powerLong.multiTime {powerMediation}

Power calculation for testing if mean changes for 2 groups are the same or not for longitudinal study with more than 2 time points

Description

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

Usage

powerLong.multiTime(es, m, nn, sx2, rho = 0.5, alpha = 0.05)

Arguments

es

effect size

m

number of subjects

nn

number of observations per subject

sx2

within subject variance

rho

within subject correlation

alpha

type I error rate

Details

We are interested in comparing the slopes of the 2 groups A and B:

\beta_{1A} = \beta_{1B}

where

Y_{ijA}=\beta_{0A}+\beta_{1A} x_{jA} + \epsilon_{ijA}, j=1, \ldots, nn; i=1, \ldots, m

and

Y_{ijB}=\beta_{0B}+\beta_{1B} x_{jB} + \epsilon_{ijB}, j=1, \ldots, nn; i=1, \ldots, m

The power calculation formula is (Equation on page 30 of Diggle et al. (1994)):

power=\Phi\left[ -z_{1-\alpha} + \sqrt{\frac{m nn s_x^2 es^2}{2(1-\rho)}} \right]

where es=d/\sigma, d is the meaninful differnce of interest, sigma^2 is the variance of the random error, \rho is the within-subject correlation, and s_x^2 is the within-subject variance.

Value

power

Note

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.

Author(s)

Weiliang Qiu [e-mail]

References

Diggle PJ, Liang KY, and Zeger SL (1994). Analysis of Longitundinal Data. page 30. Clarendon Press, Oxford

See Also

ssLong.multiTime

Examples

  # power=0.8
  powerLong.multiTime(es=0.5/10, m=196, nn=3, sx2=4.22, rho = 0.5, alpha = 0.05)