condGEE {condGEE} R Documentation

## Parameter estimation in conditional GEE for recurrent event gap times

### Description

Solves for the mean parameters (θ), the variance parameter (σ^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 (θ, 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 σ^2 V^2; the default is a vector of ones; the function should take two arguments (θ, 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-μ)/(σ 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-μ)/(σ 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`, θ and σ^2 are solved for in an alternating fashion until convergence. Note that the estimating equation for the mean parameters depends on σ^2 through the censored gap time.

### Value

a list containing:

 `eta ` the parameter estimate (θ^T,σ^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]