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Table 3 Summary of hierarchical modelling fits (parameter estimates [SEs]) for selected genetic effects (βG), prior covariates (Z'π) and prior correlations (σ2A) for simulation with homocysteine concentration as the causal variable

From: Use of pathway information in molecular epidemiology

 

No prior

N(0, σ2)

N(Zπ, σ2)

N(0, σ2eZ'ψ)

N(Z'π, σ2eZ'ψ)

N(Z'π,σ2(I-ρA)-1)

Genetic main effects

      

G3: MTD

-0.370 (0.113)

-0.341 (0.111)

-0.352 (0.109)

-0.327 (0.112)

-0.340 (0.109)

-0.106 (0.114)

G4: MTCH

-0.258 (0.133)

-0.229 (0.123)

-0.245 (0.124)

-0.216 (0.120)

-0.207 (0.117)

-0.304 (0.127)

G9: SHMT

0.300 (0.121)

0.282 (0.112)

0.272 (0.112)

0.155 (0.109)

0.336 (0.079)

0.128 (0.112)

G10: MTHFR

0.335 (0.116)

0.301 (0.110)

0.313 (0.113)

0.293 (0.110)

0.245 (0.116)

0.198 (0.114)

G11: MS

0.240 (0.112)

0.206 (0.106)

0.219 (0.114)

0.106 (0.095)

0.190 (0.102)

0.060 (0.112)

G12: SAHH

-0.809 (0.131)

-0.735 (0.126)

-0.760 (0.135)

-0.752 (0.128)

-0.760 (0.125)

-0.648 (0.127)

G13: CBS

1.492 (0.134)

1.360 (0.123)

1.417 (0.129)

1.400 (0.129)

1.419 (0.133)

1.149 (0.123)

Prior covariates

      

π1: folate (mean)

  

-0.020 (0.638)

 

-0.668 (0.192)

-0.641 (0.453)

π2: methionine (mean)

  

0.115 (0.480)

 

-0.266 (0.151)

0.203 (0.377)

π3: connections (mean)

  

0.000 (0.092)

 

0.113 (0.027)

0.022 (0.030)

ψ1: folate (variance)

   

0.171 (0.337)

-0.312 (1.536)

 

ψ2: methionine (variance)

   

-0.181 (0.327)

-0.913 (1.259)

 

ψ3: connections (variance)

   

0.472 (0.185)

0.901 (0.390)

 

Posterior variances and correlations

     

σβ = SD(β|Z)

 

0.492 (0.109)

0.658 (0.143)

1.175 (0.491)

2.362 (2.714)

0.877 (0.285)

σπ = SD(π)

  

0.864 (0.385)

 

0.858 (0.356)

0.889 (0.403)

σψ = SD(ψ)

   

0.342 (0.059)

1.350 (1.010)

 

ρ = corr(β|A)

     

0.597 (0.170)