powerLongFull: Power calculation for longitudinal study with 2 time point

In powerMediation: Power/Sample Size Calculation for Mediation Analysis

Description

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

Usage

powerLongFull(delta, 
              sigma1, 
              sigma2, 
              n, 
              rho = 0.5, 
              alpha = 0.05)

Arguments

delta	absolute difference of the mean changes between the two groups: δ=|μ_1 - μ_2| where μ_1 is the mean change over time t in group 1, μ_2 is the mean change over time t in group 2.
sigma1	the standard deviation of baseline values within a treatment group
sigma2	the standard deviation of follow-up values within a treatment group
n	sample size per group
rho	correlation coefficient between baseline and follow-up values within a treatment group.
alpha	Type I error rate.

Details

The power formula is based on Equation 8.31 on page 336 of Rosner (2006).

power=Φ≤ft(-Z_{1-α/2}+\frac{δ√{n}}{σ_d √{2}}\right)

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.

Value

power for testing for difference of mean changes.

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 [e-mail]

References

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

See Also

ssLong, ssLongFull, powerLong.

Examples

    # Example 8.33 on page 336 of Rosner (2006)
    # power=0.80
    powerLongFull(delta=5, sigma1=15, sigma2=15, n=85, rho=0.7, alpha=0.05)

Example output

[1] 0.8010713

powerMediation documentation built on March 24, 2021, 1:06 a.m.