How to conduct meta-analysis for thousands of genes at one time using R package “metafor”

Question

I'm trying to do a meta-analysis on many genes using R package "metafor", I know how to do it one gene at a time but it would be ridiculous to do so for thousands of genes. Could somebody help me out of this! Appreciate any suggestions!

I have all the results of se and HR for all the genes named 'se_summary' and 'HR_summary' respectively. I need to use both se and HR of these genes from five studies "ICGC, TCGA, G71, G62, G8" as input to conduct the meta analysis.

The code I used to do the meta analysis for one single gene (using gene AAK1 as an example) is:

library(metafor) 
se.AAK1 <- as.numeric(se_summary[rownames(se_summary) == 'AAK1',][,-1])
HR.AAK1 <- as.numeric(HR_summary[rownames(HR_summary) == 'AAK1',][,-1])
beta.AAK1 <- log(HR.AAK1)

####First I need to use the random model to see if the test for Heterogeneity is significant or not.

pool.AAK1 <- rma(beta.AAK1, sei=se.AAK1) 
summary(pool.AAK1)
#### and this gives the following output:

#>Random-Effects Model (k = 5; tau^2 estimator: REML)
#>  logLik  deviance       AIC       BIC      AICc 
#> -2.5686    5.1372    9.1372    7.9098   21.1372   

#>tau^2 (estimated amount of total heterogeneity): 0.0870 (SE = 0.1176)
#>tau (square root of estimated tau^2 value):      0.2950
#>I^2 (total heterogeneity / total variability):   53.67%
#>H^2 (total variability / sampling variability):  2.16

#>Test for Heterogeneity:
#>Q(df = 4) = 8.5490, p-val = 0.0734

#>Model Results:
#>estimate      se     zval    pval    ci.lb   ci.ub 
#> -0.3206  0.1832  -1.7500  0.0801  -0.6797  0.0385  . 
#>---
#>Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1


####If the I^2 > 50%, we still use the Random-effect Model but if the I^2 <= 50%, we then use the Fixed-effect Model 

pool.AAK1 <- rma(beta.AAK1, sei=se.AAK1, method="FE") 
summary(pool.AAK1)
####this gives the following output:

#>Fixed-Effects Model (k = 5)
#> logLik  deviance       AIC       BIC      AICc 
#> -2.5793    8.5490    7.1587    6.7681    8.4920   

#>Test for Heterogeneity:
#>Q(df = 4) = 8.5490, p-val = 0.0734

#>Model Results:
#>estimate      se     zval    pval    ci.lb    ci.ub 
#> -0.2564  0.1191  -2.1524  0.0314  -0.4898  -0.0229  * 
#>---
#>Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

This works just fine if I got only one gene, but I need to do it all at one time for all these genes and then export the output including "Heterogeneity p-val", and all the model results "estimate, se, zval, pval, ci.lb, ci.ub " to one .txt file, each row for a gene, the output should be like this:

Gene_symbol Heterogeneity_p-val estimate    se      zval    pval    ci.lb   ci.ub
AAK1        0.0734              -0.2564    0.1191   -2.1524 0.0314  -0.4898 -0.0229
A2M         0.9664               0.1688    0.1173    1.4388 0.1502  -0.0611 0.3987

In case of need, here is a piece of sample data "se_summary"

Gene_symbol ICGC_se TCGA_se G71_se  G62_se  G8_se
A1CF        0.312   0.21    0.219   0.292   0.381
A2M         0.305   0.21    0.219   0.292   0.387
A2ML1       0.314   0.211   0.222   0.289   0.389
A4GALT      0.305   0.21    0.225   0.288   0.388
A4GNT       0.306   0.211   0.222   0.288   0.385
AAAS        0.308   0.213   0.223   0.298   0.38
AACS        0.307   0.209   0.221   0.287   0.38
AADAC       0.302   0.212   0.221   0.293   0.404
AADAT       0.308   0.214   0.22    0.288   0.391
AAK1        0.304   0.209   0.22    0.303   0.438
AAMP        0.303   0.211   0.222   0.288   0.394

And a piece of sample data "HR_summary"

Gene_symbol ICGC_HR TCGA_HR G71_HR  G62_HR  G8_HR
A1CF        1.689   1.427   0.864   1.884   1.133
A2M         1.234   1.102   1.11    1.369   1.338
A2ML1       0.563   0.747   0.535   1.002   0.752
A4GALT      0.969   0.891   0.613   0.985   0.882
A4GNT       1.486   0.764   1.051   1.317   1.465
AAAS        1.51    1.178   1.076   0.467   0.681
AACS        1.4     1.022   1.255   1.006   1.416
AADAC       0.979   0.642   1.236   1.581   1.234
AADAT       1.366   1.405   1.18    1.057   1.408
AAK1        1.04    0.923   0.881   0.469   0.329
AAMP        1.122   0.639   1.473   0.964   1.284

Answer 1

Put the data in long format, with both the effect sizes and the se data side by side, then use a split and apply rma to each of these. You can make your own version of broom 's tidy function just for rma objects.

library(metafor) 
library(reshape)
se_summary<-read.table(text="
Gene_symbol ICGC_se TCGA_se G71_se  G62_se  G8_se
AADAT       0.308   0.214   0.22    0.288   0.391
AAK1        0.304   0.209   0.22    0.303   0.438
AAMP        0.303   0.211   0.222   0.288   0.394
",header=T)

HR_summary<-read.table(text="
Gene_symbol ICGC_HR TCGA_HR G71_HR  G62_HR  G8_HR
AADAT       0.308   0.214   0.22    0.288   0.391
AAK1        0.304   0.209   0.22    0.303   0.438
AAMP        0.303   0.211   0.222   0.288   0.394
                       ",header=T)

HR_summary<-melt(HR_summary,id.vars = "Gene_symbol")%>%
  mutate(.,variable=sapply(strsplit(as.character(variable), split='_', fixed=TRUE), function(x) (x[1])))%>%
  rename(gene=variable)
se_summary<-melt(se_summary,id.vars = "Gene_symbol")%>%
  mutate(.,variable=sapply(strsplit(as.character(variable), split='_', fixed=TRUE), function(x) (x[1])))%>%
  rename(gene=variable)
HR_summary<-merge(HR_summary,se_summary,by=c("Gene_symbol","gene"),suffixes=c(".HR",".se"))



tidy.rma<-function(x) {
  return(data.frame(estimate=x$b,se=x$se,zval=x$zval,ci.lb=x$ci.lb,ci.ub=x$ci.ub,k=x$k,Heterog_pv=x$QEp#the main stuff: overall ES, etc
                    #variance components( random effects stuff): nlvls is n sites
  )) #test for heterogeneity q value and p-value
}



rbindlist(lapply(split(HR_summary, droplevels(HR_summary$Gene_symbol)),
                 function(x)with(x, tidy.rma(rma(yi=value.HR, sei=value.se,method="FE")))),idcol = "Gene_symbol2")

Answer 2

point 1: if your data is collected from different populations, you should not use fixed effect model. because HR could be difference among your populations.

point 2: if you convert HR to log(HR), therefore SE should be calculated for log(HR).

your data:

  se_summary=data.frame(
    Gene_symbol=c("A1CF","A2M","A2ML1","A4GALT","A4GNT","AAAS","AACS","AADAC","AADAT","AAK1","AAMP"),
    ICGC_se=c(0.312,0.305,0.314,0.305,0.306,0.308,0.307,0.302,0.308,0.304,0.303),
    TCGA_se=c(0.21,0.21,0.211,0.21,0.211,0.213,0.209,0.212,0.214,0.209,0.211),
    G71_se=c(0.219,0.219,0.222,0.225,0.222,0.223,0.221,0.221,0.22,0.22,0.222),
    G62_se=c(0.292,0.292,0.289,0.288,0.288,0.298,0.287,0.293,0.288,0.303,0.288),
    G8_se=c(0.381,0.387,0.389,0.388,0.385,0.38,0.38,0.404,0.391,0.438,0.394))

and

 HR_summary=data.frame(
    Gene_symbol=c("A1CF","A2M","A2ML1","A4GALT","A4GNT","AAAS","AACS","AADAC","AADAT","AAK1","AAMP"),
    ICGC_HR=c(1.689,1.234,0.563,0.969,1.486,1.51,1.4,0.979,1.366,1.04,1.122),
    TCGA_HR=c(1.427,1.102,0.747,0.891,0.764,1.178,1.022,0.642,1.405,0.923,0.639),
    G71_HR=c(0.864,1.11,0.535,0.613,1.051,1.076,1.255,1.236,1.18,0.881,1.473),
    G62_HR=c(1.884,1.369,1.002,0.985,1.317,0.467,1.006,1.581,1.057,0.469,0.964),
    G8_HR=c(1.133,1.338,0.752,0.882,1.465,0.681,1.416,1.234,1.408,0.329,1.284))

1)merge data

data=cbind(se_summary,log(HR_summary[,-1]))

2) a function to calculate meta-log HR

met=function(x) {
y=rma(as.numeric(x[7:11]), sei=as.numeric(x[2:6]))
y=c(y$b,y$beta,y$se,y$zval,y$pval,y$ci.lb,y$ci.ub,y$tau2,y$I2)
y
}

3)perform function for all rows

results=data.frame(t(apply(data,1,met)))
rownames(results)=rownames(data)
colnames(results)=c("b","beta","se","zval","pval","ci.lb","ci.ub","tau2","I2")

4)results

> results
                 b        beta        se       zval        pval
A1CF    0.27683114  0.27683114 0.1538070  1.7998601 0.071882735
A2M     0.16877042  0.16877042 0.1172977  1.4388214 0.150201136
A2ML1  -0.37676308 -0.37676308 0.1182825 -3.1852811 0.001446134
A4GALT -0.18975044 -0.18975044 0.1179515 -1.6087159 0.107678477
A4GNT   0.09500277  0.09500277 0.1392486  0.6822528 0.495079085
AAAS   -0.07012629 -0.07012629 0.2000932 -0.3504680 0.725987468
AACS    0.15333550  0.15333550 0.1170061  1.3104915 0.190029610
AADAC   0.04902471  0.04902471 0.1738017  0.2820727 0.777887764
AADAT   0.23785528  0.23785528 0.1181503  2.0131593 0.044097875
AAK1   -0.32062727 -0.32062727 0.1832183 -1.7499744 0.080122725
AAMP    0.02722082  0.02722082 0.1724461  0.1578512 0.874574077
              ci.lb       ci.ub       tau2       I2
A1CF   -0.024625107  0.57828740 0.04413257 37.89339
A2M    -0.061128821  0.39866965 0.00000000  0.00000
A2ML1  -0.608592552 -0.14493360 0.00000000  0.00000
A4GALT -0.420931120  0.04143024 0.00000000  0.00000
A4GNT  -0.177919527  0.36792508 0.02455208 25.35146
AAAS   -0.462301836  0.32204926 0.12145183 62.23915
AACS   -0.075992239  0.38266324 0.00000000  0.00000
AADAC  -0.291620349  0.38966978 0.07385974 50.18761
AADAT   0.006285038  0.46942552 0.00000000  0.00000
AAK1   -0.679728455  0.03847392 0.08700387 53.66905
AAMP   -0.310767314  0.36520895 0.07266674 50.07330