## Abstract

The context is that of a sequential trial based on Brownian motion with

linear stopping boundaries, possibly truncated. Along with the monitoring

process, a secondary Gaussian process with constant mean is observed; the

mean is to be estimated once the monitoring process reaches a boundary.

We provide a formula for the conditional bias, conditioning on the final

position of the monitoring process; this formula can then be integrated

to obtain an overall bias. Special attention is given to evaluating bias -

mathematically and by Monte Carlo - of the Kaplan-Meier estimator of

one of the survival functions (and similarly for the Nelson-Aalen estimator of the corresponding cumulative hazard function) upon completion of

a survival-analysis-based.

linear stopping boundaries, possibly truncated. Along with the monitoring

process, a secondary Gaussian process with constant mean is observed; the

mean is to be estimated once the monitoring process reaches a boundary.

We provide a formula for the conditional bias, conditioning on the final

position of the monitoring process; this formula can then be integrated

to obtain an overall bias. Special attention is given to evaluating bias -

mathematically and by Monte Carlo - of the Kaplan-Meier estimator of

one of the survival functions (and similarly for the Nelson-Aalen estimator of the corresponding cumulative hazard function) upon completion of

a survival-analysis-based.

Original language | American English |
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Title of host publication | Institute of Mathematical Statistics Lecture Notes - Monograph Series |

Editors | John E. Kolassa , David Oakes |

Publisher | Institute of Mathematical Statistics |

Pages | 13-28 |

Number of pages | 16 |

ISBN (Print) | 0749-2170 |

DOIs | |

State | Published - 2003 |

### Publication series

Name | Institute of Mathematical Statistics Lecture Notes - Monograph Series |
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Volume | 43 |