metap: Meta-analysis of p-values with heterogeneity and random...
In gap: Genetic Analysis Package

metap

R Documentation

Meta-analysis of p-values with heterogeneity and random effects

Description

Performs GWAS-style meta-analysis by combining p-values across studies. Implements Fisher’s method, fixed-effect weighted Stouffer Z, and random-effects Z meta-analysis with heterogeneity statistics.

Usage

metap(
  data,
  N,
  sided = c("two", "one"),
  verbose = TRUE,
  prefixp = "p",
  prefixn = "n",
  prefixbeta = NULL,
  prefixdir = NULL
)

Arguments

`data`	data.frame containing study results.
`N`	number of studies.
`sided`	`"two"` (default) or `"one"` for one-sided p-values.
`verbose`	logical; print summary output.
`prefixp`	prefix for p-value columns (default `"p"`).
`prefixn`	prefix for sample-size columns (default `"n"`).
`prefixbeta`	optional prefix for beta columns (used for direction).
`prefixdir`	optional prefix for sign columns (+1/-1).

Details

This function implements the meta-analysis approach used in the Genetic Investigation of ANThropometric Traits (GIANT) consortium.

Missing studies are automatically excluded per row, so the number of contributing studies may vary across variants.

Fisher’s method

X^2 = -2 \sum_{i=1}^k \log(p_i) \sim \chi^2_{2k}

Fixed-effect weighted Stouffer Z

Convert p-values to Z:

z_i = \Phi^{-1}(1 - p_i/2)

Sample-size weights:

w_i = \sqrt{n_i}

Z_{FE} = \frac{\sum w_i z_i}{\sqrt{\sum w_i^2}}

Heterogeneity

Q = \sum w_i (z_i - \bar z)^2

I^2 = \max(0, (Q-(k-1))/Q)

Random-effects Z meta-analysis

DerSimonian–Laird variance:

\tau^2 = \max\left(0,\frac{Q-(k-1)}{\sum w_i - \sum w_i^2/\sum w_i}\right)

Random-effects weights:

w_i^* = 1/(1/w_i + \tau^2)

Z_{RE} = \frac{\sum w_i^* z_i}{\sqrt{\sum w_i^*}}

Value

data.frame with

fisher_p Fisher combined p-value
stouffer_FE Fixed-effect Z meta p-value
stouffer_RE Random-effects Z meta p-value
Q Cochran heterogeneity statistic
I2 Proportion heterogeneity
tau2 Between-study variance

Author(s)

ChatGPT (Jing Hua Zhao)

Examples

## Not run: 
## ------------------------------------------------------------------
## Classic GIANT consortium example (historical demo)
## Speliotes, Elizabeth K., M.D. [ESPELIOTES@PARTNERS.ORG]
## 22-2-2008 MRC-Epid JHZ
## ------------------------------------------------------------------

s <- data.frame(
  p1 = 0.1^rep(8:2, each = 7),
  n1 = rep(32000, 49),
  p2 = 0.1^rep(8:2, times = 7),
  n2 = rep(8000, 49)
)

res <- metap(s, 2)
head(res)

## Visual comparison equal vs unequal N (original demo)

np <- 7
p  <- 0.1^((np + 1):2)
z  <- qnorm(1 - p/2)
n  <- c(32000, 8000)

grid <- expand.grid(i = seq_len(np), j = seq_len(np))
za <- z[grid$i]; zb <- z[grid$j]

metaz_equalN   <- (sqrt(n[1])*za + sqrt(n[1])*zb)/sqrt(n[1]+n[1])
metaz_unequalN <- (sqrt(n[1])*za + sqrt(n[2])*zb)/sqrt(n[1]+n[2])

q  <- -log10(sort(p, decreasing=TRUE))
t1 <- matrix(-log10(sort(2*pnorm(-abs(metaz_equalN))),   decreasing=TRUE), np, np)
t2 <- matrix(-log10(sort(2*pnorm(-abs(metaz_unequalN))), decreasing=TRUE), np, np)

par(mfrow=c(1,2), bg="white", mar=c(4.2,3.8,0.2,0.2))
persp(q,q,t1, main="Equal sample sizes")
persp(q,q,t2, main="Unequal sample sizes")

## ------------------------------------------------------------------
## New example: missing studies + heterogeneity
## ------------------------------------------------------------------

set.seed(1)
dat <- data.frame(
  p1 = runif(100,1e-6,0.05),
  n1 = sample(5000:20000,100,TRUE),
  p2 = runif(100,1e-6,0.05),
  n2 = sample(5000:20000,100,TRUE)
)

## simulate missing studies
dat$p2[sample(1:100,20)] <- NA

res <- metap(dat,2)
summary(res$I2)

## End(Not run)

gap documentation built on May 28, 2026, 9:07 a.m.