gtreg {binGroup}R Documentation

Fitting Group Testing Models

Description

gtreg is a function to fit the group testing regression model specified through a symbolic description of the linear predictor and descriptions of the group testing setting.

Usage

gtreg(formula, data, groupn, sens = 1,
 spec = 1, linkf = c("logit", "probit", "cloglog"),
 method = c("Vansteelandt", "Xie"), ...)

gtreg.fit(resp, cova, groupn, sens, spec,
 linkf, optim.meth = "Nelder-Mead")

EM(resp, cova, groupn, sens, spec, linkf,
 EM.maxiter = 1000)

Arguments

formula an object of class "formula" (or one that can be coerced to that class): a symbolic description of the model to be fitted. The details of model specification are given under 'Details'.
data an optional data frame, list or environment (or object coercible by as.data.frame to a data frame) containing the variables in the model. If not found in data, the variables are taken from environment(formula), typically the environment from which gtreg is called.
groupn a vector, list or data frame of the group numbers that designates individuals to groups.
sens sensitivity of the test, set to be 1 by default.
spec specificity of the test, set to be 1 by default.
linkf a character string specifying one of the three link functions for a binomial model: "logit" (default) or "probit" or "cloglog".
method The method to fit the model, must be one of "Vansteelandt" (default) or "Xie". The option "Vansteelandt" finds estimates by directly maximizing the likelihood function based on the group responses while the option "Xie" uses the EM algorithm to maximize the likelihood function in terms of the unobserved individual responses.
resp For gtreg.fit and EM: the vector of the group response variable
cova For gtreg.fit and EM: the design matrix of the covariates
optim.meth For gtreg.fit: the method in optim to fit the full model (default is "Nelder-Mead")
EM.maxiter For EM: The maximal number of iterations in the EM algorithm if "Xie" is chosen.
... In gtreg: arguments to be passed to gtreg.fit or EM.

Details

A typical predictor has the form groupresp ~ covariates where response is the (numeric) group response vector and covariates is a series of terms which specifies a linear predictor for individual responses. Note that it is actually the unobserved individual responses, not the observed group responses, which are modeled by the covariates here. In groupresp, a 0 denotes a negative response and a 1 denotes a positive response, where the probability of an individual positive response is being modeled directly. A terms specification of the form first + second indicates all the terms in first together with all the terms in second with duplicates removed. The terms in the formula will be re-ordered so that main effects come first, followed by the interactions, all second-order, all third-order and so on; to avoid this pass a terms object as the formula.

A specification of the form first:second indicates the set of terms obtained by taking the interactions of all terms in first with all terms in second. The specification first*second indicates the cross of first and second. This is the same as first + second + first:second.

Two workhorse functions gtreg.fit and EM, which corresponds to Vansteelandt's and Xie's method respectively, are called by gtreg to carry out the model fitting. The gtreg.fit function uses the optim function to maximize the likelihood function written in terms of the group responses. The EM function applies Xie's EM algorithm to the likelihood function written in terms of the unobserved individual responses; the function uses optim to maximize the likelihood function in each M step. The EM algorithm usually converges more slowly than the method of Vansteelandt. There could be slight differences in the estimates between the two methods due to different convergence criteria.

Note the data used here should be in the form of simple pooling - meaning that each individual appears in exactly one pool. Also, no individual tests or retests are used in the model fitting.

For the background on the use of optim, see help(optim).

Value

gtreg returns an object of class "gt". See later in this section. The function summary (i.e., summary.gt) can be used to obtain or print a summary of the results. The group testing functions predict (i.e., predict.gt) and residuals (i.e., residuals.gt) can be used to extract various useful features of the value returned by gtreg. An object of class "gt" is a list containing at least the following components:

coefficients a named vector of coefficients
hessian estimated Hessian matrix of the negative log likelihood function, as an estimator of the information matrix
residuals the response residuals, difference of the observed group responses and the fitted group responses.
fitted.group.values the fitted mean values of group responses.
deviance the deviance between the fitted model and the saturated model.
aic Akaike's An Information Criterion, minus twice the maximized log-likelihood plus twice the number of coefficients
null.deviance The deviance for the null model, comparable with deviance. The null model will include only the intercept if there is one in the model.
counts For Vansteelandt's method: the number of iterations in optim; For Xie's method: the number of iterations in the EM algorithm.
df.residual the residual degrees of freedom.
df.null the residual degrees of freedom for the null model.
z the vector of group responses.
call the matched call.
formula the formula supplied.
terms the terms object used.
method the method ("Vansteelandt" or "Xie") used to fit the model.
link the link function used in the model.

Author(s)

Boan Zhang

References

Xie, M. (2001), Regression analysis of group testing samples, Statistics in Medicine, 20, 1957-1969.

Vansteelandt, S., Goetghebeur, E., and Verstraeten, T. (2000), Regression models for disease prevalence with diagnostic tests on pools of serum samples, Biometrics, 56, 1126-1133.

See Also

summary.gt, predict.gt and residuals.gt for gt methods. gtreg.mp for the group testing regression model in the matrix pooling setting.

Examples


data(hivsurv)

fit1 <- gtreg(formula = groupres ~ AGE + EDUC., data = hivsurv,
           groupn = gnum, sens = 0.9, spec = 0.9, method = "Xie")

## --- Continuing the Example from  '?sim.g':

set.seed(1125)
gt.data<-sim.g(beta.par=c(-9,0.1), number.sample=279, group.size=9)
fit2 <- gtreg(formula = groupres ~ x, data = gt.data, 
           groupn = gnum, linkf = "probit")


[Package binGroup version 1.0-4 Index]