Semiparametric estimation with recurrent event data under informative monitoring

Akim Adekpedjou and Edsel Peña

Journal of Nonparametric Statistics, 2012, vol. 24, issue 3, 733-752

Abstract: Consider a study where the times of occurrences of a recurrent event for n units are monitored. For the ith unit, Ti1, Ti2, …, denote the successive event inter-occurrence times and this unit is monitored over a random period [0, τi] with τi independent of the Tijs. Over this monitoring period, is the random number of event occurrences. The Tijs are independent and identically distributed (IID) from an unknown continuous distribution function F and the τis are IID from a distribution function G. A generalised Koziol–Green (GKG) structure wherein 1−G=(1−F)β for some β>0 is assumed. Under this model, Nelson–Aalen and product-limit type estimators of Λ=−log(1−F) and F are obtained, as well as an estimator of β. Asymptotic and small-sample properties of these estimators are obtained and the estimator of F is compared to the fully nonparametric estimator in Peña et al. [(2001), ‘Nonparametric Estimation with Recurrent Event Data’, Journal of the American Statistical Association, 96, 1299–1315] in terms of their finite-sample and asymptotic efficiency. The performance of the estimators of F are also examined when the GKG structure does not hold through a simulation study.

Date: 2012
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DOI: 10.1080/10485252.2012.698281

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