Twin pair analysis (MZ, DZ twin pairs)

Hi

I have a question on how to deal with following experimental setup.
I have data on microbiome and metabolomics for twins that are either MZ or DZ, and thus we have only pairs in the dataset.
I would like to assume the twins are unrelated, to be generalizable to another dataset that I am using. However, I am not sure how to implement this in a linear mixed model. I followed the setup from www.nature.com/articles/s41598-022-07632-3 , where they also assume twins being unrelated.

Suppose I want to model the microbe abundances (303 columns, “g”) (that have been previously regressed against confounders) , in a linear mixed model to find differential metabolites across the group of interest (here diagnosis “MD”, a categorical variable of 7 classes), I do the following.

lme <- lme(g ~ relevel(factor(MD), ref="HC"), random = list(ind = ~(0+dummy(Zygosity,"DZ")), ind =~ (0+dummy(Zygosity,"MZ"))) , data=microb.conf)

assuming a random slope for each individual, “ind” is identified as either I1 or I2, i.e. the individual in the pair, which I’m not fully understanding why.
For some of the genera I got this error message that the system is “computationally singular”. I read a lot on this, to specify the covariance structure, but I am a bit lost on how to deal with this in this specific setup.

Any help would be greatly appreciated,
thanks a lot!

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