crit2x2 {factorial2x2}

Critical values for the Equal Allocation 3, Proportional Allocation 2, and Equal Allocation 2 procedures

Description

Computes the critical values for null hypotheses rejection and corresponding nominal two-sided significance levels for the Equal Allocation 3, Proportional Allocation 2, and Equal Allocation 2 procedures

Usage

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

Arguments

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

Details

This function computes the Dunnett-corrected critical values based on the asymptotic correlations of the overall A, simple A, and simple AB logrank statistics as described in Leifer, Troendle, et al. (2020) and are derived in Lin, Gong, et al. (2016) and Slud (1994). 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.

Value

critEA3

Equal Allocation 3 procedure's critical value for all three test statistics

sigEA3

two-sided nominal significance level corresponding to critEA3

critPA2A

Proportional Allocation 2 procedure's critical value for the overall A statistic

sigPA2A

two-sided nominal significance level corresponding to critPA2A

critPA2ab

Proportional Allocation 2 procedure's critical value for the simple AB statistic

sigPA2ab

two-sided nominal significance level corresponding to critPA2ab

critEA2

Equal Allocation 2 procedure's critical value for the simple A and AB statistics

sigEA2

two-sided nominal significance level corresponding to critEA2

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

roundDown. eventProb, lgrkPower, strLgrkPower, pmvnorm

Examples

# 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)
# critEA3
# [1] -2.32

# sigEA3
# [1] 0.02034088

# critPA2A
# [1] -2.13

# sigPA2A
# [1] 0.03317161

# critPA2ab
# [1] -2.24

# sigPA2ab
# [1] 0.02509092

# critEA2
# [1] -2.22

# sigEA2
# [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)
# $critEA3
# [1] -2.34

# $critPA2A
# [1] -2.13

# $sigPA2A
# [1] 0.03317161

# $critPA2ab
# [1] -2.3

# $sigPA2ab
# [1] 0.02144822
#
# $sigEA3
# [1] 0.01928374

# $critEA2
# [1] -2.22

# $sigEA2
# [1] 0.02641877