gap (version 1.1-1)

metareg: Fixed and random effects model for meta-analysis

Description

Given $k=n$ studies with $b_1, ..., b_N$ being $\beta$'s and $se_1, ..., se_N$ standard errors from regression, the fixed effects model uses inverse variance weighting such that $w_1=1/se_1^2$, ..., $w_N=1/se_N^2$ and the combined $\beta$ as the weighted average, $\beta_f=(b_1*w_1+...+b_N*w_N)/w$, with $w=w_1+...+w_N$ being the total weight, the se for this estimate is $se_f=\sqrt{1/w}$. A normal z-statistic is obtained as $z_f=\beta_f/se_f$, and the corresponding p value $p_f=2*pnorm(-abs(z_f))$. For the random effects model, denote $q_w=w_1*(b_1-\beta_f)^2+...+w_N*(b_N-\beta_f)^2$ and $dl=max(0,(q_w-(k-1))/(w-(w_1^2+...+w_N^2)/w))$, corrected weights are obtained such that ${w_1}_c=1/(1/w_1+dl)$, ..., ${w_N}_c=1/(1/w_N+dl)$, totaling $w_c={w_1}_c+...+{w_N}_c$. The combined $\beta$ and se are then $\beta_r=(b_1*{w_1}_c+...+b_N*{w_N}_c)/w_c$ and $se_r=\sqrt(1/w_c)$, leading to a z-statistic $z_r=\beta_r/se_r$ and a p-value $p_r=2*pnorm(-abs(z_r))$. Moreover, a p-value testing for heterogeneity is $p_{heter}=pchisq(q_w,k-1,lower.tail=FALSE)$.

Usage

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

Arguments

data

Data frame to be used

N

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
• i2
  $I^2$ statistic
• k
  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

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))