Description Usage Arguments Details Value Note Author(s) References See Also Examples
View source: R/power_VSMc_linear.R
Calculate minimal detectable slope for mediator given sample size and power in simple linear regression based on Vittinghoff, Sen and McCulloch's (2009) method.
1 2 3 4 5 6 7  minEffect.VSMc(n,
power,
sigma.m,
sigma.e,
corr.xm,
alpha = 0.05,
verbose = TRUE)

n 
sample size. 
power 
power for testing b_2=0 for the linear regression y_i=b0+b1 x_i + b2 m_i + ε_i, ε_i\sim N(0, σ_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 + ε_i, ε_i\sim N(0, σ_e^2). 
corr.xm 
correlation between the predictor x and the mediator m. 
alpha 
type I error rate. 
verbose 
logical. 
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 + ε_i, ε_i\sim N(0, σ^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, if the
correlation corr.xm
between the primary predictor and mediator is nonzero.
The full model is
y_i=b_0+b_1 x_i + b_2 m_i + ε_i, ε_i\sim N(0, σ^2_{e}).
The reduced model is
y_i=b_0+b_1 x_i + ε_i, ε_i\sim N(0, σ^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.
b2 
minimum absolute detectable effect. 
res.uniroot 
results of optimization to find the optimal sample size. 
The test is a twosided test. For onesided tests, please double the
significance level. For example, you can set alpha=0.10
to obtain onesided test at 5% significance level.
Weiliang Qiu stwxq@channing.harvard.edu
Vittinghoff, E. and Sen, S. and McCulloch, C.E.. Sample size calculations for evaluating mediation. Statistics In Medicine. 2009;28:541557.
powerMediation.VSMc
,
ssMediation.VSMc
1 2 3 4  # example in section 3 (page 544) of Vittinghoff et al. (2009).
# minimum effect is =0.1
minEffect.VSMc(n = 863, power = 0.8, sigma.m = 1,
sigma.e = 1, corr.xm = 0.3, alpha = 0.05, verbose = TRUE)

[1] 0.0999804
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