# Power of the Equal Allocation 2 procedure Computes the Equal Allocation 2's procedure power to detect the simple A effect and the simple AB effect, respectively. ```r 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 ## Returns - **powerEA2simpleA**: power to detect the simple A effect - **powerEA2simpleAB**: power to detect the simple AB effect ## 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). ## Examples ```r # 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 ``` ## 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`

powerEA2 function