ssMediation.VSMc {powerMediation} | R Documentation |
Calculate sample size for testing mediation effect in linear regression based on Vittinghoff, Sen and McCulloch's (2009) method.
ssMediation.VSMc(power,
b2,
sigma.m,
sigma.e,
corr.xm,
n.lower = 1,
n.upper = 1e+30,
alpha = 0.05,
verbose = TRUE)
power |
power for testing |
b2 |
regression coefficient for the mediator |
sigma.m |
standard deviation of the mediator. |
sigma.e |
standard deviation of the random error term in the linear regression
|
corr.xm |
correlation between the predictor |
n.lower |
lower bound for the sample size. |
n.upper |
upper bound for the sample size. |
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 + \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.
n |
sample size. |
res.uniroot |
results of optimization to find the optimal sample size. |
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.
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;28:541-557.
minEffect.VSMc
,
powerMediation.VSMc
# example in section 3 (page 544) of Vittinghoff et al. (2009).
# n=863
ssMediation.VSMc(power = 0.80, b2 = 0.1, sigma.m = 1, sigma.e = 1,
corr.xm = 0.3, alpha = 0.05, verbose = TRUE)