Meta Analysis of SNPxEnvironment Interaction

Introduction

The meta-analysis of SNP-Environment interaction regression models is possible by jointly meta-analyzing and testing the SNP and SNPxE beta coefficients from an interaction regression model:

$E(Y)=\beta _{0}+\beta _{1}E+\beta _{2}{\text{SNP}}+\beta _{3}E\times {\text{SNP}}$

The joint meta-analysis:

• produces summary estimates of β₂ and β₃
• produces the estimated covariance matrix of ${\hat {\beta }}_{2}$ and ${\hat {\beta }}_{3}$
• computes a test statistics for the null hypothesis: β₂=0 and β₃=0
• computes a test of homogeneity of the regression slopes

The joint meta-analysis method has been implemented in METAL available from http://www.sph.umich.edu/csg/abecasis/Metal (Metal Documentation). Individual studies can obtain the required beta and covariance estimates for interaction regression models using QUICKTEST version 0.95 and later (http://toby.freeshell.org/software/quicktest/) and ProbABEL version 0.1-3 and later (http://mga.bionet.nsc.ru/~yurii/ABEL/GenABEL/).

Implementation

The joint meta-analysis is executed through the SCHEME INTERACTION command. The following commands must be used for each data file:

MARKERLABEL [LABEL]

ALLELELABELS [LABEL1 LABEL2]

EFFECTLABEL [LABEL]

STDERRLABEL [LABEL]

INTEFFECTLABEL [LABEL]

INTSTDERRLABEL [LABEL]

INTCOVLABEL [LABEL]

If MINMAXFREQUENCY ON is used, FREQLABEL must be specified. If AVERAGEFREQUENCY ON is used, in addition to FREQLABEL, WEIGHTLABEL also must be specified to calculate the average frequencies of alleles. Using the sample size as the weight to calculate average allele frequency is strongly suggested. In this case, frequency results in the output will be the same as frequency results from SCHEME SAMPLESIZE.

Two columns of directions will appear in the output of SCHEME INTERACTION, one for the direction of the main effect, one for the direction of the interaction term.

The output columns are:

Effect - Summarized estimate of the SNP beta coefficient

StdErr - Estimated standard error of the SNP beta coefficient

IntEffect - Summarized estimate of the SNPxE beta coefficient

IntStdErr - Estimated standard error of the SNPxE beta coefficient

IntCov - Estimated covariance between the SNP beta coefficient and the SNPxE beta coefficient

ChiSq2df - Joint test of the SNP beta coefficient and SNPxE beta coefficient

P-value - P-value of ChiSq2df

Direction - Study-specific direction of the SNP beta-coefficient

DirectionInt - Study-specific direction of the SNPxE beta-coefficient

HetChiSq - Heterogeneity test statistic

HetDf - Heterogeneity test statistic degrees of freedom

HetPVal - Heterogeneity p-value

If ANALYZE HETEROGENEITY is specified, the heterogeneity test statistic, degrees of freedom and p-value will be produced in the output columns: HetChiSq, HetDf and HetPVal.

The command, GENOMICCONTROL ON, adjusts the test statistics within each sample by λ_GC, which is either pre-specified or calculated.

For sample i, the Wald test statistic for each SNP is calculated to test the joint significance of β_SNP,i and β_SNPxE,i:

$W_{i}={\mathbf {\beta }}_{i}^{T}\Sigma _{i}^{-1}{\mathbf {\beta }}_{i}$

Under the null hypothesis, these W_i's follow a chi-square distribution of 2 df. The median statistic from this distribution is 1.386294, so

$\lambda _{GC}={\frac {{\text{median observed}}W_{i}}{1.386294}}$

for this sample.

Example

CUSTOMVARIABLE TotalSampleSize
LABEL TotalSampleSize as N
SCHEME INTERACTION

SEPARATOR TAB
MARKER SNP
ALLELE EFFECT_ALLELE NON_EFFECT_ALLELE
EFFECT  BETA
STDERR  SE 
INTEFFECT BETA_INT
INTSTDERR SE_INT
INTCOV COV
WEIGHT N 

PROCESS results1.txt
PROCESS results2.txt
PROCESS results3.txt
PROCESS results4.txt
PROCESS results5.txt

OUTFILE jointmeta .txt
ANALYZE 

OUTFILE jointmeta_het .txt
ANALYZE HETEROGENEITY

QUIT