In Stamp et al. (2023)1 we discuss the meta analysis of the pariwise comparison \(P\)-values that mvMAPIT gives. We provide three methods to compute a per-variant combined \(P\)-value:
The Fisher’s method requires independent \(P\)-values. The other two tests handle arbitrary covariances between the \(P\)-values. Here we show how these three methods compare empirically when applied to the same \(P\)-values.
Draw random uniform \(P\)-values from [0, 0.05].
Use the provided methods to compute the meta analysis \(P\)-values.
cauchy <- cauchy_combined(pvalues) %>% rename(p_cauchy = p) %>% select(-trait) fisher <- fishers_combined(pvalues) %>% rename(p_fisher = p) %>% select(-trait) harmonic <- harmonic_combined(pvalues) %>% rename(p_harmonic = p) %>% select(-trait) min_max <- pvalues %>% group_by(id) %>% summarise(p_min = min(p), p_max = max(p)) combined_wide <- fisher %>% left_join(harmonic) %>% left_join(cauchy) %>% left_join(min_max) %>% select(-id) # Joining with `by = join_by(id)` # Joining with `by = join_by(id)` # Joining with `by = join_by(id)`
The figure shows the data distribution on the diagonal and paired 2D historgam plots for all combinations of \(P\)-values. The brighter yellows correspond to higher counts, the green is in the middle of the scale, and the darker blues correspond to the low values of the histogram.
J. Stamp, A. DenAdel, D. Weinreich, L. Crawford (2023). Leveraging the Genetic Correlation between Traits Improves the Detection of Epistasis in Genome-wide Association Studies. G3 Genes|Genomes|Genetics, 13(8), jkad118; doi: https://doi.org/10.1093/g3journal/jkad118↩︎
Fisher, R.A. (1925). Statistical Methods for Research Workers. Oliver and Boyd (Edinburgh). ISBN 0-05-002170-2.↩︎
Liu, Y. and Xie, J., 2020. Cauchy combination test: a powerful test with analytic p-value calculation under arbitrary dependency structures. Journal of the American Statistical Association, 115(529), pp.393-402. https://doi.org/10.1080/01621459.2018.1554485↩︎