# ssLong.multiTime: Sample size calculation for testing if mean changes for 2... In powerMediation: Power/Sample Size Calculation for Mediation Analysis

## Description

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

## Usage

 1 ssLong.multiTime(es, power, nn, sx2, rho = 0.5, alpha = 0.05) 

## Arguments

 es effect size power power 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:

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

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

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.

## Value

subject per group

## 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 stwxq@channing.harvard.edu

## References

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

powerLong.multiTime
 1 2 # subject per group = 196 ssLong.multiTime(es=0.5/10, power=0.8, nn=3, sx2=4.22, rho = 0.5, alpha=0.05)