### Abstract

It is intuitively appealing to clinicians to stop a trial early to accept the null hypothesis H_{0} if it appears that this will be the likely outcome at the planned end of the trial. We consider procedures that calculate at each time point the conditional probability of rejecting H_{0} at the end of the trial given the current data and some value of the parameter of interest. Lan, Simon, and Halperin (1982, Communications in Statistics C1, 207-219) calculate this probability under the design alternative, and Pepe and Anderson (1992, Applied Statistics 41, 181-190) use an alternative based solely on the current data. We investigate a modification to Pepe and Anderson's (1992) procedure that has a more satisfying interpretation. We define all of these procedures as formal sequential tests with lower stopping boundaries and study them in this context. This facilitates an improved understanding of the interplay of parameters by introducing visual displays, and it leads to an approximation for power by treating it as a boundary crossing probability. We use these tools to compare the performances of the different designs under a variety of parameter configurations.

Original language | English (US) |
---|---|

Pages (from-to) | 794-806 |

Number of pages | 13 |

Journal | Biometrics |

Volume | 53 |

Issue number | 3 |

DOIs | |

State | Published - Sep 1 1997 |

### Fingerprint

### Keywords

- Boundary crossing
- Sequential design
- Stochastic curtailment

### ASJC Scopus subject areas

- Statistics and Probability
- Medicine(all)
- Immunology and Microbiology(all)
- Biochemistry, Genetics and Molecular Biology(all)
- Agricultural and Biological Sciences(all)
- Applied Mathematics

### Cite this

*Biometrics*,

*53*(3), 794-806. https://doi.org/10.2307/2533543

**Early stopping to accept H(o) based on conditional power : Approximations and comparisons.** / Betensky, Rebecca.

Research output: Contribution to journal › Article

*Biometrics*, vol. 53, no. 3, pp. 794-806. https://doi.org/10.2307/2533543

}

TY - JOUR

T1 - Early stopping to accept H(o) based on conditional power

T2 - Approximations and comparisons

AU - Betensky, Rebecca

PY - 1997/9/1

Y1 - 1997/9/1

N2 - It is intuitively appealing to clinicians to stop a trial early to accept the null hypothesis H0 if it appears that this will be the likely outcome at the planned end of the trial. We consider procedures that calculate at each time point the conditional probability of rejecting H0 at the end of the trial given the current data and some value of the parameter of interest. Lan, Simon, and Halperin (1982, Communications in Statistics C1, 207-219) calculate this probability under the design alternative, and Pepe and Anderson (1992, Applied Statistics 41, 181-190) use an alternative based solely on the current data. We investigate a modification to Pepe and Anderson's (1992) procedure that has a more satisfying interpretation. We define all of these procedures as formal sequential tests with lower stopping boundaries and study them in this context. This facilitates an improved understanding of the interplay of parameters by introducing visual displays, and it leads to an approximation for power by treating it as a boundary crossing probability. We use these tools to compare the performances of the different designs under a variety of parameter configurations.

AB - It is intuitively appealing to clinicians to stop a trial early to accept the null hypothesis H0 if it appears that this will be the likely outcome at the planned end of the trial. We consider procedures that calculate at each time point the conditional probability of rejecting H0 at the end of the trial given the current data and some value of the parameter of interest. Lan, Simon, and Halperin (1982, Communications in Statistics C1, 207-219) calculate this probability under the design alternative, and Pepe and Anderson (1992, Applied Statistics 41, 181-190) use an alternative based solely on the current data. We investigate a modification to Pepe and Anderson's (1992) procedure that has a more satisfying interpretation. We define all of these procedures as formal sequential tests with lower stopping boundaries and study them in this context. This facilitates an improved understanding of the interplay of parameters by introducing visual displays, and it leads to an approximation for power by treating it as a boundary crossing probability. We use these tools to compare the performances of the different designs under a variety of parameter configurations.

KW - Boundary crossing

KW - Sequential design

KW - Stochastic curtailment

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UR - http://www.scopus.com/inward/citedby.url?scp=0030821530&partnerID=8YFLogxK

U2 - 10.2307/2533543

DO - 10.2307/2533543

M3 - Article

VL - 53

SP - 794

EP - 806

JO - Biometrics

JF - Biometrics

SN - 0006-341X

IS - 3

ER -