Recurrent first hitting times in Wiener diffusion under several observation schemes |
| |
Authors: | G A Whitmore T Ramsay S D Aaron |
| |
Institution: | McGill University, 1001 Sherbrooke Street West, Montreal, Quebec, H3A 1G5, Canada. george.whitmore@mcgill.ca |
| |
Abstract: | Recurrent events are commonly encountered in the natural sciences, engineering, and medicine. The theory of renewal and regenerative
processes provides an elegant mathematical foundation for idealized recurrent event processes. In real-world applications,
however, the contexts tend to be complicated by a variety of practical intricacies, including observation schemes with different
phase and data structures. This paper formulates a recurrent event process as a succession of independent and identically
distributed first hitting times for a Wiener sample path as it passes through successive equally-spaced levels. We develop
exact mathematical results for statistical inferences based on several observation schemes that include observation initiated
at a renewal point, observation of a stationary process over a finite window, and other variants. We also consider inferences
drawn from different data structures, including gap times between renewal points (or fragments thereof) and counts of renewal
events occurring within an observation window. We explore the precision of estimates using simulated scenarios and develop
empirical regression functions for planning the sample size of a recurrent event study. We demonstrate our results using data
from a clinical trial for chronic obstructive pulmonary disease in which the recurrent events are successive exacerbations
of the condition. The case study demonstrates how covariates can be incorporated into the analysis using threshold regression. |
| |
Keywords: | |
本文献已被 PubMed SpringerLink 等数据库收录! |
|