UIT.power: The power function for multinomial designs under...

In ph2mult: Phase II Clinical Trial Design for Multinomial Endpoints

Description

Calculate the type I error or power of a multinomial (response and disease progression) single- or two-stage design under UIT: H_0: p_1 ≤ p_{01} \ AND \ p_2 ≥ p_{02} \ versus \ H_1: p_1 ≥ p_{11} > p_{01} \ OR \ p_2 ≤ p_{12} < p_{02} (Note: original Zee et al. (1999) set up the correct hypotheses, but did not make a match decision.)

Usage

UIT.power(method, s1.rej, t1.rej, s1.acc, t1.acc, n1, s2.rej, t2.rej, n2, p.s, p.t,
output.all)

Arguments

method	design methods according to number of stage and stopping rule, "s1" represents single-stage design stopping for both efficacy and futility, "s2" represents two-stage design stopping for both efficacy and futility, "s2.f" represents two-stage design stopping for futility only.
s1.rej	first stage responses threshold to stop the trial for efficacy. Applied for "s1" or "s2".
t1.rej	first stage disease progressions threshold to stop the trial for efficacy. Applied for "s1" or "s2".
s1.acc	first stage responses threshold to stop the trial for futility. Applied for "s2" or "s2.f".
t1.acc	first stage disease progressions threshold to stop the trial for futility. Applied for "s2" or "s2.f".
n1	first stage sample size. Applied for "s1", "s2" or "s2.f".
s2.rej	second stage responses threshold to stop the trial for efficacy. Applied for "s2" or "s2.f".
t2.rej	second stage disease progressions threshold to stop the trial for efficacy. Applied for "s2" or "s2.f".
n2	second stage sample size. Applied for "s2" or "s2.f".
p.s	pre-specified response rate, p.s=p_{01} for calculating type I error , p=p_{11} for calculating power.
p.t	pre-specified disease progression rate, p.s=p_{02} for calculating type I error, p=p_{12} for calculating power. Note: type I error calculation needs to take maximum of the power function with (p.s,p.t)=(p_{01},0) and (p.s,p.t)=(1-p_{02},p_{02})
output.all	logical, if FALSE (default), only output the value of power or type I error, otherwise, also output the probability of early termination (PET) and expected sample size (EN). Applied for "s2" or "s2.f".

Value

prob	the power function g(...,p.s,p.t): α = \max [g(...,p_{01},0), g(...,1-p_{02},p_{02}) ] or g(...,p_{11},p_{12})

References

Zee, B., Melnychuk, D., Dancey, J., & Eisenhauer, E. (1999). Multinomial phase II cancer trials incorporating response and early progression. Journal of biopharmaceutical statistics, 9(2), 351-363.

Examples

p01=0.1; p02=0.9
## Calculate type I error for single-stage design
UIT.power(method="s1", s1.rej=6, t1.rej=19, n1=25, p.s=p01, p.t=p02)
## Calculate power for single-stage design
UIT.power(method="s1", s1.rej=6, t1.rej=19, n1=25, p.s=p01+0.2, p.t=p02-0.2)

## Calculate type I error for two-stage design, output PET and EN under null hypothesis
UIT.power(method="s2", s1.rej=4, t1.rej=9, s1.acc=0, t1.acc=13, n1=13,
s2.rej=6, t2.rej=18, n2=11, p.s=p01, p.t=p02, output.all=TRUE)
## Calculate power for two-stage design
UIT.power(method="s2", s1.rej=4, t1.rej=9, s1.acc=0, t1.acc=13, n1=13,
s2.rej=6, t2.rej=18, n2=11, p.s=p01+0.2, p.t=p02-0.2)

## Calculate type I error for two-stage design stopping for futility only,
## output PET and EN under null hypothesis
UIT.power(method="s2.f", s1.acc=0, t1.acc=13, n1=13,
s2.rej=6, t2.rej=18, n2=11, p.s=p01, p.t=p02, output.all=TRUE)
## Calculate power for two-stage design
UIT.power(method="s2.f", s1.acc=0, t1.acc=13, n1=13,
s2.rej=6, t2.rej=18, n2=11, p.s=p01+0.2, p.t=p02-0.2)

ph2mult documentation built on May 2, 2019, 1:46 p.m.