Calculate Power for testing mediation effect in cox regression based on Vittinghoff, Sen and McCulloch's (2009) method.
1 2 3 4 5 6 7  powerMediation.VSMc.cox(n,
b2,
sigma.m,
psi,
corr.xm,
alpha = 0.05,
verbose = TRUE)

n 
sample size. 
b2 
regression coefficient for the mediator m in the cox regression \log(λ)=\log(λ_0)+b1 x_i + b2 m_i, where λ is the hazard function and λ_0 is the baseline hazard function. 
sigma.m 
standard deviation of the mediator. 
psi 
the probability that an observation is uncensored, so that the number of event d= n * psi, where n is the sample size. 
corr.xm 
correlation between the predictor x and the mediator m. 
alpha 
type I error rate. 
verbose 
logical. 
The power is for testing the null hypothesis b_2=0 versus the alternative hypothesis b_2\neq 0 for the cox regressions:
\log(λ)=\log(λ_0)+b_1 x_i + b_2 m_i,
where λ is the hazard function and λ_0 is the baseline hazard function.
Vittinghoff et al. (2009) showed that for the above cox 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
\log(λ)=\log(λ_0)+b_1 x_i + b_2 m_i
The reduced model is
\log(λ)=\log(λ_0)+b_1 x_i
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.
power 
power for testing if b_2=0. 
delta 
b_2σ_m√{(1ρ_{xm}^2) psi} 
, where σ_m is the standard deviation of the mediator m, ρ_{xm} is the correlation between the predictor x and the mediator m, and psi is the probability that an observation is uncensored, so that the number of event d= n * psi, where n is the sample size.
The test is a twosided test. Code for onesided tests will be added later.
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.
minEffect.VSMc.cox
,
ssMediation.VSMc.cox
1 2 3 4 5  # example in section 6 (page 547) of Vittinghoff et al. (2009).
# power = 0.7999916
powerMediation.VSMc.cox(n = 1399, b2 = log(1.5),
sigma.m = sqrt(0.25 * (1  0.25)), psi = 0.2, corr.xm = 0.3,
alpha = 0.05, verbose = TRUE)

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