condGEE {condGEE}R Documentation

Parameter estimation in conditional GEE for recurrent event gap times

Description

Solves for the mean parameters (\theta), the variance parameter (\sigma^2), and their asymptotic variance in a conditional GEE for recurrent event gap times, as described by Clement, D. Y. and Strawderman, R. L. (2009) Biostatistics 10, 451–467. Makes a parametric assumption for the length of the censored gap time, and assumes gap times within subject are conditionally uncorrelated.

Usage

condGEE(data, start, mu.fn=MU, mu.d=MU.d, var.fn=V, 
  k1=K1.norm, k2=K2.norm, robust=TRUE, asymp.var=TRUE, 
  maxiter=100, rtol=1e-6, atol=1e-8, ctol=1e-8, useFortran=TRUE)

Arguments

data

matrix of data with one row for each gap time; the first column should be a subject ID, the second column the gap time, the third column a completeness indicator equal to 1 if the gap time is complete and 0 if the gap time is censored, and the remaining columns the covariates for use in the mean and variance functions

start

vector containing initial guesses for the unknown parameter vector

mu.fn

the specification for the mean of the gap time; the default is a linear combination of the covariates; the function should take two arguments (\theta, and a matrix of covariates with each row corresponding to one gap time) and it should return a vector of means

mu.d

the derivative of mu.fn with respect to the parameter vector; the default corresponds to a linear mean function

var.fn

the specification for V^2, where the variance of the gap time is \sigma^2 V^2; the default is a vector of ones; the function should take two arguments (\theta, and a matrix of covariates with each row corresponding to one gap time) and it should return a vector of variances

k1

the function to solve for the conditional mean length of the censored gap times; its sole argument should be the vector of standardized (i.e.\ (Y-\mu)/(\sigma V)) censored gap times; the default assumes the standardized censored gap times follow a standard normal distribution, but K1.t3 and K1.exp are also provided in the package - they assume a standardized t with 3 degrees of freedom and an exponential with mean 0 and variance 1 respectively

k2

the function to solve for the conditional mean length of the square of the censored gap times; its sole argument should be the vector of standardized (i.e.\ (Y-\mu)/(\sigma V)) censored gap times; the default assumes the standardized censored gap times follow a standard normal distribution, but K2.t3 and K2.exp are also provided in the package - they assume a standardized t with 3 degrees of freedom and an exponential with mean 0 and variance 1 respectively

robust

logical, if FALSE, the mean and variance parameters are solved for simultaneously, increasing efficiency, but decreasing the leeway to misguess start and still find the root of the GEE

asymp.var

logical, if FALSE, the function returns NULL for the asymptotic variance matrix

maxiter

see multiroot; maximal number of iterations allowed

rtol

see multiroot; relative error tolerance

atol

see multiroot; absolute error tolerance

ctol

see multiroot; if between two iterations, the maximal change in the variable values is less than this amount, then it is assumed that the root is found

useFortran

see multiroot; logical, if FALSE, then an R implementation of Newton-Raphson is used

Details

Uses the function multiroot in the rootSolve package to solve the conditional GEE. As in multiroot, there is no guarantee of finding the root.

A monotone increasing transformation can be applied to the observed gap times before calling condGEE.

When robust=TRUE, \theta and \sigma^2 are solved for in an alternating fashion until convergence. Note that the estimating equation for the mean parameters depends on \sigma^2 through the censored gap time.

Value

a list containing:

eta

the parameter estimate (\theta^T,\sigma^2)^T

a.var

an estimate of the asymptotic variance matrix of the eta estimator

Author(s)

David Clement <dyc24@cornell.edu>

References

Clement, D. Y. and Strawderman, R. L. 2009 Biostatistics 10, 451–467.

Examples

  data(asthma)
  demo(asthmaExample)
[Package condGEE version 0.1-4 Index]