spass (version 1.2)

bssr.nb.inar1: Blinded Sample Size Reestimation for Longitudinal Count Data using the NB-INAR(1) Model

Description

bssr.nb.inar1 fits blinded observations and recalculates the sample size required for proving a desired alternative when testing for a rate ratio between two groups unequal to one. See 'Details' for more information.

Usage

bssr.nb.inar1(alpha, power, delta, x, n, k)

Arguments

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.

x

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

n

a vector giving the sample size within the control group and the treatment group, respecitvely.

k

planned sample size allocation factor between groups: see 'Details'.

Value

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

Details

When testing for differences between rates \(\mu_C\) and \(\mu_T\) of two groups, a control and a treatment group respectively, we usually test for the ratio between the two rates, i.e. \(\mu_T/\mu_C = 1\). The ratio of the two rates is refered to as \(\delta\), i.e. \(\delta = \mu_T/\mu_C\).

bssr.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 \(H_0: \mu_T/\mu_C \ge 1\) to level alpha. Nuisance parameters are estimated through the blinded observations x, 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. \(k = n_T/n_C\).

See Also

rnbinom.inar1 for information on the NB-INAR(1) model, n.nb.inar1 for calculating initial sample size required when performing inference, fit.nb.inar1 for calculating initial parameters required when performing sample size estimation

Examples

# NOT RUN {
#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)

#Simulate data
placebo<-rnbinom.inar1(n=50, size=1, mu=2, rho=0.5, tp=7)
treatment<-rnbinom.inar1(n=50, size=1, mu=1.6, rho=0.5, tp=7)

#Blinded sample size reestimation
blinded.data<-rbind(placebo, treatment)[sample(1:100),]
estimate<-bssr.nb.inar1(alpha=0.025, power=0.8, delta=0.8, x=blinded.data, n=c(50,50), k=1)
summary(estimate)
# }