power12_12: Power of the 1/2-1/2 procedure

Description

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.

Usage

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)

Arguments

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

Value

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

Details

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.

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. (2019). Submitted.

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

Examples

Run this code

# NOT RUN {
# 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


# }

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