Should we use the Sum of Neff when we do a meta-analysis of meta-analyzed data?

[Camille Williams]

Hi Andrew, 

I had questions on the Sum of Neff when conducting a meta-analysis and munging my meta-analyzed results. I also had a question regarding running GSEM on meta-analyzed data.

I am only working with summary statistics from binary phenotypes. 

I want to get meta-analysed summary statistics using METAL from summary statistics of a meta-analysis (publicly available online) and summary statistics from my GWAS. I will then use these new sumstats for GSEM and munge my new meta-analysed summary statistics to examine h2, look at rg with other summary statistics. 

1. For my meta-analysis with METAL, I am using the sample size method (uses p-value and direction of effect, weighted according to sample size) and not the standard error method because my effect size estimates and standard errors are not in the same units in all studies. Typically, you give the sum of the Neff (e.g., Neff UKB and Neff for the online meta-analysis). But, in light of the recent recommendations on the GenomicSEM for estimating heritability, I thought it would be better to use the sum of effective sample size (e.g., Neff UKB and the sum of Neff for the online meta-analysis). Is that correct?

2. I get my newly meta-analyzed summary statistics, where the weight column corresponds to the sum of Neff by SNP. I munge each meta-analyzed result with N = Weight because my weight corresponds to the sum of the Neff. My weight = Sum of Neff because that is the input N I provided in METAL. 

3. Before running my GSEM with SNP effects, I need to prepare the summary statistics for the GWAS. The tutorial says "Note that it is possible to back out a beta and SE when only Z-statistics are provided as long as you have the total sample size for a continuous trait or the sum of effective sample sizes across the contributing cohorts for a binary trait”. 

I found the following formula online (see screenshot for colnames). Is this line of code to calculate SE correct?

A1 <- fread("MHD_ANX/METAANALYSIS1.TBL")
A1$SE =1/sqrt(2*A1$MinFreq(1-A1$MinFreq)(A1$Weight+ A1$Zscore^2))

Thank you! 

Best, 

Camille 

[agro...@gmail.com]

Hi Camille, 

Response to your questions in order: 

1. There is definitely precedent to use effective sample size in METAL (e.g., from the opioid use disorder GWAS; https://jamanetwork.com/journals/jamapsychiatry/fullarticle/2766708) for the exact reasons that you highlighted as far as different scales. My sense is the same logic that we apply for using sum Neff for the liability conversion (it's a more accurate estimate of effective sample size that accounts for ascertainment variability across cohorts) applies here. In short, yep I would use sum of Neff. 

2. Sounds like you should be all set on the munge front to use the weight column. 

3. The sumstats function will take care of that for you; so if you use the lpm argument and provide the sum of effective N then it will automatically back out those betas from Z. 

Best, 

  Andrew

[Camille Williams]

Hi, 

Thank you for your response! However, I'm still a bit uncertain about what to write for question 3 based on what you proposed and https://github.com/GenomicSEM/GenomicSEM/wiki/2.-Important-resources-and-key-information. 

Is this correct? 

For meta-analyzed binary GWAS summary stats,  se.logit = F, OLS = F, linprob= T, prop = 0.5 and I don't need to give N because I have a weight column 

For binary GWAS summary stats with SE of logBeta, se.logit = T, OLS = F, linprob= F, and I don't need to give N 

Thanks! 

Camille 

[agro...@gmail.com]

Hi Camille, 

That's right for meta-analyzed binary GWAS analyzed using a linear model or that have Z-stats only, except that in this case you don't need to provide prop = 0.5 as the sumstats function does not take a prop argument anymore. That's also correct for binary GWAS where you are not backing out logistic beta from Z. 

Best, 

  Andrew

[Camille Williams]

Thank you!