I have measured the sugar content of some potato landraces, These data are not normally distributed, I think this is mainly because I have some few individuals with extreme phenotypes. I have read in association mapping articles that many authors use normalized phenotypic data to perform association analysis. For me it is not clear the fundamentals of using transformed data into these analysis. I would be very grateful to hear your opinion into this matter.
There are three methods for handling this problem.
(1) First, you may simply delete those individuals with extreme phenotypes (if you know exactly which individuals are true outliers).
(2) Do some phenotype transformation, such as log transformation or box-cox transformations. In practice it might be difficult to find a very suitable transformation method for your data.
(3) Use robust regression instead of standard linear regression. Robust regression is based on the assumption of non-normally distributed response variables. See http://en.wikipedia.org/wiki/Quantile_regression for an example.
If you use a linear regression or a linear mixed model for association mapping you assume Gaussian distributed residuals. This is why one tries to transform non-normally distributed phenotypes by taking a transformation function such as log, sqrt or boxcox. However, as Zitong mentioned, finding the right transformation is non-trivial.
There is a paper in Nature Communications that automatically finds the optimal transformation for non-normally distributed phenotypes when using a linear mixed model:
http://www.nature.com/ncomms/2014/140919/ncomms5890/abs/ncomms5890.html
Also one should be careful with transformations, since a transformation of the phenotype might lead to a different interpretation of the results!
A Bayesian association mapping might be an option as it will work with nonnormal and/or small data sets. You may want to check:
http://bioinformatics.oxfordjournals.org/content/25/8/1033.full
http://www.worldscientific.com/doi/abs/10.1142/S0219720014410108
.
The answer is provided by Zitong Li is a very good answer.
Best Regards
amin baghizadeh
It would be advisable if you consult local statistician with your data.
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