Hi Dear all,

I have some gene expression data samples from different tissue types
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- 120 samples from blood (B)
- 20 samples from Liver (L)
- 15 samples from Kidney (K)
- 6 samples from heart (H)
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All the samples are from different individuals, so there are in total 161
individuals from which the DNA was collected.

For each sample DNA, the expression level of 200 genes were obtained, so the
whole expression data is a 161 x 200 matrix.

The purpose of my project is to interrogate, across the 200 genes, how many
of them have an expression level consistent across all the tissue types
examined, how many of them have an expression level different between any
two of the tissue types, how many of them have an expression level unique to
only one tissue (i.e., gene20 is expressed at a very low level (0.1) in
Liver, but expressed at the same level (~0.7) across all the other tissue
types).
So my hypotheses are:
H0: Mean(B)=Mean(L)=Mean(K)=Mean(H)
H1: Mean(B)≠Mean(L)=Mean(K)=Mean(H) or Mean(L)≠Mean(B)=Mean(K)=Mean(H) or
     Mean(K)≠Mean(B)=Mean(L)=Mean(H) or Mean(H)≠Mean(B)=Mean(K)=Mean(L)
H2: Mean(B)≠Mean(L)≠Mean(K)≠Mean(H)
In my analysis, the gene expression level is the dependent value (Y), the
tissue-type is the fixed effects, the inter-individual variation and the
batch effects are the random effects. So I was suggested to use the 'lme'
function to do the analysis.We want to compare the Likelihood ratio
between models based on different hypothesis. i.e., if I want to see, for
one gene, if the expression levels are all different between any two tissue
 types, that is to compare H2 to H1, if the p value corresponding to the
D_H2H1=likelihoodRatio(H2)-likelihoodRatio(H1) in a chi-square distribution
is less than 0.05, then we will say H2 is accepted.
However, my problem is, I don't know how to specify these parameterizations
in 'lme' function based H0, H1 and H2, respectively. Can anyone help me with
that?

Thank you very much,

Karena

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