spass (version 1.2)

n.nb.inar1: Sample Size Calculation for Comparing Two Groups when observing Longitudinal Count Data with marginal Negative Binomial Distribution and Autoregressive Correlation Structure of Order One: NB-INAR(1)

Description

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.

Usage

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

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.

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.

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. \(\delta = \mu_T/\mu_C\).

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 \(H_0: \mu_T/\mu_C \ge 1\) 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. \(k = n_T/n_C\).

See Also

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.

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)
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)
# }

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