powerMediation (version 0.2.3)

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

Description

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

Usage

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 $\log(\lambda)=\log(\lambda_0)+b1 x_i + b2 m_i$, where $\lambda$ is the hazard function and $\lambda_0$ 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.

Value

• power
  power for testing if $b_2=0$.
• delta
  $b_2\sigma_m\sqrt{(1-\rho_{xm}^2) psi}$
• , where $\sigma_m$ is the standard deviation of the mediator $m$, $\rho_{xm}$ 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.

Details

The power is for testing the null hypothesis $b_2=0$ versus the alternative hypothesis $b_2\neq 0$ for the cox regressions: $$\log(\lambda)=\log(\lambda_0)+b_1 x_i + b_2 m_i$$ where $\lambda$ is the hazard function and $\lambda_0$ 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 $$\log(\lambda)=\log(\lambda_0)+b_1 x_i + b_2 m_i$$

The reduced model is $$\log(\lambda)=\log(\lambda_0)+b_1 x_i$$

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.

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

minEffect.VSMc.cox, ssMediation.VSMc.cox

Examples

# 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)