### Abstract

Lan and DeMets (1983, Biometrika 70, 659-663) proposed a flexible method for monitoring accumulating data that does not require the number and times of analyses to be specified in advance yet maintains an overall Type I error, α. Their method amounts to discretizing a preselected continuous boundary by clumping the density of the boundary crossing time at discrete analysis times and calculating the resultant discrete-time boundary values. In this framework, the cumulative distribution function of the continuous-time stopping rule is used as an alpha spending function. A key assumption that underlies this method is that future analysis times are not chosen on the basis of the current value of the statistic. However, clinical trials may be monitored more frequently when they are close to crossing the boundary. In this situation, the corresponding continuous-time boundary should be used. Here we demonstrate how to construct a continuous stopping boundary from an alpha spending function. This capability is useful also in the design of clinical trials. We use the Beta-Blocker Heart Attack Trial (BHAT) and AIDS Clinical Trials Group protocol 021 for illustration.

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

Pages (from-to) | 1061-1071 |

Number of pages | 11 |

Journal | Biometrics |

Volume | 54 |

Issue number | 3 |

DOIs | |

State | Published - Sep 1 1998 |

### Fingerprint

### Keywords

- Boundary crossing
- Brownian motion
- Discrete sequential boundary

### ASJC Scopus subject areas

- Agricultural and Biological Sciences(all)
- Public Health, Environmental and Occupational Health
- Agricultural and Biological Sciences (miscellaneous)
- Applied Mathematics
- Statistics and Probability

### Cite this

**Construction of a continuous stopping boundary from an alpha spending function.** / Betensky, Rebecca.

Research output: Contribution to journal › Article

*Biometrics*, vol. 54, no. 3, pp. 1061-1071. https://doi.org/10.2307/2533857

}

TY - JOUR

T1 - Construction of a continuous stopping boundary from an alpha spending function

AU - Betensky, Rebecca

PY - 1998/9/1

Y1 - 1998/9/1

N2 - Lan and DeMets (1983, Biometrika 70, 659-663) proposed a flexible method for monitoring accumulating data that does not require the number and times of analyses to be specified in advance yet maintains an overall Type I error, α. Their method amounts to discretizing a preselected continuous boundary by clumping the density of the boundary crossing time at discrete analysis times and calculating the resultant discrete-time boundary values. In this framework, the cumulative distribution function of the continuous-time stopping rule is used as an alpha spending function. A key assumption that underlies this method is that future analysis times are not chosen on the basis of the current value of the statistic. However, clinical trials may be monitored more frequently when they are close to crossing the boundary. In this situation, the corresponding continuous-time boundary should be used. Here we demonstrate how to construct a continuous stopping boundary from an alpha spending function. This capability is useful also in the design of clinical trials. We use the Beta-Blocker Heart Attack Trial (BHAT) and AIDS Clinical Trials Group protocol 021 for illustration.

AB - Lan and DeMets (1983, Biometrika 70, 659-663) proposed a flexible method for monitoring accumulating data that does not require the number and times of analyses to be specified in advance yet maintains an overall Type I error, α. Their method amounts to discretizing a preselected continuous boundary by clumping the density of the boundary crossing time at discrete analysis times and calculating the resultant discrete-time boundary values. In this framework, the cumulative distribution function of the continuous-time stopping rule is used as an alpha spending function. A key assumption that underlies this method is that future analysis times are not chosen on the basis of the current value of the statistic. However, clinical trials may be monitored more frequently when they are close to crossing the boundary. In this situation, the corresponding continuous-time boundary should be used. Here we demonstrate how to construct a continuous stopping boundary from an alpha spending function. This capability is useful also in the design of clinical trials. We use the Beta-Blocker Heart Attack Trial (BHAT) and AIDS Clinical Trials Group protocol 021 for illustration.

KW - Boundary crossing

KW - Brownian motion

KW - Discrete sequential boundary

UR - http://www.scopus.com/inward/record.url?scp=0031688791&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0031688791&partnerID=8YFLogxK

U2 - 10.2307/2533857

DO - 10.2307/2533857

M3 - Article

C2 - 9750252

AN - SCOPUS:0031688791

VL - 54

SP - 1061

EP - 1071

JO - Biometrics

JF - Biometrics

SN - 0006-341X

IS - 3

ER -