powerMediation (version 0.0.6)

ssMediation.VSMc: Sample size for testing mediation effect based on Vittinghoff and McCulloch's (2009) method

Description

Calculate sample size for testing mediation effect based on Vittinghoff and McCulloch's (2009) method.

Usage

ssMediation.VSMc(power, b2, sigma.m, sigma.e, corr.xm, 
  n.lower=1, n.upper=1e+30, alpha = 0.05, verbose=TRUE)

Arguments

power

power for testing $b_2=0$ for the linear regression $y_i=b0+b1 x_i + b2 m_i + \epsilon_i, \epsilon_i\sim N(0, \sigma_e^2)$.

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 $m$.

n.lower

lower bound for the sample size.

n.upper

upper bound for the sample size.

alpha

type I error rate.

verbose

logical. TRUE means printing sample size; FALSE means not printing sample size.

Value

• n
  sample size.
• res.uniroot
  results of optimization to find the optimal sample size.

Details

The test 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, powerMediation.VSMc

Examples

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