control}, γ is a fixed effect incorporating the effect of age, αbatch(i,j) is a fixed effect included to accommodate an experimental batch effect (96-well plate format), where the function batch(⋅) is a function mapping each sample to a batch (plate) ∈ {1,2,3}. The λi are independently Gaussian distributed with mean zero and variance σ2 λ, for subject i, representing inter-individual variability across tissues. κ ik are independently Gaussian distributed with mean zero and variance σ2 κ, for subject i and tissue k, representing within-individual variability. εijk is the residual error term, incorporating technical (aliquot) variability, assumed to be independently Gaussian distributed with mean zero and variance σ2 ε. The model was fitted in R, using the lme4 package[57] and the lmer() function, using maximum-likelihood. A likelihood ratio test was applied to assess the significance of the tissue effect (β), which is the parameter of main interest in the tissue differential expression analysis. The p-value of the tissue effect in each model was calculated using a likelihood ratio (LR) test with the D = −2*log(LR) as the test statistic, which can be approximated by a Chi-square distribution with one degree of freedom. The p-values were adjusted for multiple testing by FDR
