ssMediation.VSMc.cox: Sample size for testing mediation effect in cox regression...

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

View source: R/power_VSMc_cox.R

Description

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

Usage

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ssMediation.VSMc.cox(power, 
                     b2, 
                     sigma.m, 
                     psi, 
                     corr.xm, 
                     n.lower = 1, 
                     n.upper = 1e+30, 
                     alpha = 0.05, 
                     verbose=TRUE)

Arguments

power

power for testing b_2=0 for 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.

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.

n.lower

lower bound for the sample size.

n.upper

upper bound for the sample size.

alpha

type I error rate.

verbose

logical. TRUE means printing sample size; FALSE means not printing sample size.

Details

The test 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)+b1 x_i + b2 m_i

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

n

sample size.

res.uniroot

results of optimization to find the optimal 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, powerMediation.VSMc.cox

Examples

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  # example in section 6 (page 547) of Vittinghoff et al. (2009).
  # n = 1399
  ssMediation.VSMc.cox(power = 0.7999916, 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 Feb. 9, 2018, 6:10 a.m.