RandEff_to_icc: Transform random effects into ICC, CAC, IAC

In PMildenb/SteppedPower: Power Calculation for Stepped Wedge Designs

Transform random effects into ICC, CAC, IAC

Description

This function transforms standard deviations of random effects into intracluster correlation (ICC), cluster autocorrelation (CAC) and individual autocorrelation (IAC). It reproduces the formulae in Hooper et al. (2016).

Usage

RandEff_to_icc(sigResid, tau, gamma = 0, psi = 0)

Arguments

sigResid	Residual standard deviation on individual level
tau	standard deviation of random cluster intercept
gamma	standard deviation of random time effect
psi	standard deviation of random subject specific intercept

Details

The formulae used are

\sigma^2_{marg} = \sigma^2_{resid} + \tau^2 + \gamma^2 + \psi^2 \\[1ex] ICC = \frac{\tau^2 + \gamma^2}{\sigma^2_{marg}} \\[1ex] CAC = \frac{\tau^2}{\tau^2 + \gamma^2} \\[1ex] IAC = \frac{\psi^2}{\sigma^2_{resid}+\psi^2}

Value

a list containing four named elements (possibly vectors or matrices):

• icc intracluster correlation

• cac cluster autocorrelation

• iac individual autocorrelation

• sigResid Residual standard deviation on individual level

References

Hooper, R., Teerenstra, S., de Hoop, E., & Eldridge, S. (2016).
Sample size calculation for stepped wedge and other longitudinal cluster randomised trials.
Statistics in medicine, 35(26), 4718-4728. DOI: 10.1002/sim.7028

See Also

icc_to_RandEff(), RandEff_to_alpha012() or alpha012_to_RandEff()

PMildenb/SteppedPower documentation built on Nov. 24, 2024, 3:06 a.m.