gsDesign (version 3.2.1)

nNormal: Normal distribution sample size (2-sample)

Description

nNormal() computes a fixed design sample size for comparing 2 means where variance is known. T The function allows computation of sample size for a non-inferiority hypothesis. Note that you may wish to investigate other R packages such as the pwr package which uses the t-distribution. In the examples below we show how to set up a 2-arm group sequential design with a normal outcome.

nNormal() computes sample size for comparing two normal means when the variance for observations in

Usage

nNormal(
  delta1 = 1,
  sd = 1.7,
  sd2 = NULL,
  alpha = 0.025,
  beta = 0.1,
  ratio = 1,
  sided = 1,
  n = NULL,
  delta0 = 0,
  outtype = 1
)

Arguments

delta1

difference between sample means under the alternate hypothesis.

sd

Standard deviation for the control arm.

sd2

Standard deviation of experimental arm; this will be set to be the same as the control arm with the default of NULL.

alpha

type I error rate. Default is 0.025 since 1-sided testing is default.

beta

type II error rate. Default is 0.10 (90% power). Not needed if n is provided.

ratio

randomization ratio of experimental group compared to control.

sided

1 for 1-sided test (default), 2 for 2-sided test.

n

Sample size; may be input to compute power rather than sample size. If NULL (default) then sample size is computed.

delta0

difference between sample means under the null hypothesis; normally this will be left as the default of 0.

outtype

controls output; see value section below.

Value

If n is NULL (default), total sample size (2 arms combined) is computed. Otherwise, power is computed. If outtype=1 (default), the computed value (sample size or power) is returned in a scalar or vector. If outtype=2, a data frame with sample sizes for each arm (n1, n2)is returned; if n is not input as NULL, a third variable, Power, is added to the output data frame. If outtype=3, a data frame with is returned with the following columns:

n

A vector with total samples size required for each event rate comparison specified

n1

A vector of sample sizes for group 1 for each event rate comparison specified

n2

A vector of sample sizes for group 2 for each event rate comparison specified

alpha

As input

sided

As input

beta

As input; if n is input, this is computed

Power

If n=NULL on input, this is 1-beta; otherwise, the power is computed for each sample size input

sd

As input

sd2

As input

delta1

As input

delta0

As input

se

standard error for estimate of difference in treatment group means

Details

This is more of a convenience routine than one recommended for broad use without careful considerations such as those outlined in Jennison and Turnbull (2000). For larger studies where a conservative estimate of within group standard deviations is available, it can be useful. A more detailed formulation is available in the vignette on two-sample normal sample size.

References

Jennison C and Turnbull BW (2000), Group Sequential Methods with Applications to Clinical Trials. Boca Raton: Chapman and Hall.

Lachin JM (1981), Introduction to sample size determination and power analysis for clinical trials. Controlled Clinical Trials 2:93-113.

Snedecor GW and Cochran WG (1989), Statistical Methods. 8th ed. Ames, IA: Iowa State University Press.

See Also

gsDesign package overview

Examples

# NOT RUN {
# EXAMPLES
# equal variances
n=nNormal(delta1=.5,sd=1.1,alpha=.025,beta=.2)
n
x <- gsDesign(k = 3, n.fix = n, test.type = 4, alpha = 0.025, beta = 0.1, timing = c(.5,.75),
sfu = sfLDOF, sfl = sfHSD, sflpar = -1, delta1 = 0.5, endpoint = 'normal') 
gsBoundSummary(x)
summary(x)
# unequal variances, fixed design
nNormal(delta1 = .5, sd = 1.1, sd2 = 2, alpha = .025, beta = .2)
# unequal sample sizes
nNormal(delta1 = .5, sd = 1.1, alpha = .025, beta = .2, ratio = 2)
# non-inferiority assuming a better effect than null
nNormal(delta1 = .5, delta0 = -.1, sd = 1.2)
# }