additive.test(data, response.var, snp.var, exposure.var, main.vars=NULL,
strata.var=NULL, op=NULL)
genetic.model
, optim.method
, indep
, maxiter
and
reltol
(see details). The default is NULL.pval.add
P-value of the additive interaction likelihood ratio test.tb
The frequency table defined bytable(snp.var, exposure.var)
.lm.full
The output for the full model using a logistic regression model under the
retrospective (indep
=TRUE) or the prospective likelihood (indep
=FALSE).lm.full.cov
Covariance matrix for the full model.lm.full.UML
The glm() output for the full model withsnp.var
in the model.lm.base
The glm() output for the base model withoutsnp.var
in the model.optim.out
The optimization output of theoptim
function for a null model under an additive model restriction.DF
The degrees of freedom of the additive or multiplicative interaction test.LRT.add
Likelihood ratio test value for the additive interaction.LRT.mult
Likelihood ratio test value for the multiplicative interaction.pval.mult
P-value of the multiplicative interaction likelihood ratio test.pval.wald.mult
P-value of the multiplicative interaction test (Wald test).pval.UML
P-value of the multiplicative interaction test under the prospective likelihood (Wald test).pval.CML
P-value of the multiplicative interaction test under the retrospective likelihood.
Only applicable forindep
=TRUE.pval.EB
P-value of the multiplicative interaction test using Empirical Bayes-type shrinkage estimator.
Only applicable forindep
=TRUE.method
2x2, 2x3, 3x2 or 3x3.or.tb
Odds ratio table for the full model without the additive model restriction.S
The output of Synergy Index method for additive interaction under a prospective likelihood
(only applicable for the 2x2 method).AP
The output of "Attributable Proportion due to interaction" method for additive interaction under a prospective
likelihood (only applicable for the 2x2 method).RERI
The output of "Relative Excess Risk Due to Interaction" method for additive interaction (only applicable for the 2x2 method).model.info
List of information from the model.Definition of the likelihood under the gene-environment independence assumption: Let D = 0, 1 be the case-control status, G = 0, 1, 2 denote the SNP genotype, S = 1, ..., k denote the levels of the stratification variable and Z be the design matrix for all the covariates including G, the interactions, and a column for the intercept parameter. If $f_s$ denotes the allele frequency for stratum s, then $$P(G = 0) = (1 - f_s)^2$$ $$P(G = 1) = 2f_s(1 - f_s)$$ $$P(G = 2) = f_s^2.$$ If $\xi_s = \log(f_s/(1 - f_s))$, then $$\log \left( \frac{P(G = 1)}{P(G = 0)} \right) = \log(2) + \xi_s$$ and $$\log \left( \frac{P(G = 2)}{P(G = 0)} \right) = 2\xi_s$$
Let $\theta(d,g)=d*Z*\beta+I(g=1)*\log(2)+g*\xi_s.$
Then the likelihood for a subject is $P(D=d, G=g | Z, S) = \frac{\exp(\theta(d, g))}{\sum_{d,g} \exp(\theta(d, g))}$ where the sum is taken over the 6 combinations of d and g.
Options list:
Below are the names for the options list op
. All names have default values
if they are not specified.
genetic.model
1-3 where 1=dominant, 2=recessive, 3=general.
The default is 3.optim.method
One of "BFGS", "CG", "L-BFGS-B", "Nelder-Mead", "SANN".
The default is "BFGS".indep
TRUE for using a retrospective likelihood for gene-environment independence assumption.
FALSE for using a standard prospective likelihood. The default is FALSE.reltol
Stopping tolerance. The default is 1e-7.maxiter
Maximum number of iterations. The default is 500.Chatterjee, N. and Carroll, R. Semiparametric maximum likelihood estimation exploting gene-environment independence in case-control studies. Biometrika, 2005, 92, 2, pp.399-418.
snp.logistic
, snp.score
# Use the ovarian cancer data
data(Xdata, package="CGEN")
table(Xdata[, "gynSurgery.history"])
# Recode the exposure variable so that it is 0-1
temp <- Xdata[, "gynSurgery.history"] == 2
Xdata[temp, "gynSurgery.history"] <- 1
# Standard likelihood (indep = FALSE by default)
out1 <- additive.test(Xdata, "case.control", "BRCA.status", "gynSurgery.history",
main.vars=c("n.children","oral.years"), op=list(genetic.model=1))
# Retrospective likelihood (indep = TRUE) for G by E independence assumption
out2 <- additive.test(Xdata, "case.control", "BRCA.status", "gynSurgery.history",
main.vars=~n.children+oral.years, strata.var="ethnic.group",
op=list(indep=TRUE, genetic.model=1))
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