factorial2x2 (version 0.1.0)

power13_13_13: Power of the 1/3-1/3-1/3 procedure

Description

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.

Usage

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)

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

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

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

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

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 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.

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.

See Also

crit2x2, lgrkPower, strLgrkPower, pmvnorm

Examples

# NOT RUN {
# 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
# }