# ssLong: Sample size calculation for longitudinal study with 2 time... 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 2 time point.

## Usage

 1 2 3 4 ssLong(es, rho = 0.5, alpha = 0.05, power = 0.8) 

## Arguments

 es effect size of the difference of mean change. rho correlation coefficient between baseline and follow-up values within a treatment group. alpha Type I error rate. power power for testing for difference of mean changes.

## Details

The sample size formula is based on Equation 8.30 on page 335 of Rosner (2006).

n=\frac{2σ_d^2 (Z_{1-α/2} + Z_{power})^2}{δ^2}

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

n=\frac{4(1-ρ)(Z_{1-α/2}+Z_{β})^2}{d^2}

where d=δ/σ.

## Value

required sample size 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

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

ssLongFull, powerLong, powerLongFull.
 1 2 3  # Example 8.33 on page 336 of Rosner (2006) # n=85 ssLong(es=5/15, rho=0.7, alpha=0.05, power=0.8)