- independence of the genetic factor and nongenetic attributes in the control population,
- independence of the genetic factor and nongenetic attributes, plus Hardy-Weinberg proportions (HWP) in control genotype frequencies, or
- simple dependence between the genetic and nongenetic covariates in the control population.

`luca(pen.model, gLabel, dat, HWP = FALSE, dep.model = NULL)`

pen.model

an R formula specifying the disease penetrance model
relating a genetic factor and a number of nongenetic attributes (the
predictors or transformations thereof) to disease status. A typical

`pen.model`

has the form `d ~ g + a + g:a`

gLabel

a character string specifying the name of the genetic factor in

`pen.model`

.dat

a data frame containing the variables in *no* default value. Each row of

`pen.model`

,
currently, with `dat`

is
considered as one multivariate observation for a subject. Note that the
genetic term must be a

HWP

a logical value indicating whether the genotype frequencies
in controls should be assumed to follow Hardy-Weinberg proportions.
When

`TRUE`

, the genetic term must be a `genotype`

object.dep.model

an R formula specifying the dependence between the
genetic factor and nongenetic attributes. (See the Details section below for
more on the dependence model.) When

`NULL`

(default),
it indicates independence between the genetic factor and nonge- An object of class
`"luca"`

with the following components: call the function call coefficients estimates of parameters in the covariate model (lebelled as `covmod.XX`

) and the penetrance model (labelled as`penmod.YY`

where`YY`

denotes the name of a term in the model). The covariate model parameters depend on the covariate assumptions and are 1) control-population log-odds for each level of the genetic factor relative to a baseline level under independence, 2) control-population log-odds for each allele relative to a baseline allele under independence plus HWP, or 3) the parameters from the polychotomous regression model under dependence (see the Details section for a description of this model).var the variance-covariance matrix of the parameter estimates. iter number of iterations in the iterative search for parameter estimates - The function
`summary.luca`

(or`summary`

) can be used to obtain a summary of the results in a similar style to the`lm`

and`glm`

summaries.

`luca`

may be used
to screen for `coxph.fit`

from the `survival`

package is used to fit the conditional logistic regression.A dependence model such as `g ~ a`

specifies a polychotomous
regression model for the genetic factor `g`

as a function of the
nongenetic attribute `a`

. The polychotomous regression for `g`

given `a`

holds when the conditional distribution of `a`

given
`g`

is from the exponential family of distributions, with a constant
dispersion parameter across the levels of the genetic factor.
Alternately, `g`

and `a`

may be conditionally independent
given a third variable `a2`

. Typically, `a2`

is also a term in
the penetrance model (`pen.model`

). To model conditional independence
of `g`

and `a`

given `a2`

, specify the dependence model
(`dep.model`

) as `g ~ a2`

. See Shin, McNeney and Graham (2007)
for details. `luca`

also allows dependence models of the form
`g ~ a1 + a2 + ...`

for multiple attributes `a1`

, `a2`

, ...
However, there is no formal justification for the use of such a model to capture the
dependence between `g`

and multiple nongenetic attributes.

`summary.luca`

, `glm`

, `coxph`

, `clogit`

data(lucaDat) # typical penetrance model: pen.model<-formula(d~I(allele.count(g,"C"))+a+a2+I(allele.count(g,"C")):a) #1. Assuming independence and HWP fitHWP<-luca(pen.model=pen.model, gLabel="g", dat=lucaDat, HWP=TRUE) fitHWP$coef fitHWP$var summary.luca(fitHWP) # OR 'summary(fitHWP)' #2. Assuming independence only fitDefault<-luca(pen.model=pen.model, gLabel="g", dat=lucaDat) fitDefault$coef fitDefault$var #3. Allowing for dependence between genetic and nongenetic factors # General dependence model fitDep1<-luca(pen.model=pen.model, gLabel="g", dat=lucaDat, dep.model=formula(g~a)) fitDep1$coef fitDep1$var # When 'g' and 'a' are conditioanally independent given the third variable 'a2': fitDep2<-luca(pen.model=pen.model, gLabel="g", dat=lucaDat, dep.model=formula(g~a2)) fitDep2$coef fitDep2$var