fit.nb.gf {spass}

Fitting Longitudinal Data from a Gamma Frailty Model with Frailty of Autoregressive Correlation Structure of Order One

Description

fit.nb.gf fits data using the pseudo maximum likelihood of a Gamma frailty model

Usage

fit.nb.gf(
  dataC,
  dataE,
  trend = c("constant", "exponential"),
  lower,
  upper,
  method = "L-BFGS-B",
  start,
  approx = 20,
  rho = FALSE,
  H0 = FALSE,
  h0 = 0
)

Arguments

dataC

a matrix containing count data from the control group, which is to be fitted. Columns correspond to time points, rows to observations.

dataE

a matrix containing count data from the experiment group, which is to be fitted. Columns correspond to time points, rows to observations.

trend

the trend which assumed to underlying in the data.

lower

vector of lower bounds for estimated parameters lambda, size and rho, respectively.

upper

vector of upper bounds for estimated parameters lambda, size and rho, respectively.

method

algorithm used for minimization of the likelihood, see optim for details.

start

vector of starting values for estimated parameters mu, size and rho, respectively, used for optimization.

approx

numer of iterations in numerical calculation of the sandwich estimator, see 'Details'.

rho

indicates whether or not to calculate the correlation coefficient of Gamma frailties. Must be TRUE or FALSE.

H0

indicates whether or not to calculate the hessian and outer gradient matrix under the null hypothesis, see 'Details'.

h0

the value against which is tested under the null

Details

the function fit.nb.gf fits a Gamma frailty model as found in Fiocco (2009). The fitting function allows for incomplete follow up, but not for intermittent missingness.

When calculating the expected sandwich estimator required for the sample size, certain terms can not be computed analytically and have to be approximated numerically. The value approx defines how close the approximation is to the true expected sandwich estimator. High values of approx provide better approximations but are compuationally more expensive.

If parameter H0 is set to TRUE, the hessian and outer gradient are calculated under the assumption that lambda[2] \geq h0 if trend = "constant" or lambda[3] \geq h0 if trend = "exponential".

Value

fit.nb.gf returns estimates of the trend parameters lambda, dispersion parameter size, Hessian matrix hessian, outer gradient product matrix ogradient and, if inquired, correlation coefficient rho.

Source

fit.nb.gf uses code contributed by Thomas Asendorf.

References

Fiocco M, Putter H, Van Houwelingen JC, (2009), A new serially correlated gamma-frailty process for longitudinal count data Biostatistics Vol. 10, No. 2, pp. 245-257.

See Also

rnbinom.gf for information on the Gamma frailty model, n.nb.gf for calculating initial sample size required when performing inference, bssr.nb.gf for blinded sample size reestimation within a running trial, optim for more information on the used minimization algorithms.

Examples

#Generate data from the Gamma frailty model
random<-get.groups(n=c(1000,1000), size=c(0.7, 0.7), lambda=c(0.8, -0.5), rho=c(0.6, 0.6),
  tp=7, trend="constant")
fit.nb.gf(dataC=random[1001:2000,], dataE=random[1:1000,], trend="constant")