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

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Description

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

Usage

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

Arguments

power

power for testing b_2=0 for the linear regression y_i=b0+b1 x_i + b2 m_i + ε_i, ε_i\sim N(0, σ_e^2).

b2

regression coefficient for the mediator m in the linear regression y_i=b0+b1 x_i + b2 m_i + ε_i, ε_i\sim N(0, σ_e^2).

sigma.m

standard deviation of the mediator.

sigma.e

standard deviation of the random error term in the linear regression y_i=b0+b1 x_i + b2 m_i + ε_i, ε_i\sim N(0, σ_e^2).

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 linear regressions:

y_i=b_0+b_1 x_i + b_2 m_i + ε_i, ε_i\sim N(0, σ^2_{e})

Vittinghoff et al. (2009) showed that for the above linear 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

y_i=b_0+b_1 x_i + b_2 m_i + ε_i, ε_i\sim N(0, σ^2_{e}).

The reduced model is

y_i=b_0+b_1 x_i + ε_i, ε_i\sim N(0, σ^2_{e}).

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, powerMediation.VSMc

Examples

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  # example in section 3 (page 544) of Vittinghoff et al. (2009).
  # n=863
  ssMediation.VSMc(power = 0.80, b2 = 0.1, sigma.m = 1, sigma.e = 1, 
    corr.xm = 0.3, alpha = 0.05, verbose = TRUE)

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