In zhanghfd/CCMO: Case-Control Mother-Offspring Pair Genetic Association Studies

1. Methods

The R package CCMO implements two powerful statistical methods for disease-gene association analysis using case-control mother-offspring data.

1.2 Data description

The data for each mother-offspring pair are $(D,G^c,G^m,X)$, where $D$ is the disease status of the offspring (should be coded as 1 for case and 0 for control), $G^c$ and $G^m$ are the genotypes of offspring and mother, and $X$ is a $p$-vector of maternal covariates.

Suppose a SNP has two alleles A and B (B is the minor allele), then genotypes can be coded either as 0 (for genotype AA), 1 (for genotype AB), or 2 (for genotype BB). Alternatively, the genotypes can be normalized according to specified mode of inheritance \begin{itemize} \item Additive: 0 for AA, 1/2 for AB, and 1 for BB; \item Recessive: 0 for AA or AB, 1 for BB; \item Dominant: 0 for AA, 1 for AB or BB. \end{itemize} In what follows, we adopt the normalized genotypes.

1.3 Testing maternal and offspring genetic effects and envirionment effects

1.3.1 Reference

Zhang H, Mukherjee B, Arthur V, Hu G, Hochner H, Chen J (2020). An Efficient and Computationally Robust Statistical Method for Analyzing Case-Control Mother-Offspring Pair Genetic Association Studies. Annals of Applied Statistics 14: 560–-584.

1.3.2 Model description

The method assumes that the offspring genotype is conditionally independent of the maternal covariates given maternal covariates. The penetrance model is as follows: \begin{eqnarray} &&\mbox{pr}(D=1|G^o,G^m,X)\ &=&\mbox{expit}(\beta_0+\beta_{G^c}G^c+\beta_{G^m}G^m+\beta_oX_o+\beta_{G^cX}G^cX_c+\beta_{G^mX}G^mX_m+\beta_{G^cG^m}G^cG^m), \end{eqnarray} where expit$(t)=e^t/(1+e^t)$, $X_o$, $X_c$, and $X_m$ are functions of the covariates $X$, $\beta_{G^c}$ and $\beta_{G^m}$ are main genetic effects for offspring (child) and mother, respectively, $\beta_o$ is the main maternal environmental effect, $\beta_{G^cX}$ is the offspring gene-environment interaction effct, $\beta_{G^mX}$ is the maternal gene-environment interaction effect, and $\beta_{G^cG^m}$ is the gene-gene interaction effect. The maternal genotype is associated with the maternal covariates through the following double additive logit (daLOG) model: $$\mbox{pr}(G^m=1|X)=\frac{\xi(\theta,F)e^{k\eta'X_{G^m}}}{\sum_l\xi_l(\theta,F)e^{l\eta'X_{G^m}}},$$ where $\eta$ is a regression parameter vector, $X_{G^m}$ is a function of $X$, $\xi_k(\theta,F)$ is the probability of $G^m=k$ with $\theta$ being the minor allele frequency and $F$ being the inbreeding coefficient.

1.3.4 Usage of main functions singleSNP and multipleSNP

\begin{description} \item singleSNP(Y, Gc, Gm, Xo = NULL, Xc = NULL, Xm = NULL, X.Gm = NULL, G.main = c("Gc", "Gm"), G.int = FALSE, mode = "add", prev = 0.01, ind = FALSE, HWE = TRUE, normalized.genotype = FALSE)

\item multipleSNP(Y, Gc, Gm, Xo = NULL, Xc = NULL, Xm = NULL, X.Gm = NULL, G.main = c("Gc", "Gm"), G.int = FALSE, mode = "add", prev = 0.01, ind = FALSE, HWE = TRUE, normalized.genotype = FALSE, test = NULL) \end{description}

Users should specify $X_c$, $X_m$, $X_o$, $X_{G^m}$ according to their requirements, each of them can be omitted in the model by setting it to be the default value NULL. Each of the two main genetic effects can be included in the penetrance model by specifying G.main, and the gene-gene interaction effect can be included by setting G.int to be TRUE.

The mode of inheritance can be specified through mode ('rec' for recessive, 'add' for additive, 'dom' for dominant). Hardy-Weiberg equilibrium can be incorporated in the method through HWE. The independence of $G^m$ and $X$ can be incorprated by setting ind to be TRUE.

1.4 Testing parent-of-origin effects

1.4.1 Reference

Zhang K, Zhang H, Hochner H, Chen J (2021). Covariate Adjusted Inference of Parent-of-Origin Effects Using Case-Control Mother-Child Paired Multi-Locus Genotype Data. Manuscript.

1.4.2 Model description

The penetrance model for parent-of-origin effects (POEs) is as follows: \begin{eqnarray} &&\mbox{pr}(D=1|G^c,G^m,G^c_m,G^c_p,X)\ &=&\mbox{expit}(\beta_0+\beta_{G^c}G^c+\beta_{G^m}G^m+\beta_{POE}(G^c_m-G^c_p)+\beta_{X}X), \end{eqnarray} $\beta_{G^c}$ and $\beta_{G^m}$ are main genetic effects for offspring (child) and mother, respectively, $\beta_X$ is the main maternal environmental effect, $\beta_{POE}$ is the POE. The genotypes should be coded either as 0 (for genotype AA), 1 (for genotype AB), or 2 (for genotype BB) and we consider using haplotypes data to improve the inference efficiency for assessing POEs. In additional to multi-locus genotypes, disease statuses, and covariates, the inputs for the POE analysis function MultiLociPOE shoud include possible haplotypes in the population of interest, which can be generated by the function MultiLociPOE.input.

1.4.3 Usage of main function MultiLociPOE

The usage of the function MultiLociPOE is as follows:

\begin{description} \item MultiLociPOE(Y,gmm,gcc,X,loci,hap,f,ppi) \end{description}

Users should specify test loci and prevalence \code{f}, and make sure that the genotypes are coded as 0 (for genotype AA), 1 (for genotype AB), or 2 (for genotype BB).

\begin{description} \item MultiLociPOE.input(gmm,gcc,type) \end{description}

Users can use MultiLociPOE.input to generate inputs for MultiLociPOE. Users should specify type corresponding to the format of the genotype data. Here, '0' means the genotypes are coded as 0, 1, 2; '1' means the genotypes are normalized as 0, 1/2, 1; '2' means the genotypes are coded as something like "A/A", "A/B", "B/B".

2. Illustration of main functions

2.1 singleSNP

We use the dataset contained in the R package for illustration.

library(CCMO)
data("SampleData",package="CCMO")
dim(SampleData)
head(SampleData)

This dataset has maternal and offspring genotypes for 10 SNPs and two maternal covariates from 2000 mother-offspring pairs. Here we analyze the first SNP. Suppose we are interested in two main genetic effects, maternal gene-environment interaction effects, and offspring gene-environment interaction effects. The R code for analyzing the data is as follows:

# library(CCMO)
Y = SampleData[,1]
Gc = SampleData[,2]
Gm = SampleData[,12]
X = SampleData[,-(1:21)]
fit = singleSNP(Y,Gc,Gm,Xo=X,Xc=X,Xm=X,X.Gm=X)

The result is a list, whose elements can be accessed through

names(fit)

The estimation and significance test results produced by the new method are stored in

fit$new

The covariance matrix of the estimates by the new method is stored in

fit$cov.new

The corresponding results by the standard logistic regression are included for comparison

fit$log
fit$cov.log

2.2 OmnibusTest

Multiple effects can be simultineously tested using the function OmnibusTest. Suppose we want to test four gene-environment interaction effects simultineously, then we should specify the indices of the two interaction effects when calling OmnibusTest:

fit = OmnibusTest(fit,test=7:10)
fit$Omnibus

The results include the Wald test statistic, degrees of freedom, and p-value for each of two methods (i.e., new and log).

2.3 multipleSNP

Suppose we want to analyze the 10 SNPs simultaneously. The function multipleSNP calls multiple CPU cores to save computational time, as shown below

Gc = SampleData[,2:11]
Gm = SampleData[,12:21]
system.time(fit1 <- multipleSNP(Y,Gc,Gm,Xo=X,Xc=X,Xm=X,X.Gm=X,cores=1))
system.time(fit2 <- multipleSNP(Y,Gc,Gm,Xo=X,Xc=X,Xm=X,X.Gm=X,cores=2))

Of course, the saved computational time depends on the number of CPU cores. The output is a list of length 10 (the number of SNPs). For example, the results of the 2nd SNP can be accessed through

fit2[[2]]

Omnibus test can be carried out by specifying the target variable indices through test:

fit <- multipleSNP(Y,Gc,Gm,Xo=X,Xc=X,Xm=X,X.Gm=X,test=7:10)
fit[[2]]$Omnibus

2.4 MultiLociPOE

# library(CCMO)
Y = POESampleData[,1]
gmm = POESampleData[,2:6]
gcc = POESampleData[,7:11]
X = POESampleData[,12]
data = MultiLociPOE.input(gmm,gcc,0)
gmm = data$gmm
gcc = data$gcc
hap = data$hap
ppi = data$ppi
loci = 1
f = 0.01
fit = MultiLociPOE(Y,gmm,gcc,X,loci,hap,f,ppi)

The result is a list, whose elements can be accessed through

names(fit)

The estimation and significance test results produced by the new method are stored in

fit$new

The covariance matrix of the estimates by the new method is stored in

fit$cov.new

The corresponding results by the standard logistic regression are included for comparison

fit$log
fit$cov.log

zhanghfd/CCMO documentation built on March 18, 2021, 12:18 a.m.