## Power calculation for Biomarker-Informed Design with Hierarchical Model

### Description

Given the Biomarker-Informed design information, returns the overall power and probability of the arm is selected as the winner.

### Usage

```BioInfo.Power(uCtl, u0y, u0x, rhou, suy, sux, rho, sy, sx, Zalpha, N1, N, nArms, nSims)
```

### Arguments

 `uCtl` mean value for the control group. `u0y` mean parameter of the group 1 for the parent model. `u0x` mean parameter of the group 2 for the parent model. `rhou` correlation coefficient between two groups for the parent model. `suy` standard deviation of the group 1 for the parent model. `sux` standard deviation of the group 2 for the parent model. `rho` correlation coefficient between two groups for the lower level model. `sy` standard deviation of the group 1 for the lower level model. `sx` standard deviation of the group 2 for the lower level model. `Zalpha` crtical point for rejection. `N1` sample size per group at interim analysis. `N` sample size per group at final analysis. `nArms` number of active groups. `nSims` number of simulation times.

### Value

The evaluated power and probability of selecting the arm as the winner.

Yalin Zhu

### References

Chang, M. (2014). Adaptive design theory and implementation using SAS and R. CRC Press.

### Examples

```## Determine critical value Zalpha for alpha (power) =0.025
u0y=c(0,0,0); u0x=c(0,0,0)
BioInfo.Power(uCtl=0, u0y, u0x, rhou=1, suy=0, sux=0, rho=1, sy=4, sx=4,
Zalpha=2.772, N1=100, N=300, nArms=3, nSims=1000)
## Power simulation
u0y=c(1,0.5,0.2)
u0x=c(2,1,0.5)
BioInfo.Power(uCtl=0, u0y, u0x, rhou=0.2, suy=0.2, sux=0.2, rho=0.2, sy=4, sx=4,
Zalpha=2.772, N1=100, N=300, nArms=3, nSims=500)

```