# 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

 ```1 2``` ```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

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20``` ```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.