powerEA3 {factorial2x2}

Power of the Equal Allocation 3 procedure

Description

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

Usage

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
)

Arguments

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

Details

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.

Value

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

References

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.

See Also

crit2x2, lgrkPower, strLgrkPower, pmvnorm

Examples

# 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