powerMediation (version 0.0.6)

powerMediation.VSMc: Power for testing mediation effect based on Vittinghoff and McCulloch's (2009) method

Description

Calculate Power for testing mediation effect based on Vittinghoff 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.

Value

• power
  power for testing if $b_2=0$.
• delta
  $b_2\sigma_m\sqrt{1-\rho_{xm}}/\sigma_e$, 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.

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 $H_a: b_2\neq 0$.

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

powerMediation.VSMc(n=100, b2=0.8, sigma.m=0.1, sigma.e=0.2, corr.xm=0.5, 
    alpha = 0.05, verbose = TRUE)