exactcp {BinGSD} | R Documentation |

Compute conditional power of single-arm group sequential design with binary endpoint based on binomial distribution.

exactcp(d, p_1, i, z_i)

`d` |
An object of the class exactdesign or exactprob. |

`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 `exactdesign`

or `exactprob`

,
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 exact test, the test statistic at analysis *k* is *Z_k=∑_{s=1}^{n_k}X_s*
which follows binomial distribution *b(n_k,p)*. Actually, *Z_k* is the total
number of responses up to the kth analysis.

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

Note that *Z_{1}, …, Z_{K}* is a non-decreasing sequence, thus the conditional power is 1 when the interim statistic
*z_i>=u_K*.

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.

Christopher Jennison, Bruce W. Turnbull. Group Sequential Methods with Applications to Clinical Trials. Chapman and Hall/CRC, Boca Raton, FL, 2000.

`exactprob`

, `asymcp`

,
`exactdesign`

.

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=exactdesign(tt1) tt3=exactprob(p_1=c(0.4,0.5,0.6,0.7,0.8,0.9),d=tt2) exactcp(tt2,p_1=c(0.4,0.5,0.6,0.7,0.8,0.9),1,2) exactcp(tt3,p_1=c(0.4,0.5,0.6,0.7,0.8,0.9),3,19)

[Package *BinGSD* version 0.0.1 Index]