Statistical Methodology 9 (2012) 501–512
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Statistical Methodology
journal homepage: www.elsevier.com/locate/stamet
Nonparametric estimators for a survivor function of paired
recurrent events
P.G. Sankaran
a,*
, M. Manoharan
b
, P. Anisha
a
a
Department of Statistics, Cochin University of Science and Technology, Cochin-682 022, India
b
Department of Statistics, University of Calicut, Malappuram-673 635, Calicut, India
article info
Article history:
Received 24 November 2009
Received in revised form
5 September 2011
Accepted 10 January 2012
Keywords:
Recurrent event data
Bivariate survivor function
Nonparametric estimation
Dabrowska’s estimator
abstract
Recurrent event data arise in longitudinal studies where each
study subject may experience multiple events during the follow-
up. In many situations in survival studies, pairs of individuals can
potentially experience recurrent events. The analysis of such data
is not straightforward as it involves two kinds of dependences,
namely, dependence between the individuals in the same pair and
dependence among a sequence of pairs. In the present paper, we
introduce a new stochastic model for the analysis of such recurrent
event data. Nonparametric estimators for a bivariate survivor
function are developed. Asymptotic properties of the estimators
are discussed. Simulation studies are carried out to assess the finite
sample properties of the estimator. We illustrate the procedure
with real life data on eye disease.
© 2012 Elsevier B.V. All rights reserved.
1. Introduction
In survival analysis, many applications involve repeated events where a study subject may
experiences any number of events over a follow-up time. Such data are called repeated event data or
recurrent event data. Recurrent event data arise in a wide variety of situations, including biomedicine,
public health, psychology, engineering, demography and economics. Examples of recurrent events in
life length studies are repeated hospitalizations of patients with chronic diseases and the breakdown
of mechanical or electrical systems. The analysis of recurrent event data using statistical methods is,
therefore, a topic of interest in survival studies.
Two different time scales are usually employed in the literature for the analysis of recurrent events.
The two types are the times since entering the study and the times since the last event. For the
*
Corresponding author.
E-mail addresses: sankaranpg@yahoo.com, sankaran.p.g@gmail.com (P.G. Sankaran).
1572-3127/$ – see front matter © 2012 Elsevier B.V. All rights reserved.
doi:10.1016/j.stamet.2012.01.001