powerMediation.VSMc.cox: Power for testing mediation effect in cox regression based on...

Description Usage Arguments Details Value Note Author(s) References See Also Examples

View source: R/power_VSMc_cox.R

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. 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 [email protected]

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)

powerMediation documentation built on Sept. 12, 2017, 9:03 a.m.