factorial2x2: Design and Analysis of 2x2 Factorial Trial

Description Usage Arguments Details Value References See Also Examples

Computes the power of the 1/2-1/2 procedure, that is, the power to detect the simple A effect or the simple AB effect.

1 2	power12_12(n, hrA, hrAB, probA_C, probAB_C, crit12, cormat = matrix(c(1, 0.5, 0.5, 1), byrow = TRUE, nrow = 2), niter = 5, abseps = 0.001)

`n`	total subjects with n/4 subjects in each of the C, A, B, and AB groups
`hrA`	group A to group C hazard ratio; `hrA` < 1 corresponds to group A superiority
`hrAB`	group AB to group C hazard ratio; `hrAB` < 1 corresponds to group AB superiority
`probA_C`	event probability averaged across the A and C groups
`probAB_C`	event probability averaged across the AB and C groups
`crit12`	logrank statistic critical value for both the simple A and simple AB effects
`cormat`	asymptotic correlation matrix for the simple A and simple AB logrank statistics
`niter`	number of times we call `pmvnorm` to average out its randomness
`abseps`	`abseps` setting in the `pmvnorm` call

For a 2-by-2 factorial design, this function computes the probability that either the simple A or the simple AB logrank statistics reject their null hypotheses using a crit12 critical value. When the two-sided familywise type I error is 0.05, we may use crit2x2 to compute crit12 = -2.22 which corresponds to a 0.0264 two-sided significance level. This is described in Leifer, Troendle, et al. (2019). The pmvnorm function from the mvtnorm package is used to calculate the power that both (intersection) the simple A and simple B effects are detected. pmvnorm uses a random seed in its algorithm. To smooth out the randomness, pmvnorm is called niter times and the average value over the niter calls is taken to be that power.

`poweroverA`	power to detect the overall A effect
`powerA`	power to detect the simple A effect
`powerAB`	power to detect the simple AB effect
`power12.12`	power to detect the simple A or simple AB effects, i.e., power of the 1/2-1/2 procedure

Leifer, E.S., Troendle, J.F., Kolecki, A., Follmann, D. Joint testing of overall and simple effect for the two-by-two factorial design. (2019). Submitted.

Slud, E.V. Analysis of factorial survival experiments. Biometrics. 1994; 50: 25-38.

crit2x2, lgrkPower, pmvnorm

# Corresponds to scenario 5 in Table 2 from Leifer, Troendle, et al. (2019).
rateC <- 0.0445  # one-year C group event rate
hrA <- 0.80
hrB <- 0.80
hrAB <- 0.72
mincens <- 4.0
maxcens <- 8.4
evtprob <- eventProb(rateC, hrA, hrB, hrAB, mincens, maxcens)
probA_C <- evtprob$probA_C
probAB_C <- evtprob$probAB_C
corAa  <- 1/sqrt(2)
corAab <- 1/sqrt(2)
coraab <- 1/2
dig <- 2
alpha <- 0.05
crit12 <- crit2x2(corAa, corAab, coraab, dig, alpha)$crit12
n <- 4600
power12_12(n, hrA, hrAB, probA_C, probAB_C,
  crit12, cormat = matrix(c(1,0.5,0.5,1), byrow = TRUE, nrow = 2),
  niter = 1, abseps = 1e-03)

# $powerA
# [1] 0.6203837

# $powerAB
# [1] 0.9226679

# $powerAandAB
# [1] 0.6018828

# $power12.12
# [1] 0.9411688