power.mmrm.ar1: Linear mixed model sample size calculations.
In longpower: Sample Size Calculations for Longitudinal Data

power.mmrm.ar1

R Documentation

Linear mixed model sample size calculations.

Description

This function performs the sample size calculation for a mixed model of repeated measures with AR(1) correlation structure. See Lu, Luo, & Chen (2008) for parameter definitions and other details.

Usage

power.mmrm.ar1(
  N = NULL,
  rho = NULL,
  ra = NULL,
  sigmaa = NULL,
  rb = NULL,
  sigmab = NULL,
  lambda = 1,
  times = 1:length(ra),
  delta = NULL,
  sig.level = 0.05,
  power = NULL,
  alternative = c("two.sided", "one.sided"),
  tol = .Machine$double.eps^2
)

Arguments

`N`	total sample size
`rho`	AR(1) correlation parameter
`ra`	retention in group a
`sigmaa`	standard deviation of observation of interest in group a
`rb`	retention in group a (assumed same as `ra` if left blank)
`sigmab`	standard deviation of observation of interest in group b. If NULL, `sigmab` is assumed same as `sigmaa`. If not NULL, `sigmaa` and `sigmab` are averaged.
`lambda`	allocation ratio
`times`	observation times
`delta`	effect size
`sig.level`	type one error
`power`	power
`alternative`	one- or two-sided test
`tol`	numerical tolerance used in root finding.

Details

See Lu, Luo, & Chen (2008).

Value

The number of subject required per arm to attain the specified power given sig.level and the other parameter estimates.

Author(s)

Michael C. Donohue

References

Lu, K., Luo, X., Chen, P.-Y. (2008) Sample size estimation for repeated measures analysis in randomized clinical trials with missing data. International Journal of Biostatistics, 4, (1)

Examples


# reproduce Table 2 from Lu, Luo, & Chen (2008)
tab <- c()
for(J in c(2,4))
for(aJ in (1:4)/10)
for(p1J in c(0, c(1, 3, 5, 7, 9)/10)){
  rJ <- 1-aJ
  r <- seq(1, rJ, length = J)
  # p1J = p^(J-1)
  tab <- c(tab, power.mmrm.ar1(rho = p1J^(1/(J-1)), ra = r, sigmaa = 1, 
    lambda = 1, times = 1:J,
    delta = 1, sig.level = 0.05, power = 0.80)$phi1)
}
matrix(tab, ncol = 6, byrow = TRUE)

# approximate simulation results from Table 5 from Lu, Luo, & Chen (2008)
ra <- c(100, 76, 63, 52)/100
rb <- c(100, 87, 81, 78)/100

power.mmrm.ar1(rho=0.6, ra=ra, sigmaa=1, rb = rb, 
               lambda = sqrt(1.25/1.75), power = 0.904, delta = 0.9)
power.mmrm.ar1(rho=0.6, ra=ra, sigmaa=1, rb = rb, 
               lambda = 1.25/1.75, power = 0.910, delta = 0.9)
power.mmrm.ar1(rho=0.6, ra=ra, sigmaa=1, rb = rb, 
               lambda = 1, power = 0.903, delta = 0.9)
power.mmrm.ar1(rho=0.6, ra=ra, sigmaa=1, rb = rb,
               lambda = 2, power = 0.904, delta = 0.9)

power.mmrm.ar1(N=81, ra=ra, sigmaa=1, rb = rb, 
               lambda = sqrt(1.25/1.75), power = 0.904, delta = 0.9)
power.mmrm.ar1(N=87, rho=0.6, ra=ra, sigmaa=1, rb = rb,
               lambda = 1.25/1.75, power = 0.910)
power.mmrm.ar1(N=80, rho=0.6, ra=ra, sigmaa=1, rb = rb, 
               lambda = 1, delta = 0.9)
power.mmrm.ar1(N=84, rho=0.6, ra=ra, sigmaa=1, rb = rb,
               lambda = 2, power = 0.904, delta = 0.9, sig.level = NULL)

# Extracting paramaters from gls objects with AR1 correlation

# Create time index:
Orthodont$t.index <- as.numeric(factor(Orthodont$age, levels = c(8, 10, 12, 14)))
with(Orthodont, table(t.index, age))

fmOrth.corAR1 <- gls( distance ~ Sex * I(age - 11), 
  Orthodont,
  correlation = corAR1(form = ~ t.index | Subject),
  weights = varIdent(form = ~ 1 | age) )
summary(fmOrth.corAR1)$tTable

C <- corMatrix(fmOrth.corAR1$modelStruct$corStruct)[[1]]
sigmaa <- fmOrth.corAR1$sigma *
          coef(fmOrth.corAR1$modelStruct$varStruct, unconstrained = FALSE)['14']
ra <- seq(1,0.80,length=nrow(C))
power.mmrm(N=100, Ra = C, ra = ra, sigmaa = sigmaa, power = 0.80)
power.mmrm.ar1(N=100, rho = C[1,2], ra = ra, sigmaa = sigmaa, power = 0.80)

longpower documentation built on Jan. 11, 2023, 5:12 p.m.