The design function for multinomial designs under union-intersection test (UIT)

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Description

Search the type I error or power of a multinomial (response and disease progression) single- or two-stage design under IUT: 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}

Usage

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UIT.design(method, s1.rej, t1.rej, s1.acc, t1.acc, n1, s2.rej, t2.rej, n2,
s1.rej.delta=0, t1.rej.delta=0, s1.acc.delta=0, t1.acc.delta=0,
s2.rej.delta=0, t2.rej.delta=0, n1.delta=0, n2.delta=0, p0.s, p0.t, p1.s, p1.t,
signif.level = 0.05, power.level = 0.85, output.all = FALSE, show.time = TRUE)

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".

s1.rej.delta

pre-specified search difference for s1.rej.

t1.rej.delta

pre-specified search difference for t1.rej.

s1.acc.delta

pre-specified search difference for s1.acc.

t1.acc.delta

pre-specified search difference for t1.acc.

s2.rej.delta

pre-specified search difference for s2.rej.

t2.rej.delta

pre-specified search difference for t2.rej.

n1.delta

pre-specified search difference for n1.

n2.delta

pre-specified search difference for n2.

p0.s

pre-specified response rate under null hypothesis.

p0.t

pre-specified disease progression rate under null hypothesis.

p1.s

pre-specified response rate under alternative hypothesis.

p1.t

pre-specified disease progression rate under alternative hypothesis. 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})

signif.level

pre-specified significant level.

power.level

pre-specified power level.

output.all

logical; if TRUE, output all possible designs satisfying type I error and power restrictions, otherwise, only output the design with maximum power .

show.time

logical; if TRUE (default), show the calculation time for the search function.

Value

boundset

the boundaries set satisfying the design types properties: s.rej, t.rej and N for "s1", s1.rej, t1.rej, s1.acc, t1.acc and N1 for first stage and s2.rej, t2.rej and N2 for the second stage of "s2", s1.acc, t1.acc and N1 for first stage and s2.rej, t2.rej and N2 for the second stage of "s2.f",

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.

Simon, R. (1989). Optimal two-stage designs for phase II clinical trials. Controlled clinical trials 10(1), 1-10.

Examples

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## Calculate type I error for single-stage design
UIT.design(method="s1",s1.rej=18, t1.rej = 12, n1=80,
p0.s = 0.15, p0.t = 0.25, p1.s = 0.3, p1.t= 0.1)

## Designs for two-stage design, output PET and EN under null hypothesis
UIT.design(method="s2",s1.rej = 11, t1.rej = 4, s1.acc=8, t1.acc = 5, n1=40,
s2.rej=18, t2.rej = 11, n2=40, p0.s = 0.15, p0.t = 0.25, p1.s = 0.3, p1.t= 0.1, output.all=TRUE)