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 |