asymcp {BinGSD} | R Documentation |

Compute conditional power of single-arm group sequential design with binary endpoint based on asymptotic test, given the interim result.

asymcp(d, p_1, i, z_i)

`d` |
An object of the class asymdesign or asymprob. |

`p_1` |
A scalar or vector representing response rate or probability of success under the alternative hypothesis. The value(s) should be within (p_0,1). |

`i` |
Index of the analysis at which the interim statistic is given. Should be an integer ranges from 1 to K-1. i will be rounded to its nearest whole value if it is not an integer. |

`z_i` |
The interim statistic at analysis i. |

Conditional power quantifies the conditional probability of crossing the upper bound given the interim result *z_i*,
*1≤ i<K*. Having inherited sample sizes and boundaries from `asymdesign`

or `asymprob`

,
given the interim statistic at *i*th analysis *z_i*, the conditional power is defined as

*α _{i,K}(p|z_i)=P_{p}(Z_K≥ u_K, Z_{K-1}>l_{K-1}, …, Z_{i+1}>l_{i+1}|Z_i=z_i)*

With asymptotic test, the test
statistic at analysis *k* is
*Z_k=\hat{θ}_k√{n_k/p/(1-p)}=(∑_{s=1}^{n_k}X_s/n_k-p_0)√{n_k/p/(1-p)}*,
which follows the normal distribution *N(θ √{n_k/p/(1-p)},1)*
with *θ=p-p_0*. In practice, *p* in *Z_k* can be substituted
with the sample response rate *∑_{s=1}^{n_k}X_s/n_k*.

The increment statistic *Z_k√{n_k/p/(1-p)}-Z_{k-1}√{n_{k-1}/p/(1-p)}* also follows a normal distribution independently
of *Z_{1}, …, Z_{k-1}*. Then the conditional power can be easily obtained using a procedure similar
to that for unconditional boundary crossing probabilities.

A list with the elements as follows:

K: As in d.

n.I: As in d.

u_K: As in d.

lowerbounds: As in d.

i: i used in computation.

z_i: As input.

cp: A matrix of conditional powers under different response rates.

p_1: As input.

p_0: As input.

Alan Genz et al. (2018). mvtnorm: Multivariate Normal and t Distributions. R package version 1.0-11.

`asymprob`

, `asymdesign`

,
`exactcp`

.

I=c(0.2,0.4,0.6,0.8,0.99) beta=0.2 betaspend=c(0.1,0.2,0.3,0.3,0.2) alpha=0.05 p_0=0.3 p_1=0.5 K=4.6 tol=1e-6 tt1=asymdesign(I,beta,betaspend,alpha,p_0,p_1,K,tol) tt2=asymprob(p_1=c(0.4,0.5,0.6,0.7,0.8,0.9),d=tt1) asymcp(tt1,p_1=c(0.4,0.5,0.6,0.7,0.8,0.9),1,2) asymcp(tt2,p_1=c(0.4,0.5,0.6,0.7,0.8,0.9),3,2.2)

[Package *BinGSD* version 0.0.1 Index]