Normal distribution sample size (2-sample)

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.

Author

Keaven Anderson keaven_anderson@merck.com

Examples


# EXAMPLES
# equal variances
n=nNormal(delta1=.5,sd=1.1,alpha=.025,beta=.2)
n
#> [1] 151.9543
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)
#>   Analysis                 Value Efficacy Futility
#>  IA 1: 50%                     Z   2.9626   0.6475
#>      N: 86           p (1-sided)   0.0015   0.2587
#>                  ~delta at bound   0.6109   0.1335
#>              P(Cross) if delta=0   0.0015   0.7413
#>            P(Cross) if delta=0.5   0.2954   0.0378
#>  IA 2: 75%                     Z   2.3590   1.3115
#>     N: 128           p (1-sided)   0.0092   0.0948
#>                  ~delta at bound   0.3972   0.2208
#>              P(Cross) if delta=0   0.0096   0.9155
#>            P(Cross) if delta=0.5   0.7309   0.0650
#>      Final                     Z   2.0141   2.0141
#>     N: 171           p (1-sided)   0.0220   0.0220
#>                  ~delta at bound   0.2937   0.2937
#>              P(Cross) if delta=0   0.0219   0.9781
#>            P(Cross) if delta=0.5   0.9000   0.1000
summary(x)
#> [1] "Asymmetric two-sided group sequential design with non-binding futility bound, 3 analyses, sample size 171, 90 percent power, 2.5 percent (1-sided) Type I error. Efficacy bounds derived using a Lan-DeMets O'Brien-Fleming approximation spending function (no parameters). Futility bounds derived using a Hwang-Shih-DeCani spending function with gamma = -1."
# unequal variances, fixed design
nNormal(delta1 = .5, sd = 1.1, sd2 = 2, alpha = .025, beta = .2)
#> [1] 327.1413
# unequal sample sizes
nNormal(delta1 = .5, sd = 1.1, alpha = .025, beta = .2, ratio = 2)
#> [1] 170.9486
# non-inferiority assuming a better effect than null
nNormal(delta1 = .5, delta0 = -.1, sd = 1.2)
#> [1] 168.1188