powerMediation (version 0.3.4)

ssLong: 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

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.

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 ${\mu }_1={\mu }_2$.

When ${\sigma }_1={\sigma }_2=\sigma$, then formula reduces to $$n=\frac{4(1-\rho )(Z_{1-\alpha /2}+Z_{\beta }{)}^2}{d^2}$$ where $d=\delta /\sigma$.

References

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

See Also

ssLongFull, powerLong, powerLongFull.

Examples

# NOT RUN {
    # Example 8.33 on page 336 of Rosner (2006)
    # n=85
    ssLong(es=5/15, rho=0.7, alpha=0.05, power=0.8)
# }