# Power of the Equal Allocation 3 procedure Computes the Equal Allocation 3 procedure's power to detect the overall A effect, the simple A effect, or the simple AB effect, respectively. ```r 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 ## Returns - **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 ## 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. ## Examples ```r # 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 ``` ## 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`

powerEA3 function