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

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Description

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

Usage

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

Arguments

power

power for testing b_2=0 for the poisson regression \log(E(Y_i))=b0+b1 x_i + b2 m_i.

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.

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 poisson regressions:

\log(E(Y_i))=b_0+b_1 x_i + b_2 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

n

sample size.

res.uniroot

results of optimization to find the optimal sample size.

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.poisson, powerMediation.VSMc.poisson

Examples

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

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