powerMediation (version 0.2.3)

ssLongFull: Sample size calculation for longitudinal study with 2 time point

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

ssLongFull(delta, 
           sigma1, 
           sigma2, 
           rho = 0.5, 
           alpha = 0.05, 
           power = 0.8)

Arguments

delta

absolute difference of the mean changes between the two groups: $\delta=|\mu_1 - \mu_2|$ where $\mu_1$ is the mean change over time $t$ in group 1, $\mu_2$ is the mean change over time $t$ in group 2.

sigma1

the variance of baseline values within a treatment group

sigma2

the variance of follow-up values within a treatment group

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.

Value

• required sample size per group

Details

The sample size formula is based on Equation 8.30 on page 335 of Rosner (2006). $$n=\frac{2\sigma_d^2 (Z_{1-\alpha/2} + Z_{power})^2}{\delta^2}$$ where $\sigma_d = \sigma_1^2+\sigma_2^2-2\rho\sigma_1\sigma_2$, $\delta=|\mu_1 - \mu_2|$, $\mu_1$ is the mean change over time $t$ in group 1, $\mu_2$ is the mean change over time $t$ in group 2, $\sigma_1^2$ is the variance of baseline values within a treatment group, $\sigma_2^2$ is the variance of follow-up values within a treatment group, $\rho$ 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 $\mu_1 = \mu_2$.

References

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

See Also

ssLong, powerLong, powerLongFull.

Examples

# Example 8.33 on page 336 of Rosner (2006)
    # n=85
    ssLongFull(delta=5, sigma1=15, sigma2=15, rho=0.7, alpha=0.05, power=0.8)