Is there a way to do GWAS on phenotype data that is not normally distributed?

For example, if you were measuring a trait as a proportion, and the majority of the data consisted of 0.00 with a long tail of variation. Or, perhaps the data was skewed the other way where the majority of the observations were 100% with a long tail towards zero.

Is there a GWAS method that is appropriate for these types of distributions?

  • $\begingroup$ Welcome to the site. I might be a bit dense but I don't understand the problem. In GWAS one looks which variants are associated with which trait. If you don't have information (or there is no variation in your dataset) for a given trait you can't relate the genome variants with it. $\endgroup$
    – llrs
    May 16 '18 at 6:55
  • 1
    $\begingroup$ @Llopis There is still variation in a non-normal dataset. For example, 80% of your observations for a phenotypic trait may be measured at 0.00, but that leaves 20% at a value >0.00. Every test I have seen however requires the assumption that the data is normally distributed. My question is are there any methods for performing GWAS on non-normally distributed phenotype data. $\endgroup$
    – jhurst5
    May 16 '18 at 15:06
  • $\begingroup$ Thanks for clarifying, now I understand better your problem. Perhaps it would help -to get an answer- to list some methods that assume normality in the data. $\endgroup$
    – llrs
    May 18 '18 at 8:45
  • $\begingroup$ Yes, but like any other statistical test, you need to know the distribution of your data and pick an appropriate statistical test for it. $\endgroup$
    – David S
    Dec 15 '20 at 22:20

Yes, that can be done.

A common approach for these types of analysis is to carry out a transformation on the data first in order for it to have a normal distribution (the most general approach called an inverse normal transformation, among other names), then run the test on the transformed data.

As an example, for data that are positive and zero-skewed, a log transformation may be appropriate.

The transformation approach does require variation in the data values, though. For a trait that is exactly zero for most values, it might be better to treat it as a binary/categorical trait for the purpose of association testing, rather than a quantitative trait. Most association testing packages should allow associations for binary traits to be tested.


as mentioned in previous answers, transformations are frequently used. One commonly used method is quantile normal transformation. Basically you calculate the quantile from the original data and match it to a standard normal distribution. This transforms your data to a standard normal distribution. Even for traits that are naturally normal distributed like height, it is still a good idea to do this transformation as it has been shown to improve power as well.


Sure, you would use the negative binomial distribution when the majority of data was around 0. In other words the data is clustered with the standard deviation far greater than the mean. Most general linear modelling (GLM) will incorporate this approach.


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