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I am having some issues interpreting the output of the glm model I am using for an eQTL analysis (an analysis of genotype vs. gene expression for a particular gene). My model is as follows:

fit <- glm(Expression ~ genotype + prep.no + sex, family = poisson, data = data)

Gene expression is given as a count value (derived from RNASeq data that has been corrected for library size), and genotype is simply a 0, 1 or 2 value denoting the number of minor alleles carried by an individual at a particular SNP locus. I know that both preparation number and the sex of an individual influences gene expression, and so I wish to correct for these two factors. Testing the model with a SNP that has previously been confirmed to influence expression of my gene, I get the following:

    Call:
glm(formula = Expression ~ genotype + prep.no + sex, family = poisson(link = "log"), 
data = ERAPdata)

Deviance Residuals: 
 Min        1Q    Median        3Q       Max  
-24.9946   -5.8912   -0.3892    4.6403   25.2830  

Coefficients:
             Estimate Std. Error  z value Pr(>|z|)    
(Intercept)  8.081717   0.004232 1909.463  < 2e-16 ***
genotype1   -0.025497   0.003396   -7.507 6.05e-14 ***
genotype2   -0.091365   0.007384  -12.374  < 2e-16 ***
prep.no2    -0.006075   0.005313   -1.143 0.252864    
prep.no3     0.001074   0.005412    0.198 0.842676    
prep.no4    -0.007511   0.005791   -1.297 0.194621    
prep.no5    -0.006958   0.005539   -1.256 0.209031    
prep.no6     0.023217   0.005812    3.994 6.49e-05 ***
prep.no7     0.026062   0.007411    3.517 0.000437 ***
sex1         0.015740   0.003433    4.584 4.56e-06 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

(Dispersion parameter for poisson family taken to be 1)

    Null deviance: 9662.4  on 131  degrees of freedom
Residual deviance: 9384.5  on 122  degrees of freedom
AIC: 10711

Number of Fisher Scoring iterations: 4

Considering the significant value of genotype1, is it correct to interpret this as: relative to genotype0, individuals with genotype1 have a decrease in expression of -0.025?
If I wish to repeat this across many SNPs, should I only be considering the significance of genotype2 for comparison's sake (as this is a pairwise comparison between the opposite homozygotes at a given SNP, and expression of the hets with genotype1 is expected to fall somewhere between levels of the homozygotes if there is in fact a genotype effect)? Also, in terms of correcting for the batch and gender effect, how is the model doing this? I thought including the terms was all that was required. How do I find the significance on genotype once gender and prep.no are controlled for? As they also have a significant effect on expression (above), they are obviously an issue.

Any comments or suggestions would be very much appreciated!

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  • $\begingroup$ Why not treat genotype as continuous, i.e., assuming the additive model? Here you treat it as a factor, right? There are some tests to deal with a factor, say F test. $\endgroup$
    – Randel
    Commented Jul 23, 2014 at 3:20
  • $\begingroup$ I didn't think of that! Yes I am currently treating it as a factor but switching to a continuous variable should do the trick - accounting for all three levels of genotype when calculating significance. Thank you!! $\endgroup$
    – Aimee
    Commented Jul 23, 2014 at 7:22

1 Answer 1

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Welcome to the site, @Aimee!

As commented above, if treating genotype as continuous, then the interpretation would be, the log incidence ratio of expression for the increase of one minor allele count, with batch and gender effects controlled. Note that here is the Poisson family and log link, so the interpretation would be different from linear regressions. In this way, a single z test for genotype would be enough.

The batch and gender effects have been controlled in the model, so you do not need to worry about their significance. The test and interpretation of genotype are both conducted with the batch and gender effects controlled.

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  • $\begingroup$ Thanks again Randel! This is a massive help and clears up a lot of things. I've been worrying about this GLM for days! $\endgroup$
    – Aimee
    Commented Jul 24, 2014 at 0:30

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