powerMediation.VSMc.poisson {powerMediation}

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

Description

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

Usage

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

Arguments

n

sample size.

b2

regression coefficient for the mediator m in the poisson regression \log(E(Y_i))=b0+b1 x_i + b2 m_i.

sigma.m

standard deviation of the mediator.

EY

the marginal mean 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 poisson regressions:

\log(E(Y_i))=b0+b1 x_i + b2 m_i

Vittinghoff et al. (2009) showed that for the above poisson 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(E(Y_i))=b_0+b_1 x_i + b_2 m_i

The reduced model is

\log(E(Y_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_2\sigma_m\sqrt{(1-\rho_{xm}^2) EY}

, 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 EY is the marginal mean of the outcome.

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 [e-mail]

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.poisson, ssMediation.VSMc.poisson

Examples

  # example in section 5 (page 546) of Vittinghoff et al. (2009).
  # power = 0.7998578
  powerMediation.VSMc.poisson(n = 1239, b2 = log(1.35), 
    sigma.m = sqrt(0.25 * (1 - 0.25)), EY = 0.5, corr.xm = 0.5,
    alpha = 0.05, verbose = TRUE)