# Power of the Proportional Allocation 2 procedure Computes the Proportional Allocation 2 procedure's power to detect the overall A effect or the simple AB effect, respectively. ```r powerPA2(n, hrA, hrB, hrAB, avgprob, probAB_C, critPA2A, critPA2ab, dig) ``` ## 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 - `probAB_C`: event probability averaged across the AB and C groups - `critPA2A`: rejection critical value for the overall A stratified logrank statistic - `critPA2ab`: rejection critical value for the simple AB ordinary logrank statistic - `dig`: number of decimal places to which we `roundDown` the critical value for the overall A test as calculated in `powerPA2` by `strLgrkPower` ## Returns - **powerPA2overallA**: power to detect the overall A effect - **powerPA2simpleAB**: power to detect the simple AB effect ## Details The Proportional Allocation 2 procedure uses a two-sided 2/3 * alpha significance level to test the overall A effect and the remaining Dunnett-corrected type 1 error to thest the simple AB effect. When the familywise error is alpha = 0.05, this corresponds to a critical value `critPA2A` = -2.13. Then `crit2x2` is used to compute a critical value `critPA2ab` = -2.24 to test the simple AB effect. This corresponds to a two-sided 0.0251 significance level. This controls the asymptotic familywise type I error for the two hypothesis tests at the two-sided 0.05 level. This is because of the `1/sqrt(2)` asymptotic correlation between the logrank test statistics for the overall A and simple AB effects (Slud, 1994). The overall A effect's significance level 2/3 * 0.05 is prespecified and the simple AB effect's significance level 0.0251 is computed using `crit2x2`. ## 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) avgprob <- evtprob$avgprob probAB_C <- evtprob$probAB_C dig <- 2 alpha <- 0.05 corAa <- 1/sqrt(2) corAab <- 1/sqrt(2) coraab <- 1/2 critvals <- crit2x2(corAa, corAab, coraab, dig, alpha) critPA2A <- critvals$critPA2A critPA2ab <- critvals$critPA2ab n <- 4600 powerPA2(n, hrA, hrB, hrAB, avgprob, probAB_C, critPA2A, critPA2ab, dig) # $powerPA2overallA # [1] 0.6582819 # $powerPA2simpleAB # [1] 0.9197286 ``` ## 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`, `eventProb`, `lgrkPower`, `strLgrkPower` ## Author(s) Eric Leifer, James Troendle

powerPA2 function