factorial2x2: Design and Analysis of 2x2 Factorial Trial

Description Usage Arguments Details Value References See Also Examples

Computes the critical values for null hypotheses rejection and corresponding nominal two-sided significance levels for the 2/3-1/3, 1/3-1/3-1/3, and 1/2-1/2 procedures.

1 2	crit2x2(corAa, corAab, coraab, dig = 2, alpha = 0.05, niter = 5, abseps = 1e-05, tol = 1e-04)

`corAa`	correlation between the overall A and simple A log hazard ratio estimates
`corAab`	correlation between the overall A and simple AB log hazard ratio estimates
`coraab`	correlation between the simple A and simple AB log hazard ratio estimates
`dig`	number of decimal places to which we `roundDown` the critical value
`alpha`	two-sided familywise error level to control
`niter`	number of times we compute the critical values to average out the randomness from the `pmvnorm` function call
`abseps`	`abseps` setting in the `pmvnorm` function call
`tol`	`tol` setting in the uniroot function call

pmvnorm uses a random seed in its algorithm. To smooth out the randomness, pmvnorm is called niter times. The roundDown function is used in conjunction with the dig argument to insure that any rounding of the (negative) critical values will be done conservatively to control the familywise type I error at the desired level.

`crit23A`	2/3-1/3 procedure's critical value for the overall A statistic
`sig23A`	two-sided nominal significance level corresponding to `crit23A`
`crit23ab`	2/3-1/3 procedure's critical value for the simple AB statistic
`sig23ab`	two-sided nominal significance level corresponding to `crit23ab`
`crit13`	1/3-1/3-1/3 procedure's critical value for all three test statistics
`sig13`	two-sided nominal significance level corresponding to `crit13`
`crit12`	1/2-1/2 procedure's critical value for the simple A and AB statistics
`sig12`	two-sided nominal significance level corresponding to `crit12`

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.

roundDown. eventProb, lgrkPower, strLgrkPower, pmvnorm

# Example 1:  Compute the nominal significance levels for rejection using
# the asymptotic correlations derived in Slud (1994)
corAa  <- 1/sqrt(2)
corAab <- 1/sqrt(2)
coraab <- 1/2

crit2x2(corAa, corAab, coraab, dig = 2, alpha = 0.05, niter = 5)
# crit23A
# [1] -2.13

# sig23A
# [1] 0.03317161

# crit23ab
# [1] -2.24

# sig23ab
# [1] 0.02509092

# crit13
# [1] -2.32

# sig13
# [1] 0.02034088

# crit12
# [1] -2.22

# sig12
# [1] 0.02641877

# Example 2:  Compute the nominal critical values and significance levels for rejection
# using the estimated correlations for simdat.
corAa  <- 0.6123399
corAab <- 0.5675396
coraab <- 0.4642737

crit2x2(corAa, corAab, coraab, dig = 2, alpha = 0.05, niter = 5)
# $crit23A
# [1] -2.13

# $sig23A
# [1] 0.03317161

# $crit23ab
# [1] -2.3

# $sig23ab
# [1] 0.02144822
#
# $crit13
# [1] -2.34
# $sig13
# [1] 0.01928374

# $crit12
# [1] -2.22