minEffect.VSMc {powerMediation}R Documentation

Minimum detectable slope

Description

Calculate minimal detectable slope given sample size and power for simple linear regression.

Usage

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

Arguments

n sample size.
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).
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 minimum absolute detectable effect; FALSE means not printing minimum absolute detectable effect.

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.

Value

b2 minimum absolute detectable effect.
res.uniroot results of optimization to find the optimal sample size.

Note

The test is a two-sided test. Code for one-sided tests will be added later.

Author(s)

Weiliang Qiu stwxq@channing.harvard.edu

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

powerMediation.VSMc, ssMediation.VSMc

Examples

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

[Package powerMediation version 0.0.6 Index]