powerMediation.VSMc {powerMediation}

Power for testing mediation effect in linear regression based on Vittinghoff, Sen and McCulloch's (2009) method

Description

Calculate Power for testing mediation effect in linear regression based on Vittinghoff, Sen and McCulloch's (2009) method.

Usage

powerMediation.VSMc(n, 
                    b2, 
                    sigma.m, 
                    sigma.e, 
                    corr.xm, 
                    alpha = 0.05, 
                    verbose = TRUE)

Arguments

n

sample size.

b2

regression coefficient for the mediator m in the linear regression y_i=b0+b1 x_i + b2 m_i + \epsilon_i, \epsilon_i\sim N(0, \sigma_e^2).

sigma.m

standard deviation of the mediator.

sigma.e

standard deviation of the random error term in the linear regression y_i=b0+b1 x_i + b2 m_i + \epsilon_i, \epsilon_i\sim N(0, \sigma_e^2).

corr.xm

correlation between the predictor x and the mediator m.

alpha

type I error rate.

verbose

logical. TRUE means printing power; FALSE means not printing power.

Details

The power is for testing the null hypothesis b_2=0 versus the alternative hypothesis b_2\neq 0 for the linear regressions:

y_i=b_0+b_1 x_i + b_2 m_i + \epsilon_i, \epsilon_i\sim N(0, \sigma^2_{e})

Vittinghoff et al. (2009) showed that for the above linear regression, testing the mediation effect is equivalent to testing the null hypothesis H_0: b_2=0 versus the alternative hypothesis H_a: b_2\neq 0.

The full model is

y_i=b_0+b_1 x_i + b_2 m_i + \epsilon_i, \epsilon_i\sim N(0, \sigma^2_{e})

The reduced model is

y_i=b_0+b_1 x_i + \epsilon_i, \epsilon_i\sim N(0, \sigma^2_{e})

Vittinghoff et al. (2009) mentioned that if confounders need to be included in both the full and reduced models, the sample size/power calculation formula could be accommodated by redefining corr.xm as the multiple correlation of the mediator with the confounders as well as the predictor.

Value

power

power for testing if b_2=0.

delta

b_2\sigma_m\sqrt{1-\rho_{xm}^2}/\sigma_e, where \sigma_m is the standard deviation of the mediator m, \rho_{xm} is the correlation between the predictor x and the mediator m, and \sigma_e is the standard deviation of the random error term in the linear regression.

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

Vittinghoff, E. and Sen, S. and McCulloch, C.E.. Sample size calculations for evaluating mediation. Statistics In Medicine. 2009;28:541-557.

See Also

minEffect.VSMc, ssMediation.VSMc

Examples

  # example in section 3 (page 544) of Vittinghoff et al. (2009).
  # power=0.8
  powerMediation.VSMc(n = 863, b2 = 0.1, sigma.m = 1, sigma.e = 1, 
    corr.xm = 0.3, alpha = 0.05, verbose = TRUE)