The potential interaction between susceptibility genotypes (G) and environmental exposures (E) has recently received a lot of attention in epidemiologic studies for understanding the etiology of complex human diseases. Statistical assessment of the GxE interaction can be performed in nontraditional case-only designs achieving a great statistical power improvement over traditional case-control/cohort designs studies. Although the standard methods of meta-analysis can be applied to assess GxE interaction, the fact that the available studies have to follow all the same design remains a major problem. In the present study we propose a novel multivariate method for meta-analysis that can incorporate studies with different type of data performed under different designs. Based on the proposed method neither individual patient data nor the simultaneous evaluation of both genetic and environmental effect are necessary. The method is simple and fast and can be extended to account for multiple genes resulting thus in the estimation of GxG interactions. The assumptions inherently made by different designs (e.g. combining case-only and case-control studies) can also be assessed. As an example we investigate the interaction of NAT2 polymorphism and smoking in bladder cancer illustrating that the multidimensional multivariate methods outperformed the classical univariate analysis. We conclude that the proposed method constitutes a useful framework for performing meta-analysis for GxE interaction
Nikolaos Nikolakakis, Niki Dimou, Katerina Pantavou, Pantelis Bagos A Multivariate Method for Meta-Analysis of Studies Investigating Gene-Environment Interactions, 10th Conference of the Hellenic Society for Computational Biology and Bioinformatics (HSCBB), Biomedical Research Foundation Academy of Athens (BRFAA/IIBEAA), Athens, Greece, 9-11 October 2015.
Nikolaos Nikolakakis, Niki Dimou, Katerina Pantavou, Pantelis Bagos Methodology for meta-analysis of studies detecting gene-environment interactions, 37th Scientific Conference of the Hellenic Society of Biological Sciences, Volos, Greece, 21-23 May 2015.
clear
set more off
input study n101 n001 n111 n011 n100 n000 n110 n010 n1x1 n0x1 n1x0 n0x0
1 63 50 171 90 51 33 165 124 234 140 216 157
2 14 16 140 83 . . . . 154 99 . .
3 22 17 99 92 44 30 65 64 121 109 109 94
4 22 15 101 40 6 5 11 17 123 55 17 22
5 23 20 72 34 11 11 25 22 95 54 36 33
6 13 8 70 39 . . . . 83 47 . .
7 14 9 51 31 . . . . 65 40 . .
8 11 5 55 30 6 12 39 44 66 35 45 56
9 25 19 32 22 29 44 20 23 57 41 49 67
10 3 5 52 31 10 11 24 25 55 36 34 36
11 4 6 42 25 11 20 17 32 46 31 28 52
12 2 1 42 22 . . . . 44 23 . .
13 2 28 1 19 . . . . 3 47 . .
14 7 11 9 20 7 38 6 40 16 31 13 78
15 3 3 9 11 . . . . 12 14 . .
16 5 2 4 12 39 21 28 21 9 14 67 42
17 88 49 301 169 190 102 255 148 389 218 445 250
18 5 21 12 47 8 54 2 82 17 68 10 136
19 12 5 111 73 29 24 82 79 123 78 111 103
20 28 30 22 21 45 35 14 16 50 51 59 51
21 13 89 29 194 8 10 98 209 42 283 106 219
22 91 66 637 340 199 131 438 362 728 406 637 493
23 78 49 253 140 131 104 151 126 331 189 282 230
24 . . . . 172 127 54 41 . . 226 168
25 . . . . 1056 780 1310 949 . . 2366 1729
26 . . . . 38 32 13 20 . . 51 52
27 . . . . 75 38 156 96 . . 231 134
28 . . . . 223 161 223 190 . . 446 351
29 . . . . 127 126 117 102 . . 244 228
30 . . . . 54 45 68 58 . . 122 103
31 . . . . 183 167 66 69 . . 249 236
32 . . . . 65 39 93 67 . . 158 106
33 . . . . 132 67 121 77 . . 253 144
34 . . . . 181 106 193 121 . . 374 227
35 . . . . 251 172 482 324 . . 733 496
36 . . . . 82 56 136 90 . . 218 146
37 . . . . 30 95 6 9 . . 36 104
38 . . . . . . . . 74 37 118 89
39 . . . . . . . . 21 9 16 11
40 . . . . . . . . 76 38 26 20
41 . . . . . . . . 42 18 94 60
42 . . . . . . . . 12 41 13 88
43 . . . . . . . . 11 53 43 127
44 . . . . . . . . 22 94 7 115
45 . . . . . . . . 52 37 56 91
46 . . . . . . . . 8 104 24 195
47 . . . . . . . . 32 21 56 40
48 . . . . . . . . 5 11 21 13
49 . . . . . . . . 47 10 11 9
50 . . . . . . . . 179 118 172 117
51 . . . . . . . . 35 21 163 157
52 . . . . . . . . 18 51 13 75
end
*Univariate meta-analysis*
* synergy factor *
gen sf=log((n111*n001*n100*n010)/(n110*n000*n101*n011))
replace sf=log(((0.5+n111)*(0.5+n001)*(0.5+n100)*(0.5+n010))/((0.5+n110)*(0.5+n000)*(0.5+n101)*(0.5+n011))) if n101==0|n001==0|n111==0|n011==0|n100==0|n000==0|n110==0|n010==0
gen stsf =sqrt(1/n101+1/n001+1/n111+1/n011+1/n100+1/n000+1/n110+1/n010)
replace stsf=sqrt(1/(n101+0.5)+1/(n001+0.5)+1/(n111+0.5)+1/(n011+0.5)+1/(n100+0.5)+1/(n000+0.5)+1/(n110+0.5)+1/(n010+0.5)) if n101==0|n001==0|n111==0|n011==0|n100==0|n000==0|n110==0|n010==0
metan sf stsf, eform random xlab(0.1,1,3)
* Univariate Meta-analysis case only *
gen a1=log((n111*n001)/(n101*n011))
replace a1=log(((0.5+n111)*(0.5+n001))/((0.5+n101)*(0.5+n011))) if n101==0|n001==0|n111==0|n011==0
gen sta1=sqrt(1/n101+1/n001+1/n111+1/n001)
replace sta1=sqrt(1/(n101+0.5)+1/(n001+0.5)+1/(n111+0.5)+1/(n011+0.5)) if n101==0|n001==0|n111==0|n011==0
metan a1 sta1, eform random xlab(0.1,1,3)
* Univariate Meta-analysis control only *
gen a2=log((n000*n110)/(n100*n010))
replace a2=log(((0.5+n000)*(0.5+n110))/((0.5+n100)*(0.5+n010))) if n000==0|n110==0|n100==0|n010==0
gen sta2=sqrt(1/n000+1/n110+1/n100+1/n010)
replace sta2=sqrt(1/(n100+0.5)+1/(n110+0.5)+1/(n100+0.5)+1/(n010+0.5)) if n000==0|n110==0|n100==0|n010==0
metan a2 sta2, eform random xlab(0.1,1,3)
*Multivariate meta-analysis*
*case only*
gen b1=log((n111*n001)/(n101*n011))
replace b1=log(((0.5+n111)*(0.5+n001))/((0.5+n101)*(0.5+n011))) if n101==0|n001==0|n111==0|n011==0
gen V11=(1/n101+1/n001+1/n111+1/n001)
replace V11=(1/(n101+0.5)+1/(n001+0.5)+1/(n111+0.5)+1/(n011+0.5)) if n101==0|n001==0|n111==0|n011==0
replace V11=. if b1==.
*control only*
gen b2=log((n000*n110)/(n100*n010))
replace b2=log(((0.5+n000)*(0.5+n110))/((0.5+n100)*(0.5+n010))) if n000==0|n110==0|n100==0|n010==0
gen V22=(1/n000+1/n110+1/n100+1/n010)
replace V22=(1/(n100+0.5)+1/(n110+0.5)+1/(n100+0.5)+1/(n010+0.5)) if n000==0|n110==0|n100==0|n010==0
replace V22=. if b2==.
*gene marginal*
gen b3=log((n1x1*n0x0)/(n1x0*n0x1))
replace b3=log(((0.5+n1x1)*(0.5+n0x0))/((0.5+n1x0)*(0.5+n0x1))) if n1x1==0|n0x0==0|n1x0==0|n0x1==0
gen V33=(1/n1x1+1/n0x0+1/n1x0+1/n0x1)
replace V33=log(1/(n1x1+0.5)+1/(n0x0+0.5)+1/(n1x0+0.5)+1/(n0x1+0.5)) if n1x1==0|n0x0==0|n1x0==0|n0x1==0
replace V33=. if b3==.
*gene only*
gen b4=log((n101*n000)/(n100*n001))
replace b4=log(((0.5+n101)*(0.5+n000))/((0.5+n100)*(0.5+n001))) if n101==0|n000==0|n100==0|n001==0
gen V44=(1/n101+1/n000+1/n100+1/n001)
replace V44=(1/(n101+0.5)+1/(n000+0.5)+1/(n100+0.5)+1/(n001+0.5)) if n101==0|n000==0|n100==0|n001==0
replace V44=. if b4==.
gen V12=0
replace V12=. if b1==.
replace V12=. if b2==.
gen V13=0
replace V13=. if b1==.
replace V13=. if b3==.
gen V14=-(1/n101)-(1/n001) if n101!=.|n001!=.
replace V14=-(1/(n101+0.5))-(1/(n001+0.5)) if n101==0|n001==0
replace V14=. if b1==.
replace V14=. if b4==.
gen V23=0
replace V23=. if b2==.
replace V23=. if b3==.
gen V24=(1/n000)+(1/n100) if n000!=.|n100!=.
replace V24=-(1/(n000+0.5))-(1/(n100+0.5)) if n000==0|n100==0
replace V24=. if b2==.
replace V24=. if b4==.
gen V34=(1/n1x1)+(1/n0x0)+(1/n1x0)+(1/n0x1)
replace V34=. if b3==.
replace V34=. if b4==.
* Fitting of bivariate model*
mvmeta b V, mm var(b1 b2)
di exp(_b[b1]), exp(_b[b2])
lincom b1 -b2,or
* Fitting of trivariate A model*
mvmeta b V, mm vars(b1 b2 b3)
di exp(_b[b1]), exp(_b[b2]), exp(_b[b3])
lincom b1 -b2,or
* Fitting of trivariate B model*
mvmeta b V, mm vars(b1 b2 b4)
di exp(_b[b1]), exp(_b[b2]), exp(_b[b4])
lincom b1 -b2,or
* Fitting of tetravariate model*
mvmeta b V, mm vars(b1 b2 b3 b4) noposdef
di exp(_b[b1]), exp(_b[b2]), exp(_b[b3]), exp(_b[b4])
lincom b1 -b2,or