Minimum detectable slope for mediator in poisson regression based on Vittinghoff, Sen and McCulloch's (2009) method

Description

Calculate minimal detectable slope for mediator given sample size and power in poisson regression based on Vittinghoff, Sen and McCulloch's (2009) method.

Usage

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

Arguments

n

sample size.

power

power for testing b_2=0 for 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 minimum absolute detectable effect; FALSE means not printing minimum absolute detectable effect.

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, if the correlation corr.xm between the primary predictor and mediator is non-zero.

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

b2

minimum absolute detectable effect.

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

powerMediation.VSMc.poisson, ssMediation.VSMc.poisson

Examples

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  # example in section 5 (page 546) of Vittinghoff et al. (2009).
  # minimum effect is = log(1.35) = 0.3001046
  minEffect.VSMc.poisson(n = 1239, power = 0.7998578, 
    sigma.m = sqrt(0.25 * (1 - 0.25)), 
    EY = 0.5, corr.xm = 0.5, 
    alpha = 0.05, verbose = TRUE)

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