powerLong.multiTime: Power calculation for testing if mean changes for 2 groups...
In powerMediation: Power/Sample Size Calculation for Mediation Analysis

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

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

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

`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

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

β_{1A} = β_{1B}

where

Y_{ijA}=β_{0A}+β_{1A} x_{jA} + ε_{ijA}, j=1, …, nn; i=1, …, m

and

Y_{ijB}=β_{0B}+β_{1B} x_{jB} + ε_{ijB}, j=1, …, nn; i=1, …, m

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

power=Φ≤ft[ -z_{1-α} + √{\frac{m nn s_x^2 es^2}{2(1-ρ)}} \right]

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

power

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

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

ssLong.multiTime