R: Normal distribution sample size (2-sample)

nNormal {gsDesign} | R Documentation

## 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.

### 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.

### 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

### Author(s)

Keaven Anderson keaven_anderson@merck.com

### 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

    # 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)

[Package gsDesign version 3.2.0 Index]