n.nb.inar1: 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.inar1 calculates the required sample size for proving a desired alternative when testing for a rate ratio between two groups unequal to one. Also gives back power for a specified sample size. See 'Details' for more information.

n.nb.inar1(
  alpha,
  power = NULL,
  delta,
  muC,
  size,
  rho,
  tp,
  k,
  npow = NULL,
  nmax = Inf
)

`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 rate ratio which is to be proven.
`muC`	the rate observed within the control group.
`size`	dispersion parameter (the shape parameter of the gamma mixing distribution). Must be strictly positive, need not be integer (see `rnbinom.inar1`).
`rho`	correlation coefficient of the underlying autoregressive correlation structure. Must be between 0 and 1 (see `rnbinom.inar1`).
`tp`	number of observed time points. (see `rnbinom.inar1`)
`k`	sample size allocation factor between groups: see 'Details'.
`npow`	sample size for which a power is to be calculated. Can not be specified if power is also specified.
`nmax`	maximum total sample size of both groups. If maximum is reached a warning message is broadcasted.

When testing for differences between rates μ_C and μ_T of two groups, a control and a treatment group respectively, we usually test for the ratio between the two rates, i.e. μ_T/μ_C = 1. The ratio of the two rates is refered to as δ, i.e. δ = μ_T/μ_C.

n.nb.inar1 gives back the required sample size for the control and treatment group required to prove an existing alternative theta with a specified power power when testing the null hypothesis H_0: μ_T/μ_C ≥ 1 to level alpha. If power is not specified but instead npow, the power achieved with a total sample size of npow is calculated.

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.

rnbinom.inar1 returns the required sample size within the control group and treatment group.

rnbinom.inar1 uses code contributed by Thomas Asendorf.

rnbinom.inar1 for information on the NB-INAR(1) model, fit.nb.inar1 for calculating initial parameters required when performing sample size estimation, bssr.nb.inar1 for blinded sample size reestimation within a running trial.

#Calculate required sample size to find significant difference with
#80% probability when testing the Nullhypothesis H_0: mu_T/mu_C >= 1
#assuming the true effect delta is 0.8 and rate, size and correlation
#parameter in the control group are 2, 1 and 0.5, respectively.

estimate<-n.nb.inar1(alpha=0.025, power=0.8, delta=0.8, muC=2, size=1, rho=0.5, tp=7, k=1)
summary(estimate)

estimate<-n.nb.inar1(alpha=0.025, npow=200, delta=0.8, muC=2, size=1, rho=0.5, tp=7, k=1)
summary(estimate)

Loading required package: mvtnorm
Loading required package: multcomp
Loading required package: survival
Loading required package: TH.data
Loading required package: MASS

Attaching package: 'TH.data'

The following object is masked from 'package:MASS':

    geyser

Loading required package: Rcpp
Loading required package: geepack
Initial Sample Size Calculation
---------------------------------
alpha level:           0.025
testing power:         0.8
rate ratio:            0.8
rate control group     2
dispersion parameter:  1
correlation parameter: 0.5
time points:           7
allocation factor:     1

Sample Size
---------------------------------
control group:   171
treatment group: 171Initial Sample Size Calculation
---------------------------------
alpha level:           0.025
testing power:         0.57
rate ratio:            0.8
rate control group     2
dispersion parameter:  1
correlation parameter: 0.5
time points:           7
allocation factor:     1

Sample Size
---------------------------------
control group:   100
treatment group: 100