Testing Maternal-Fetal Genotype Incompatibility With Mother-Offspring Pair Data

1. Department of Epidemiology and Biostatistics, Michigan State University, East Lansing, Michigan 48824 USA 2. Division of Biostatistics, Department of Pediatrics, University of Arkansas for Medical Sciences, Little Rock, AR, 72202 USA 3. Department of Statistics and Probability, Michigan State University, East Lansing, Michigan 48824 USA 4. Department of Mathematical Science, Peking University, Beijing, China 100871 5. Perinatology Research Branch, NICHD/NIH, Hutzel Women’s Hospital, Detroit, Michigan 48201 USA


P R O T E O M I C S A N D G E N O M I C S R E S E A R C H P R O T E O M I C S A N D G E N O M I C S R E S E A R C H P R O T E O M I C S A N D G E N O M I C S R E S E A R C H ISSN NO: 2326-0793
Freely Available Online

Methods
We develop a two-stage model for testing the MFG incompatibility, and further conduct a simulation study.

The two-stage method for MFG incompatibility
Step 1. Determination of allelic effect Step 1 determines the allelic effect between the two alleles and its scenario at each SNP. We first examine the minor allele frequency and the HWE for each SNP. Only those SNPs having a minor allele frequency (p ≥ 0.01) and satisfying the HWE are kept for further study on the examination of allelic effect.
The HWE is examined with a chi-square test in the combined mother and offspring control populations with a cut-off p-value > 0.0001 of the chi-square test.
To study the gene-gene interaction between the mother and her offspring at a given SNP, a composite SNP genotype of the mother and offspring pair is derived by combining the two. For example, if the mother genotype at a given SNP is 'AA' and the offspring genotype is 'AB', the composite genotype is 'AA_AB'.
There are seven possible composite genotypes, see Table 1 for details. Among them, three are compatible: 'AA_AA', 'AB_AB' and 'BB_BB', and the rest are incompatible.
The allelic effect is examined through a subgroup analysis using only those mother-offspring pairs that had compatible genotypes, i.e. 'AA_AA', 'BB_BB', and 'AB_AB'. In doing so, the MFG incompatibility effect is not present and any significance is attributable to the allelic effect.

Step 2. Testing of MFG incompatibility
Step 2 tests the MFG incompatibility effect following each scenario determined in Step 1. A total of 4 scenarios were adopted accordingly to test the MFG incompatibility, see Table 2

Strong allelic interaction effect:
Where the heterozygous effect is the largest or smallest.
A logistic regression model was fitted to all motheroffspring pairs to test the MFG incompatibility adjusting for mother's AB genotype effect β AB , mother's AA genotype effect β AA , and father's allele A contribution λ A conditioning on the incompatible MFG.

Additive or multiplicative allelic effect:
Where the heterozygous effect is between the two homozygous effects.
To test the MFG incompatibility effect, a logistic regression model was fitted to all mother-offspring pairs adjusting for mother's allele A effect β A and father's allele A contribution λ A conditioning on the incompatible MFG.
It is worthwhile to note that for some SNPs, one minor allele may lead to small counts of the homozygous composite genotype of mother-offspring pairs of that allele, such as small counts of 'AA_AA' composite genotype when allele A has a small frequency. As a result, only a small number of samples may be observed in the compatible group with double homozygous minor allele. This often leads to non-significant MFG incompatibility in either Scenario 1 or 2 although it is difficult to distinguish between these two scenarios with a small frequency allele.

Simulation studies
We conducted simulations to study the power of the 2-stage test on the incompatibility for every scenario in

Data generation
We assumed the allele frequency p for allele A and q=1-p for allele B. Table 3 provides the distribution of the MFG under the HWE. In all scenarios, p was generated from a uniform distribution U[0, 1]. The incompatibility index C was then generated from a Bernoulli distribution with C = 1 for incompatible MFG: P(C=1) = p 2 q + pq 2 + p 2 q + pq 2 = 2pq, Other variables were generated according to the scenarios as follows.   Table 4.

Simulation Result
We fitted logistic regression model to the generated The simulation was repeated 50,000 times for each of these scenarios to accommodate the unspecified OR value. The power of the study was calculated for each OR interval. It was observed that the power of test increased with the OR as shown in Table 5 and Figure 1.
Further simulation was conducted to evaluate the specificity of the test. Ten SNPs were generated and the disease phenotype was generated only by SNP1 in Scenario 1, but independent of SNPs 2-9. The logistic regression model was fitted with 5000 repeats for each OR value, and the power was calculated for each SNP.
The simulations demonstrated that the power increased with the OR and that the false positive rate was about 1% (Table 6 and Fig. 2).
3. Application to a case -control study of SGA has combined maternal and fetal genotypes together to study the association between SGA and the incompatibility of the mother and offspring genotypes.
In this study, we choose the candidate genes (IGF1 and IGF2 and their receptors) to test the MFG incompatibility effect at each single SNP locus.

Two-stage MFG incompatibility test
In the logistic regression analysis, mother's age β AB is the effect of mother's genotype AB, and β AA is the effect of mother's genotype AA. λ A is the father's allele A effect given incompatibility. γ is the MFG incompatibility effect. β A is the effect of mother's allele A.
Odds Ratio (OR)