Z statistics from meta-analysis for genomic SEM

[Lucy]

For summary statistics which have Z statistics (rather than effect sizes and standard errors, or odds ratio and standard errors) and p-values from METAL meta-analysis, how would you use the munge() function? It looks like the munge() function requires effect sizes/odds ratio and standard errors, and doesn't work if you have just Z statistics.

Also, if you have Z statistics from METAL from multiple binary traits (and not both binary and continuous traits together), in the sumstats() function would you do se.logit=F, OLS=T, and linprob=F and not state the sample/population prevalence (i.e., have them be NA)?

[agro...@gmail.com]

Hi Lucy, 

The munge function should work if you only have Z-statistics; it only requires that the effect column be signed (i.e., it is not the absolute value of Z-statistics). For the sumstats function, you do need an effect and standard error column. If you just have Z-statistics for binary traits you can back out the logistic beta and it's SE by calculating the SE as 1/sqrt(sum(eff_N/4)*MAF) and the logistic beta as Z/sqrt(sum(eff_N/4)*MAF). Where sum(eff_N/4) is the sum of the effective sample sizes  across the contributing cohorts (I think METAL automatically outputs a sum of effective sample sizes column that you could use for these equations). Then you would treat these just like they were a logistic beta and it's SE and set se.logit = T, OLS=F, and linprob=F. 

Best, 

  Andrew

[Lucy]

Hi Andrew,

Thank you very much. So we can use the Z statistics as the effect size for the munge() function because for the effect size part you're only using the sign of the effect size which is the sign of the Z-statistics? I noticed my original Z-statistics is slightly different from the munge() function's final Z statistics, but pretty close.

Thanks, I'll do that.

[Lucy]

Also, by any chance do you mean logistic beta = Z / sqrt(sum(eff_N/4)*MAF*(1-MAF)) and SE = 1/sqrt(sum(eff_N/4)*MAF*(1-MAF)), where sum(eff_N/4) =  sum of the effective sample sizes across the contributing cohorts from the Weight output of METAL?

On Monday, June 21, 2021 at 9:55:20 PM UTC-4 agro...@gmail.com wrote:

[agro...@gmail.com]

Hi Lucy, 

Yes, that's right as far as the equations being  logistic beta = Z / sqrt(sum(eff_N/4)*MAF*(1-MAF)) and  SE = 1/sqrt(sum(eff_N/4)*MAF*(1-MAF)). Great catch! I think METAL outputs sum(eff_N), but you'll want to confirm that, which you would then divide by 4 in the context of these equations. 

As far as the slight discrepancies between Z in your input and output file from munge, the reason for that is that munge backs out Z using the p-values in the summary statistics files, and then attaches a sign to it based on the effect column (whether that be a Z-statistic, beta, OR, etc.). So the difference should be attributable to rounding, and really minimal, but if you are seeing any larger differences let me know and we can take a look. 

-Andrew