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

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Description

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

Usage

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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.

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.

Value

power

power for testing if b_2=0.

delta

b_2σ_m√{(1-ρ_{xm}^2) p (1-p)}

, 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 p is the marginal prevalence of the outcome.

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.logistic, ssMediation.VSMc.logistic

Examples

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  # 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)

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