# powerMediation.VSMc.cox: Power for testing mediation effect in cox regression based on... In powerMediation: Power/Sample Size Calculation for Mediation Analysis

## Description

Calculate Power for testing mediation effect in cox regression based on Vittinghoff, Sen and McCulloch's (2009) method.

## Usage

 1 2 3 4 5 6 7 powerMediation.VSMc.cox(n, b2, sigma.m, psi, corr.xm, alpha = 0.05, verbose = TRUE)

## Arguments

 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. TRUE means printing power; FALSE means not printing power.

## Details

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.

## Value

 power power for testing if b_2=0. delta b_2σ_m√{(1-ρ_{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.

## Note

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.

## 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.