Materials And Methods
A total of 991 mother-offspring pairs (406 SGA cases and 585 controls) were included in this case-control study conducted in Chile. SGA was defined as birth weight below 10th percentile for the corresponding gestational age [Kramer 1987]. Clinical and socio-demographic data were summarized in Table S1
, which shows no statistical significance between the two groups in maternal age, maternal BMI, smoking status and baby’s gender. Parity was marginally significant with p=0.048. The control group had a larger mean gestational age and larger mean birth weight as expected.
Template DNA was obtained for genotyping through whole genome amplification of genomic DNA extracted from blood samples of patients following an automated DNA isolation protocol (BioRobot 9604, Qiagen, Valencia, CA, USA). Genotyping of single nucleotide polymorphisms (SNPs) was carried out using the massARRAYTM System (Sequenom Inc. San Diego, CA, USA) by the high-throughput genotyping facility at Genaissance Inc (New Haven, CT, USA). SNP genotyping quality control was conducted through genotyping consistency of repeated samples. More than 1300 SNPs were genotyped in this candidate gene based case-control study for several phenotypes of pregnancy complication, including preeclampsia, SGA, etc. We focus on the IGF-I and IGF-II genes and their receptors only in this study.
A total of 44 SNPs were genotyped in IGF-I, IGF-II, IGF1R and IGF2R genes. Among them, 5 SNPs were found to be homozygous in the study population and 13 SNPs had one minor allele of frequency less than 0.01 and thus were excluded. HWE was examined in the combined mother and offspring control population and all of the 26 remaining SNPs satisfied the HWE with a cut-off p-value > 0.0001. Ten SNPs out of these 26 remaining SNPs were found to have one minor allele with frequency equal to or smaller than 0.1 (homozygous genotype probability ≤ 0.01) and were excluded from the MFG incompatibility test. Thus the MFG incompatibility test was conducted on the remaining 16 SNPs.
We develop a two-stage model for testing the MFG incompatibility, and further conduct a simulation study.
1. 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.
Table 1. Composite genotypes of the mother-offspring pair
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 for details of these scenarios and the parameterization of the MFG test. SNPs with a small frequency allele (allele frequency p ≤ 0.1) are not tested for the MFG incompatibility effect.
Table 2. Parameterization of logistic regression model testing MFG incompatibility
( Note: Table 2 is divided and listed in accordance to each scenario )
No allelic effect: f(AA_AA) = f(AB_AB) = f(BB_BB), where function f represents the composite genotype effect.
A logistic regression model was then fitted to all mother-offspring pairs to test the association between the disease and the MFG incompatibility (1 for incompatible pairs and 0 for compatible) adjusting for environmental covariates.
Allele A effect: f (AA_AA) ≠ f (AB_AB) = f (BB_BB), where the heterozygous genotype has the same effect as one homozygous but significantly different from the other.
To test the MFG incompatibility effect, a logistic regression model was fitted to all mother-offspring pairs adjusting for the individual ‘AA’ genotype effect βAA of either mother or offspring genotype and the father’s allele A contribution λA conditioning on the incompatible MFG.
Heterozygosity effect: f(AA_AA) = f(BB_BB) ≠ f(AB_AB), where the two homozygous genotypes had the same effect but significantly different from the heterozygous.
To test the MFG incompatibility effect, a logistic regression model was fitted to all mother-offspring pairs adjusting for mother’s ‘AB’ genotype effect βAB and father’s allele A contribution λA conditioning on the incompatible MFG.
Unequal genotype effects (significantly different effects), including the following two cases.
4.1 Strong allelic interaction effect:
f(AB_AB) > f(AA_AA) > f(BB_BB) or
f(AB_AB) < f(AA_AA) < f(BB_BB)
Where the heterozygous effect is the largest or smallest.
A logistic regression model was fitted to all mother-offspring pairs to test the MFG incompatibility adjusting for mother’s AB genotype effect βAB, mother’s AA genotype effect βAA, and father’s allele A contribution λA conditioning on the incompatible MFG.
4.2 Additive or multiplicative allelic effect:
f(AA_AA) > f(AB_AB) > f(BB_BB)
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 βA and father’s allele A contribution λA 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.
We conducted simulations to study the power of the 2-stage test on the incompatibility for every scenario in Table 2. In each simulation, we generated 1000 subjects, each of which had a binary indicator for disease phenotypes (Y), MFG incompatibility effect (C), allelic effect (A) and father’s allelic contribution effect given incompatibility (F). The genotype data were generated under the assumption of HWE. The logistic regression was applied to detect the incompatibility effect at the level of 0.05.
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) = p2q + pq2 + p2q + pq2 = 2pq,
P(C=0) = 1–2pq = p2 + q2
Table 3. Distribution of maternal-fetal genotype under HWE with allele frequencies (p,q).
Other variables were generated according to the scenarios as follows.
No allelic effect.
Two probabilities r1 and r2 for having disease with incompatible and compatible MFG, respectively, were generated from uniform distribution U[0, 1], and 1000 subjects were generated with probabilities Pr(Y=1|C=1) = r1,
Pr(Y =1|C=0) =r2.
Allele A effect.
First, six probabilities r1, r2……r6 ~ U [0, 1] of having the disease were generated according to different values of C, A, and F, where F was generated with Bernoulli probabilities Pr(F=1|C=1)=(p2q+pq2)/2pq = 0.5 and Pr(F=1|C=0)=0. A was the ‘AA’ genotype effect of the mother or the fetus or both, and was simulated by Pr(A=1|F=1,C=1)=p, Pr(A=1|F=0, C=1)=p, and Pr(A=1|F=0,C=0)=p3/ (p2+q2). Y was the disease phenotype and was simulated with the probabilities r1, …, r6 as listed in Table 4.
Table 4 Parameters in Simulation Studies
First, six probabilities r1, r2……r6 of having the disease were generated from uniform distribution U[0, 1] according to different values of C, A, F. F was generated by Bernoulli trials with probabilities Pr(F=1|C=1)= (p2q+pq2)/2pq=0.5 and Pr(F=1|C=0)= 0. A was the effect of genotype ‘AB’ in mother or fetus or both and was generated with Pr(A=1|F=1,C=1)=p, Pr(A=1|F=0,C=1)=q, and Pr(A=1|F=0,C=0)=pq/(p2+q2). Y was generated by Bernoulli trials with probabilities r1, …, r6 as listed in Table 4.
Strong allelic interaction effect.
First, seven probabilities r1, r2……r7 of having the disease were generated from uniform distribution U[0, 1] according to different values of C, A, F to accommodate three genotype effects βAB, βAA and βBB. F was generated with the probabilities Pr(F=1|C=0)=0 and Pr(F=1|C=1) = (p2q+pq2)/2pq = 0.5. A was the additive effect of allele A and was generated with Bernoulli probabilities
Pr (A=1 | F=1, C=1) = p,
Pr (A=0 | F=1, C=1) = 0,
Pr (A=-1 | F=1, C=1) = q,
Pr(A=1 | F=0, C=1) = q,
Pr (A=0 | F=0, C=1) = p,
Pr (A=-1 | F=0, C=1) = 0,
Pr(A=1 | F=0, C=0) = pq/(p2+q2),
Pr (A=0 | F=0, C=0) = p3/(p2+q2),
Pr (A=-1 | F=0, C=0) = q3/(p2+q2),
where A = 1 for genotype ‘AB’ in mother or fetus, 0 for genotype ‘AA’, and -1 for genotype ‘BB’. Y was generated by Bernoulli trials with probabilities r1,…r7 as in Table 4.
We fitted logistic regression model to the generated data with 1000 subjects and calculated the power of the test defined as out of the total number of simulations the number of times when the associated SNP was selected by statistical significance of the test. In scenario 1, the simulation was conducted with different odds ratio (OR) of disease between compatible and incompatible groups. The power of the study was calculated for each of the OR value 3, 2 , 1, 1/2 or 1/3. The simulation was repeated 5,000 times for each value of OR. In scenarios 2-4, because of the random selection of the allelic effect and father effect, the OR was not controlled at first, but rather calculated after the allelic effect and father effect were generated. The ORs were categorized into different intervals of (0,1/3), [1/3,1/2), [1/2,2), [2,3) and [3,∞]. 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.
Table 5. Power of MFG incompatibility test by OR in Scenarios 2-4 simulation a
Figure 1. The power of the two-stage MFG test by the OR between the compatible and incompatible groups for scenarios 1 - 4.
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).
Table 6. Power of MFG incompatibility test in Scenario 1 simulation based on 5000 repeats with 1000 subjects
Figure 2.The specificity of the two-stage method for MFG test by OR.
3. Application to a case – control study of SGA
We demonstrate our method by studying the MFG incompatibility effect of SNPs on low birth weight in a case-control study of SGA neonates with candidate genes. While the definition of SGA can be found in the literature (Alkalay et al., 1998, Saenger et al., 2007), the etiology remains complex. While it was suggested that most of the genetic influence originated in the fetal genome, other results (Ounsted et al. 1988) also suggested that not only fetal genes but also genes regulating the maternal uterine environment could be important in determining the size at birth, especially for the SGA neonates.
Insulin-like growth factor (IGF) genes are known to have a major influence on fetal and postnatal growth, and their expression presents in all fetal tissues along the gestation process. On one hand, the cord concentrations of IGF1 and IGF2 have been shown to be highly correlated with birth weight (Ong et al., 2002). On the other hand, while some polymorphisms in genes encoding IGF1, IGF2 and their respective receptors have been reported to be associated with birth weight (Vaessen et al. 2002), but failed to be confirmed in other studies (Frayling et al. 2002). Similarly, the reported association in studies with offspring population remains unconfirmed by one another. So far, no study 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.
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