ssMediation.VSMc.cox: Sample size for testing mediation effect in cox regression... In powerMediation: Power/Sample Size Calculation for Mediation Analysis

Description

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

Usage

 ```1 2 3 4 5 6 7 8 9``` ```ssMediation.VSMc.cox(power, b2, sigma.m, psi, corr.xm, n.lower = 1, n.upper = 1e+30, alpha = 0.05, verbose=TRUE) ```

Arguments

 `power` power for testing b_2=0 for the cox regression \log(λ)=\log(λ_0)+b1 x_i + b2 m_i, where λ is the hazard function and λ_0 is the baseline hazard function. `b2` regression coefficient for the mediator m in the cox regression \log(λ)=\log(λ_0)+b1 x_i + b2 m_i, where λ is the hazard function and λ_0 is the baseline hazard function. `sigma.m` standard deviation of the mediator. `psi` the probability that an observation is uncensored, so that the number of event d= n * psi, where n is the sample size. `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 cox regressions:

\log(λ)=\log(λ_0)+b1 x_i + b2 m_i

Vittinghoff et al. (2009) showed that for the above cox 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(λ)=\log(λ_0)+b_1 x_i + b_2 m_i

The reduced model is

\log(λ)=\log(λ_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. 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 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.

`minEffect.VSMc.cox`, `powerMediation.VSMc.cox`
 ```1 2 3 4 5``` ``` # example in section 6 (page 547) of Vittinghoff et al. (2009). # n = 1399 ssMediation.VSMc.cox(power = 0.7999916, b2 = log(1.5), sigma.m = sqrt(0.25 * (1 - 0.25)), psi = 0.2, corr.xm = 0.3, alpha = 0.05, verbose = TRUE) ```