The GWAS effect type

Each GWAS file holder, that is a study-level file(s) where analyses data are combined together, or an analysis-level file(s), where analyses are separated, has an effect type associated with it.

The normalisation process will use this effect type information to determine how the effect size summary statistic will be standardised. Upon standardisation the effect type and effect size may then be changed to it’s normalised form.

The table below indicates the effect types that are available for use in the metadata descriptions and what they are normalised to. All the effect type strings are represented in lower-case, even if that is not the way they would normally be used in scientific literature.

The various transformations are motivated by the normalisation pipelines original use, that is to use summary statistics in techniques such as Mendelian randomisation.

In essence, effect sizes from binary traits are log transformed and those from continuous traits are converted to some sort of beta coefficient (i.e., a mean difference).

GWAS effect types

Metadata effect type	Description	Outputted effect type
beta	The beta coefficient (i.e., the mean difference) from a linear model, typically given in QTL analyses.	beta
or	Odds ratio from a logistic regression model, typically given for binary traits.	log_or
rr	Risk ratio, typically given for binary traits.	log_rr
hr	Hazard ratio, typically given for time to event analyses.	log_hr
log_or	log transformed odds ratio, typically given for binary traits.	log_or
log_rr	log transformed risk ratio, typically given for binary traits.	log_hr
log_hr	log transformed hazard ratio, typically given for to to event analyses.	log_hr
z_score_cc	Z-score, seen in some eQTL studies. These are converted to standardised betas, equivalaent to correlation coefficients.	cc
z_score_log_or	Z-scores that need to be converted to log odds ratios.	log_or
direction_beta	The effect size is a signed effect direction, 1/-1, that needs to be imputed to a beta coefficient.	beta
direction_log_or	The effect size is a signed effect direction, 1/-1, that needs to be imputed to a log odds ratio.	log_or

Some more information on the transformations of the effect types/sizes is given below.

z_score_cc

When the effect size is a z-score (Z), or equivalently a z-statistic, it is transformed to a standardised beta (or correlation) coefficient. This transformation requires the allele frequency and the sample size to be known for each variant. For the sample size (N), if a variant specific sample size is known then it is used, if only a global sample size is known, then it will be used instead. For the allele frequency (AF), if a study specific allele frequency is known, then it is used, if not then the reference population allele frequency defined in the cohort metadata is used. The formulas for these transformations are defined below. See the eQTLgen README file for the source of these transformations.

The beta:

\[beta = \frac{Z}{\sqrt{2{AF}{(1-AF)}{(N+Z^2)}}}\]

The standard error:

\[se = \frac{1}{\sqrt{2AF{(1-AF)}{(N+Z^2)}}}\]