VarClosed_Kasza {SteppedPower}

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)