Description Usage Arguments Details Value Note Author(s) References See Also Examples

View source: R/powerLongitudinal.R

Power calculation for testing if mean changes for 2 groups are the same or not for longitudinal study with 2 time point.

1 2 3 4 | ```
powerLong(es,
n,
rho = 0.5,
alpha = 0.05)
``` |

`es` |
effect size of the difference of mean change. |

`n` |
sample size per group. |

`rho` |
correlation coefficient between baseline and follow-up values within a treatment group. |

`alpha` |
Type I error rate. |

The power formula is based on Equation 8.31 on page 336 of Rosner (2006).

*
power=Φ≤ft(-Z_{1-α/2}+\frac{δ√{n}}{σ_d √{2}}\right)
*

where *σ_d = σ_1^2+σ_2^2-2ρσ_1σ_2*, *δ=|μ_1 - μ_2|*,
*μ_1* is the mean change over time *t* in group 1,
*μ_2* is the mean change over time *t* in group 2,
*σ_1^2* is the variance of baseline values within a treatment group,
*σ_2^2* is the variance of follow-up values within a treatment group,
*ρ* is the correlation coefficient between baseline and follow-up values within a treatment group,
and *Z_u* is the u-th percentile of the standard normal distribution.

We wish to test *μ_1 = μ_2*.

When *σ_1=σ_2=σ*, then formula reduces to

*
power=Φ≤ft(-Z_{1-α/2} + \frac{|d|√{n}}{2√{1-ρ}}\right)
*

where *d=δ/σ*.

power for testing for difference of mean changes.

The test is a two-sided test. For one-sided tests, please double the
significance level. For example, you can set `alpha=0.10`

to obtain one-sided test at 5% significance level.

Weiliang Qiu stwxq@channing.harvard.edu

Rosner, B.
*Fundamentals of Biostatistics*. Sixth edition. Thomson Brooks/Cole. 2006.

`ssLong`

, `ssLongFull`

,
`powerLongFull`

.

1 2 3 | ```
# Example 8.34 on page 336 of Rosner (2006)
# power=0.75
powerLong(es=5/15, n=75, rho=0.7, alpha=0.05)
``` |

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