n.nb.gf: Sample Size Calculation for Comparing Two Groups when...
In spass: Study Planning and Adaptation of Sample Size

Description Usage Arguments Details Value Source See Also Examples

n.nb.gf calculates required sample sizes for testing trend parameters in a Gamma frailty model

n.nb.gf(
  alpha = 0.025,
  power = 0.8,
  lambda,
  size,
  rho,
  tp,
  k = 1,
  h,
  hgrad,
  h0,
  trend = c("constant", "exponential", "custom"),
  approx = 20
)

`alpha`	level (type I error) to which the hypothesis is tested.
`power`	power (1 - type II error) to which an alternative should be proven.
`lambda`	the set of trend parameters assumed to be true at the beginning prior to trial onset
`size`	dispersion parameter (the shape parameter of the gamma mixing distribution). Must be strictly positive, need not be integer (see `rnbinom.gf`).
`rho`	correlation coefficient of the autoregressive correlation structure of the underlying Gamma frailty. Must be between 0 and 1 (see `rnbinom.gf`).
`tp`	number of observed time points. (see `rnbinom.gf`)
`k`	sample size allocation factor between groups: see 'Details'.
`h`	hypothesis to be tested. The function must return a single value when evaluated on lambda.
`hgrad`	gradient of function h
`h0`	the value against which h is tested, see 'Details'.
`trend`	the trend which assumed to underlying in the data.
`approx`	numer of iterations in numerical calculation of the sandwich estimator, see 'Details'.

The function calculates required samples sizes for testing trend parameters of trends in longitudinal negative binomial data. The underlying one-sided null-hypothesis is defined by H_0: h(η, λ) ≥q h_0 vs. the alternative H_A: h(η, λ) < h_0. For testing these hypothesis, the program therefore requires a function h and a value h0.

n.nb.gf gives back the required sample size for the control and treatment group, to prove an existing alternative h(η, λ) - h_0 with a power of power when testing at level alpha. For sample sizes n_C and n_T of the control and treatment group, respectively, the argument k is the sample size allocation factor, i.e. k = n_T/n_C.

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.

n.nb.gf returns the required sample size within the control group and treatment group.

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

rnbinom.gf for information on the Gamma frailty model, fit.nb.gf for calculating initial parameters required when performing sample size estimation, bssr.nb.gf for blinded sample size reestimation within a running trial.

##The example is commented as it may take longer than 10 seconds to run.
##Please uncomment prior to execution.

##Example for constant rates
#h<-function(lambda.eta){
#   lambda.eta[2]
#}
#hgrad<-function(lambda.eta){
#   c(0, 1, 0)
#}

##We assume the rate in the control group to be exp(lambda[1]) = exp(0) and an
##effect of lambda[2] = -0.3. The \code{size} is assumed to be 1 and the correlation
##coefficient \code{\rho} 0.5. At the end of the study, we would like to test
##the treatment effect specified in lambda[2], and therefore define function
##\code{h} and value \code{h0} accordingly.

#estimate<-n.nb.gf(lambda=c(0,-0.3), size=1, rho=1, tp=6, k=1, h=h, hgrad=hgrad,
#   h0=0.2, trend="constant", approx=20)
#summary(estimate)

##Example for exponential trend
#h<-function(lambda.eta){
#   lambda.eta[3]
#}
#hgrad<-function(lambda.eta){
#   c(0, 0, 1, 0)
#}

#estimate<-n.nb.gf(lambda=c(0, 0, -0.3/6), size=1, rho=0.5, tp=7, k=1, h=h, hgrad=hgrad,
#   h0=0, trend="exponential", approx=20)
#summary(estimate)