powerMediation (version 0.3.4)

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

Description

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

Usage

powerMediation.VSMc.logistic(n, 
                             b2, 
                             sigma.m, 
                             p, 
                             corr.xm, 
                             alpha = 0.05, 
                             verbose = TRUE)

Arguments

n

sample size.

b2

regression coefficient for the mediator \(m\) in the logistic regression \(\log(p_i/(1-p_i))=b0+b1 x_i + b2 m_i\).

sigma.m

standard deviation of the mediator.

p

the marginal prevalence of the outcome.

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

\(b_2\sigma_m\sqrt{(1-\rho_{xm}^2) p (1-p)}\)

, 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 p is the marginal prevalence of the outcome.

Details

The power is for testing the null hypothesis \(b_2=0\) versus the alternative hypothesis \(b_2\neq 0\) for the logistic regressions: $$\log(p_i/(1-p_i))=b0+b1 x_i + b2 m_i$$

Vittinghoff et al. (2009) showed that for the above logistic 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 $$\log(p_i/(1-p_i))=b_0+b_1 x_i + b_2 m_i $$

The reduced model is $$\log(p_i/(1-p_i))=b_0+b_1 x_i$$

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.logistic, ssMediation.VSMc.logistic

Examples

# NOT RUN {
  # example in section 4 (page 545) of Vittinghoff et al. (2009).
  # power = 0.8005793
  powerMediation.VSMc.logistic(n = 255, b2 = log(1.5), sigma.m = 1, 
    p = 0.5, corr.xm = 0.5, alpha = 0.05, verbose = TRUE)
# }