VarClosed_Kasza: Closed formula for treatment variance in open cohort settings

In SteppedPower: Power Calculation for Stepped Wedge Designs

Closed formula for treatment variance in open cohort settings

Description

From Kasza et al "Sample size and power calculations for open cohort longitudinal cluster rondomized trials" 2020

Usage

VarClosed_Kasza(trtMat, tau, gamma = 0, psi = 0, sigma, N, chi)

Arguments

trtMat	a matrix trtMat to define treatment allocation, where rows and columns correspond to cluster and timepoints, respectively
tau	numeric, standard deviation of random intercepts
gamma	numeric, random time effect
psi	numeric, random subject specific intercept.
sigma	numeric, residual error on subject level.
N	numeric, number of individuals per cluster.
chi	Attrition factor

Value

numeric, variance of the estimator for treatment effect

Examples

##  test setting, from Hussey&Hughes 2007  ####
trtMat <- construct_DesMat(c(6,6,6,6))$trtMat
tau <- .025 ; sigma <- sqrt(.041*.959) ; N <- 100 ;
gamma <- 0.01 ; psi <- .1 ; chi <- .7

tmp <- VarClosed_Kasza(trtMat, tau=tau, sigma=sigma, gamma=0, psi=0, N=N, chi=0)
tTestPwr((.05-.032), sqrt(tmp), df = Inf)
glsPower(Cl = rep(6,4), N=N, mu0=.05, mu1=.032, verbose=0,
        sigma=sigma, gamma=0, tau=tau, psi=0)

tmp <- VarClosed_Kasza(trtMat, tau=tau, sigma=sigma, gamma=gamma, psi=psi, N=N, chi=0)
tTestPwr((.05-.032), sqrt(tmp), df = Inf)
glsPower(Cl = rep(6,4), N=N, mu0=.05, mu1=.032, verbose=0,
        sigma=sigma, gamma=gamma, tau=tau, psi=psi)

tmp <- VarClosed_Kasza(trtMat, tau=tau, sigma=sigma, gamma=gamma, psi=psi, N=N, chi=1)
tTestPwr((.05-.032), sqrt(tmp), df = Inf)
glsPower(Cl = rep(6,4), N=N, mu0=.05, mu1=.032, verbose=0,
         sigma=sigma, gamma=sqrt(gamma^2+psi^2/N), tau=tau, psi=0)

tmp <- VarClosed_Kasza(trtMat, tau=tau, sigma=sigma, gamma=gamma, psi=psi, N=N, chi=chi)
tTestPwr((.05-.032), sqrt(tmp), df = Inf)
glsPower(Cl = rep(6,4), N=N, mu0=.05, mu1=.032, verbose=0,
         sigma=sigma, gamma=sqrt(gamma^2+chi*psi^2/N), tau=tau, psi=sqrt(1-chi)*psi)

SteppedPower documentation built on Sept. 13, 2023, 1:07 a.m.