metareg: Fixed and random effects meta-analysis (vectorised...

In gap: Genetic Analysis Package

Fixed and random effects meta-analysis (vectorised implementation)

Description

Performs inverse-variance weighted fixed- and random-effects meta-analysis across multiple studies supplied in wide format.

Usage

metareg(data, N, verbose = FALSE, prefixb = "b", prefixse = "se")

Arguments

data	A data frame containing regression coefficients and standard errors in wide format.
N	Integer. Number of studies included in the meta-analysis.
verbose	Logical. If TRUE, prints a completion message.
prefixb	Character. Prefix for regression coefficients. Default is "b" (columns ⁠b1, b2, …, bN⁠).
prefixse	Character. Prefix for standard errors. Default is "se" (columns ⁠se1, se2, …, seN⁠).

Details

The function is designed for high-throughput settings (e.g. GWAS), where each row represents an independent meta-analysis.

The function accepts wide-format input with estimates b_1,\ldots,b_N and standard errors se_1,\ldots,se_N. Missing values are automatically ignored on a per-row basis.

Fixed effects model

For k studies, inverse-variance weights are defined as

w_i = 1 / se_i^2

The pooled estimate is

\beta_f = \frac{\sum_i b_i w_i}{\sum_i w_i}

with standard error

se_f = \sqrt{1 / \sum_i w_i}

and test statistic

z_f = \beta_f / se_f

with p-value

p_f = 2\,\Phi(-|z_f|)

.

Random effects model (DerSimonian–Laird)

Cochran's Q statistic:

Q = \sum_i w_i (b_i - \beta_f)^2

Between-study variance:

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

Corrected weights:

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

Random-effects pooled estimate:

\beta_r = \frac{\sum_i b_i w_i^*}{\sum_i w_i^*}

with standard error

se_r = \sqrt{1/\sum_i w_i^*}

and p-value

p_r = 2\,\Phi(-|z_r|)

.

Heterogeneity p-value:

p_{heter} = P(\chi^2_{k-1} > Q)

.

The heterogeneity statistic is reported as

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

.

Value

A data frame with one row per meta-analysis containing:

• beta_f Fixed-effects pooled estimate

• se_f Standard error of fixed-effects estimate

• z_f Z statistic (fixed effects)

• p_f P value (fixed effects)

• beta_r Random-effects pooled estimate

• se_r Standard error of random-effects estimate

• z_r Z statistic (random effects)

• p_r P value (random effects)

• p_heter Cochran's Q heterogeneity test p-value

• i2 I^2 heterogeneity statistic

• k Number of studies contributing to each row

• eps Smallest double-precision number used for stability

Author(s)

ChatGPT

References

\insertRef

higgins03gap

Examples

## Not run: 
df <- data.frame(
  b1 = 1,  se1 = 2,
  b2 = 2,  se2 = 6,
  b3 = 3,  se3 = 8
)
metareg(df, 3)

df2 <- data.frame(
  b1 = c(1,2), se1 = c(2,4),
  b2 = c(2,3), se2 = c(4,6),
  b3 = c(3,4), se3 = c(6,8)
)
metareg(df2, 3)

## End(Not run)

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