factorial2x2: Design and Analysis of 2x2 Factorial Trial

Description Usage Arguments Details Value Author(s) References See Also Examples

Computes the power of the 2/3-1/3 procedure, that is, the power to detect the overall A effect or the simple AB effect.

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power23_13(n, hrA, hrB, hrAB, avgprob, probAB_C, crit23A, crit23ab, dig,
  cormat = matrix(c(1, sqrt(0.5), sqrt(0.5), 1), byrow = TRUE, nrow = 2),
  niter = 5, abseps = 0.001)

`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
`crit23A`	rejection critical value for the overall A stratified logrank statistic
`crit23ab`	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 `power23_13` by `strLgrkPower`
`cormat`	asymptotic correlation matrix for the overall 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

The 2/3-1/3 procedure uses a two-sided 2/3 * alpha = 0.033 significance level to test the overall A effect. When the familywise error is alpha = 0.05, this corresponds to a critical value crit23A = -2.13. Then crit2x2 is used to compute a critical value crit23ab = -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. The pmvnorm function from the mvtnorm package is used to calculate the power that both (intersection) the overall A and simple AB effects are detected. Since this involves bivariate normal integration over an unbounded region in R^2, pmvnorm uses a random seed for this computation. To smooth out the randomness, pmvnorm is called niter times and the average value over the niter calls is taken to be that power.

`poweroverA`	power to detect the overall A effect
`powerAB`	power to detect the simple AB effect
`poweroverAandAB`	power to detect the overall A and simple AB effects
`power23.13`	power to detect the overall A or simple AB effects, i.e., power of the 2/3-1/3 procedure

Eric Leifer, James Troendle

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.

crit2x2, eventProb, lgrkPower, strLgrkPower, pmvnorm

 # Corresponds to scenario 5 in Table 2 from Leifer, Troendle, et al. (2019).
 rateC <- 0.0445  # one-year C group event rate
 hrA <- 0.80
 hrB <- 0.80
 hrAB <- 0.72
 mincens <- 4.0
 maxcens <- 8.4
 eventvec <- eventProb(rateC, hrA, hrB, hrAB, mincens, maxcens)
 avgprob <- eventvec$avgprob
 probAB_C <- 0.5 * (eventvec$probAB + eventvec$probC)
 dig <- 2
 alpha <- 0.05
 corAa  <- 1/sqrt(2)
 corAab <- 1/sqrt(2)
 coraab <- 1/2
 critvals <- crit2x2(corAa, corAab, coraab, dig, alpha)
 crit23A <- critvals$crit23A
 crit23ab <- critvals$crit23ab
 n <- 4600
 power23_13(n, hrA, hrB, hrAB, avgprob, probAB_C,
            crit23A, crit23ab, dig, cormat =
            matrix(c(1, sqrt(0.5), sqrt(0.5), 1), byrow = TRUE,
            nrow = 2), niter = 1, abseps = 1e-03)
# $poweroverA
# [1] 0.6582819

# $powerAB
# [1] 0.9197286

# $poweroverAandAB
# [1] 0.6490042

# $power23.13
# [1] 0.9290062