ssLong {powerMediation}R Documentation

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.

Details

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

n=2σd2(Z1α/2+Zpower)2δ2 n=\frac{2\sigma_d^2 (Z_{1-\alpha/2} + Z_{power})^2}{\delta^2}

where σd=σ12+σ222ρσ1σ2\sigma_d = \sigma_1^2+\sigma_2^2-2\rho\sigma_1\sigma_2, δ=μ1μ2\delta=|\mu_1 - \mu_2|, μ1\mu_1 is the mean change over time tt in group 1, μ2\mu_2 is the mean change over time tt in group 2, σ12\sigma_1^2 is the variance of baseline values within a treatment group, σ22\sigma_2^2 is the variance of follow-up values within a treatment group, ρ\rho is the correlation coefficient between baseline and follow-up values within a treatment group, and ZuZ_u is the u-th percentile of the standard normal distribution.

We wish to test μ1=μ2\mu_1 = \mu_2.

When σ1=σ2=σ\sigma_1=\sigma_2=\sigma, then formula reduces to

n=4(1ρ)(Z1α/2+Zβ)2d2 n=\frac{4(1-\rho)(Z_{1-\alpha/2}+Z_{\beta})^2}{d^2}

where d=δ/σd=\delta/\sigma.

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.

See Also

ssLongFull, powerLong, powerLongFull.

Examples

    # Example 8.33 on page 336 of Rosner (2006)
    # n=85
    ssLong(es=5/15, rho=0.7, alpha=0.05, power=0.8)

[Package powerMediation version 0.3.4 Index]