factorial2x2: Design and Analysis of 2x2 Factorial Trial

Description Usage Arguments Details Value References See Also Examples

Computes the power of the 1/3-1/3-1/3 procedure, that is, the power to detect the overall A effect, the simple A effect, or the simple AB effect.

power13_13_13(n, hrA, hrB, hrAB, avgprob, probA_C, probAB_C, crit13, dig,
  cormat12 = matrix(c(1, sqrt(0.5), sqrt(0.5), 1), byrow = T, nrow = 2),
  cormat23 = matrix(c(1, 0.5, 0.5, 1), byrow = T, nrow = 2),
  cormat123 = matrix(c(1, sqrt(0.5), sqrt(0.5), sqrt(0.5), 1, 0.5,
  sqrt(0.5), 0.5, 1), byrow = T, nrow = 3), 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
`hrB`	group B 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
`avgprob`	event probability averaged across the C, A, B, and AB groups
`probA_C`	event probability averaged across the A and C groups
`probAB_C`	event probability averaged across the AB and C groups
`crit13`	rejection critical value for the overall A, simple A, and simple AB logrank statistics
`dig`	number of decimal places to `roundDown` the critical value to
`cormat12`	asymptotic correlation matrix for the overall A and simple A, respectively, simple AB logrank statistics
`cormat23`	asymptotic correlation matrix for the simple A and simple AB logrank statistics
`cormat123`	asymptotic correlation matrix for the overall A, 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 overall A or the simple A or the simple AB logrank statistics reject their null hypotheses at the crit13 critical value. As described in Leifer, Troendle, et al. (2019), the crit13 = -2.32 critical value corresponds to controlling the famiywise error of the 1/3-1/3-1/3 procedure at the two-sided 0.05 significance level. The critical value -2.32 may be computed using the crit2x2 function. The pmvnorm function from the mvtnorm package is used to calculate the powers for rejecting the pairwise and three-way intersections of Since these powers involve bivariate, respectively, trivariate, normal integration over an unbounded region in R^2, respectively, R^3, pmvnorm uses a random seed for these computations. To smooth out the randomness, pmvnorm is called niter times and the average value over the niter calls is taken to be those powers.

`poweroverA`	power to detect the overall A effect
`powerA`	power to detect the simple A effect
`powerAB`	power to detect the simple AB effect
`power13.13.13`	power to detect the overall A, simple A, or simple AB effects, i.e., power of the 1/3-1/3-1/3 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, strLgrkPower, pmvnorm

# Corresponds to scenario 5 in Table 2 from Leifer, Troendle, et al. (2019).
rateC <- 0.0445
hrA <- 0.80
hrB <- 0.80
hrAB <- 0.72
mincens <- 4.0
maxcens <- 8.4
evtprob <- eventProb(rateC, hrA, hrB, hrAB, mincens, maxcens)
avgprob <- evtprob$avgprob
probAB_C <- evtprob$probAB_C
probA_C <- evtprob$probA_C
dig <- 2
alpha <- 0.05
corAa  <- 1/sqrt(2)
corAab <- 1/sqrt(2)
coraab <- 1/2
crit13 <- crit2x2(corAa, corAab, coraab, dig, alpha)$crit13
n <- 4600
power13_13_13(n, hrA, hrB, hrAB, avgprob, probA_C, probAB_C,
  crit13, dig, cormat12 = matrix(c(1, sqrt(0.5), sqrt(0.5), 1), byrow = TRUE,
  nrow = 2), cormat23 = matrix(c(1, 0.5, 0.5, 1), byrow = TRUE, nrow = 2),
  cormat123 = matrix(c(1, sqrt(0.5), sqrt(0.5), sqrt(0.5), 1, 0.5,
  sqrt(0.5), 0.5, 1), byrow=TRUE, nrow = 3), niter = 1, abseps = 1e-03)

# $poweroverA
# [1] 0.5861992

# $powerA
# [1] 0.5817954

# $powerAB
# [1] 0.9071236

# $power13.13.13
# [1] 0.9302078