Download Figure 1 The Proposed Generalized Linear Mixed Models

Design matrix for fixed and random effects
Model (A)
Yij ~ gamma(ij ,  )
Log (ij )  ij    ui
i  1,..., g ; j  1,..., si
u1 ,..., ug ~ N (0,  2 I )
Model (B)
Yij ~ gamma(ij ,  )
Log (ij )  ij    ui
i  1,..., g ; j  1,..., si
u1 ,..., u g ~ N (0, G )
Parameters
SNP A
SNP B
SNP C
Parameters
SNP A
SNP B
SNP C

u1
u2
u3
intercept gene 1 gene 2 gene 3
1
1
0
0
1
1
1
0
1
0
1
1

u1
u2
u3
intercept gene 1 gene 2 gene 3
1
1
0
0
1
1
1
0
1
0
1
1
Covariance matrix G
 2



2


2

 

 1
e d12 /  e d13 /  


 2 e d21 / 
1
e d23 /  
e d31 /  e d32 / 
1 

dii '  distance between physical locations of
gene i and gene i’
Supplementary Fig. 1 The proposed Generalized Linear Mixed Models, with design matrix and covariance
matrix for a hypothetical gene set with three genes and three SNPs: SNP A is on gene 1, SNP B is on genes 1
and 2, SNP C is on genes 2 and 3. For both models, the outcome variable for the mixed models is the chi-square
statistic for Cochran-Armitage trend test for single SNP.