powerEA3: Power of the Equal Allocation 3 procedure
In factorial2x2: Design and Analysis of a 2x2 Factorial Trial

Description Usage Arguments Details Value References See Also Examples

Computes the Equal Allocation 3 procedure's power to detect the overall A effect, the simple A effect, or the simple AB effect, respectively.

powerEA3(
  n,
  hrA,
  hrB,
  hrAB,
  avgprob,
  probA_C,
  probAB_C,
  critEA3,
  dig,
  cormat12 = matrix(c(1, sqrt(0.5), sqrt(0.5), 1), byrow = T, 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
`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
`critEA3`	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
`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 Dunnet-corrected critEA3 critical value. As described in Leifer, Troendle, et al. (2019), the critEA3 = -2.32 critical value corresponds to controlling the famiywise error of the Equal Allocation 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 power for simultaneously detecting the overall and simple A effects. This is used to compute the power for detecting the overall A and/or simple A effects, which is computed as the sum of the powers for each of the effects minus the power for simultaneously detecting both effects. Since the power for simultaneously detecting both effects involves bivariate normal integration over an unbounded region in R^2, pmvnorm uses a random seed for these computations. Note that cRAN suggested we not include the random seed as an argument in this function. To smooth out the randomness, pmvnorm is called niter times and the average value over the niter calls is taken to be those powers.

`powerEA3overallA`	power to detect the overall A effect
`powerEA3simpleA`	power to detect the simple A effect
`powerEA3simpleAB`	power to detect the simple AB effect
`powerEA3anyA`	power to detect either the overall A or simple A effects

Leifer, E.S., Troendle, J.F., Kolecki, A., Follmann, D. Joint testing of overall and simple effect for the two-by-two factorial design. (2020). Submitted.

Lin, D-Y., Gong, J., Gallo, P., et al. Simultaneous inference on treatment effects in survival studies with factorial designs. Biometrics. 2016; 72: 1078-1085.

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. (2020).
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$probA_C
dig <- 2
alpha <- 0.05
corAa  <- 1/sqrt(2)
corAab <- 1/sqrt(2)
coraab <- 1/2
critEA3 <- crit2x2(corAa, corAab, coraab, dig, alpha)$critEA3
n <- 4600
powerEA3(n, hrA, hrB, hrAB, avgprob, probA_C, probAB_C,
  critEA3, dig, cormat12 = matrix(c(1, sqrt(0.5), sqrt(0.5), 1), byrow = TRUE,
  nrow = 2), niter = 1, abseps = 1e-03)

# $powerEA3overallA
# [1] 0.5861992

# $powerEA3simpleA
# [1] 0.5817954

# $powerAB
# [1] 0.9071236

# $powerEA3anyA
# [1] 0.7060777