Description Usage Arguments Details Value Source See Also Examples

`bssr.nb.gf`

fits blinded observations and recalculates the sample size required for sustaining power at desired alternative when testing for
trend parameters in a Gamma frailty models. See 'Details' for more information.

1 2 3 4 5 6 7 8 9 10 11 | ```
bssr.nb.gf(
data,
alpha = 0.025,
power = 0.8,
delta,
h0 = 0,
tp,
k,
trend = c("constant", "exponential", "custom"),
approx = 20
)
``` |

`data` |
a matrix or data frame containing count data which is to be fitted. Columns correspond to time points, rows to observations. |

`alpha` |
level (type I error) to which the hypothesis is tested. |

`power` |
power (1 - type II error) to which an alternative should be proven. |

`delta` |
the relevant effect size, which is assumed to be true, see 'Details'. |

`h0` |
the value against which h is tested, see 'Details'. |

`tp` |
number of observed time points. (see |

`k` |
sample size allocation factor between groups: 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 recalculates a sample size for testing in constant and exponential trends.

Under a constant trend, the means in control and experiment group are equal to *λ_1* and *λ_1 + λ_2*, respectively.
The treatment effect `delta`

is therefore equal to *λ_2*.

Under an exponential trend, the means in control and experiment group are equal to *exp(λ_1+t \cdot λ_2)* and *λ_1 + t\cdot λ_2 + t\cdot λ_3*, respectively.
The treatment effect `delta`

is therefore equal to *λ_3*.

`bssr.nb.gf`

returns the required sample size for the control and treatment group required to prove an existing
alternative `delta`

with a specified power `power`

when testing the null hypothesis *H_0: δ ≥ h_0* at level `alpha`

.
Nuisance parameters are estimated through the blinded observations `data`

, thus not further required.
For sample sizes *n_C* and *n_T* of the control and treatment group, respectively, the argument `k`

is the desired
sample size allocation factor at the end of the study, i.e. *k = n_T/n_C*.

`bssr.nb.gf`

returns the required sample size within the control group and treatment group.

`bssr.nb.gf`

uses code contributed by Thomas Asendorf.

`rnbinom.gf`

for information on the Gamma Frailty model, `n.nb.gf`

for calculating
initial sample size required when performing inference, `fit.nb.gf`

for calculating
initial parameters required when performing sample size estimation.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 | ```
##The example is commented as it may take longer than 10 seconds to run.
##Please uncomment prior to execution.
##Example for constant rates
#set.seed(12)
#h<-function(lambda.eta){
# lambda.eta[2]
#}
#hgrad<-function(lambda.eta){
# c(0, 1, 0)
#}
##Calculate initial sample size
#estimate<-n.nb.gf(lambda=c(0,-0.3), size=1, rho=0.5, tp=6, k=1, h=h, hgrad=hgrad,
# h0=0, trend="constant", approx=20)
##Generate and permutate data with different nuisance parameters
#random<-get.groups(n=round(estimate$n/2), size=c(0.8, 0.8), lambda=c(0.5, -0.3),
# rho=c(0.4, 0.4), tp=6, trend="constant")
#random<-random[sample(1:nrow(random), nrow(random)), ]
##Recalculate sample size with data
#reestimate<-bssr.nb.gf(data=random, alpha=0.025, power=0.8, delta=-0.3, h0=0,
# tp=6, k=1, trend="constant", approx = 20)
#summary(reestimate)
``` |

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