powerEA2 {factorial2x2}

Power of the Equal Allocation 2 procedure

Description

Computes the Equal Allocation 2's procedure power to detect the simple A effect and the simple AB effect, respectively.

Usage

powerEA2(n, hrA, hrAB, probA_C, probAB_C, crit12)

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

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

Details

For a 2-by-2 factorial design, this function computes the probability that either the simple A, respectively, simple AB logrank statistics reject their null hypotheses using a Dunnett-corrected 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. (2020).

Value

powerEA2simpleA

power to detect the simple A effect

powerEA2simpleAB

power to detect the simple AB effect

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

Examples

# Corresponds to scenario 4 in Table 2 from Leifer, Troendle, et al. (2020).
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
critEA2 <- crit2x2(corAa, corAab, coraab, dig, alpha)$critEA2
n <- 4600
powerEA2(n, hrA, hrAB, probA_C, probAB_C, critEA2)

# $powerEA2simpleA
# [1] 0.6203837

# $powerEA2simpleAB
# [1] 0.9226679