.file("extdata", "ad_brain_de.rds",
                          package = "metaXpress"))
ss <- suppressWarnings(mx_small_study(ad$de_results,
                                      genes = c("GFAP", "VGF", "SST")))
ss
#>   gene_id n_studies egger_intercept  egger_se egger_pvalue egger_padj
#> 1     SST         4       2.3710865 3.5614876    0.5740746  0.8611119
#> 2     VGF         4      -0.2196817 4.1596622    0.9626820  0.9626820
#> 3    GFAP         4       1.0189531 0.5046195    0.1809088  0.5427264