Exponential Gap-Time Estimation with Correlated Recurrent Event Models: Application to Neural Firing Data


Time to occurrence of an event in a recurrent event data setting could be affected by many factors such as unobservable frailty, and informative censoring. Unobservable frailty induces a subject specific correlation among the inter-event times. Informative censoring controls the per subject accumulation of events. There are some analytical tools for estimating survivor function parameters in the presence of recurrent events. These generally lack the joint effect of correlation, informative censoring and randomness of the per subject observation window. Our method applies to correlated recurrent event data under informative censoring; specifically studies in which the survival time for a subject is censored because of deterioration of their physical condition or due to the accumulation of their events occurrences. In this paper, we approach the inter-event times estimation problem through a fully parametric baseline hazard model where recurrent events and censoring intensity are reconciled through the generalised Koziol-Green model for recurrent events. We further outline a general computational procedure for estimating parameters with correlated recurrent event data under informative censoring. The method is developed for exponential inter-event times. Algebraic formulas that extend it to Weibull inter-event times are proposed. We examine the sampling distribution properties of the estimators analytically and also via simulation. We apply our method to a neural activity biomedical data set.


Mathematics and Statistics

Keywords and Phrases

Correlated Recurrence Times; Informative Censoring; Frailty Model; Koziol-green Model; Stochastic Integration

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Document Type

Article - Journal

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© 2012 South African Statistical Association, All rights reserved.

Publication Date

01 Jan 2012

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