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

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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. Code for one-sided tests will be added later.

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.

See Also

minEffect.VSMc.cox, ssMediation.VSMc.cox

Examples

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  # 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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