metareg: Fixed and random effects model for meta-analysis

Description

Given $k = n$ studies with $b_{1}, . . ., b_{N}$ being $β$ 's and $s e_{1}, . . ., s e_{N}$ standard errors from regression, the fixed effects model uses inverse variance weighting such that $w_{1} = 1 / s e_{1}^{2}$ , ..., $w_{N} = 1 / s e_{N}^{2}$ and the combined $β$ as the weighted average, $β_{f} = (b_{1} * w_{1} + . . . + b_{N} * w_{N}) / w$ , with $w = w_{1} + . . . + w_{N}$ being the total weight, the se for this estimate is $s e_{f} = \sqrt{1 / w}$ . A normal z-statistic is obtained as $z_{f} = β_{f} / s e_{f}$ , and the corresponding p value $p_{f} = 2 * p n o r m (- a b s (z_{f}))$ . For the random effects model, denote $q_{w} = w_{1} * (b_{1} - β_{f})^{2} + . . . + w_{N} * (b_{N} - β_{f})^{2}$ and $d l = m a x (0, (q_{w} - (k - 1)) / (w - (w_{1}^{2} + . . . + w_{N}^{2}) / w))$ , corrected weights are obtained such that ${w_{1}}_{c} = 1 / (1 / w_{1} + d l)$ , ..., ${w_{N}}_{c} = 1 / (1 / w_{N} + d l)$ , totaling $w_{c} = {w_{1}}_{c} + . . . + {w_{N}}_{c}$ . The combined $β$ and se are then $β_{r} = (b_{1} * {w_{1}}_{c} + . . . + b_{N} * {w_{N}}_{c}) / w_{c}$ and $s e_{r} = \sqrt{(} 1 / w_{c})$ , leading to a z-statistic $z_{r} = β_{r} / s e_{r}$ and a p-value $p_{r} = 2 * p n o r m (- a b s (z_{r}))$ . Moreover, a p-value testing for heterogeneity is $p_{h e t e r} = p c h i s q (q_{w}, k - 1, l o w e r . t a i l = F A L S E)$ .

Usage

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

Arguments

data

Data frame to be used

Number of studies

verbose

A control for screen output

prefixb

Prefix of estimate; default value is "b"

prefixse

Prefix of standard error; default value is "se"

Value

The returned value is a data frame with the following variables:

p_f

P value (fixed effects model)

p_r

P value (random effects model)

beta_f

regression coefficient

beta_r

regression coefficient

se_f

standard error

se_r

standard error

z_f

z value

z_r

z value

p_heter

heterogeneity test p value

$I^{2}$ statistic

No of tests used

eps

smallest double-precision number

References

JPT Higgins, SG Thompson, JJ Deeks, DG Altman. Measuring inconsistency in meta-analyses. BMJ 327:557-60

Examples

Run this code

# NOT RUN {
abc <- data.frame(chromosome=1,rsn='abcd',startpos=1234,
                  b1=1,se1=2,p1=0.1,b2=2,se2=6,p2=0,b3=3,se3=8,p3=0.5)
metareg(abc,3)
abc2 <- 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))
print(metareg(abc2,3))
# }