Semiparametric Estimation with Correlated Recurrent Event Data under Informative Monitoring

Consider a recurrent event data where frailty models are used to account for correlations among the inter-event times within each unit under study. In this talk we consider the problem of semiparametric estimation of the inter-event time distribution under informative monitoring and the Gamma frailty model. We propose a semiparametric estimator of the baseline survivor function. We show that the estimator under the i.i.d. setting is inconsistent in the presence of frailty. We present results of simulaiton study where we discuss the performence of our proposed estimator to that derived under the i.i.d. setting. Finally, these estimators will be demonstrated by applying to biomedical and engineering data sets

Semiparametric Inference with Correlated Recurrence Time Data

We consider a study which monitors the occurrences of a recurrent event for n subjects or units. Recurrent event data have many features which are worth looking into in the estimation process. In this manuscript, we consider the problem of estimating the distribution function of the inter-event times by taking into account two of these features: correlation among the inter-event times and the dependence and informative aspect of the right-censoring random variables. The parametric approach to the problem has been dealt with in Zamba and Adekpedjou (2011) [25]. The semiparametric approach is considered in this article. We derive a Kaplan-Meier type estimator of the distribution function under the gamma frailty model and an informative monitoring model for recurrent events by extending an approach due to Sellke (1988) [20]. The sampling distribution properties of the proposed estimators are examined through simulation studies. Furthermore, the performance of our proposed estimator is assessed with respect to the existing ones. The procedures are applied to a recurrent event dataset

Some Aspects Pertaining to Recurrent Event Modeling and Analysis.

This article presents some results pertaining to recurrent event modeling and analysis. In particular, we consider the problem of detecting outliers and also examine the impact of an informative monitoring period in terms of loss of efficiency. Aside from the ideas and analytical results, we demonstrate these aspects through an application to the well-used air-conditioning reliability data set in [18]

Estimation and Efficiency with Recurrent Event Data under Informative Monitoring

This article deals with studies that monitor occurrences of a recurrent event for n subjects or experimental units. It is assumed that the ith unit is monitored over a random period [0, τi]. The successive inter-event times Ti 1, Ti 2, ..., are assumed independent of τi. The random number of event occurrences over the monitoring period is Ki = max { k ∈ { 0, 1, 2, ... } : Ti 1 + Ti 2 + ⋯ + Tik ≤ τi }. The Tij\u27s are assumed to be i.i.d. from an unknown distribution function F which belongs to a parametric family of distributions C = { F (· ; θ) : θ ∈ Θ ⊂ Rp }. The τi\u27s are assumed to be i.i.d. from an unknown distribution function G. The problem of estimating θ, and consequently the distribution F, is considered under the assumption that the τi\u27s are informative about the inter-event distribution. Specifically, 1 - G = (1 - F)β for some unknown β \u3e 0, a generalized Koziol-Green [cf., Koziol, J., Green, S., 1976. A Cramer-von Mises statistic for randomly censored data. Biometrika 63, 139-156; Chen, Y., Hollander, M., Langberg, N., 1982. Small-sample results for the Kaplan-Meier estimator. J. Amer. Statist. Assoc. 77, 141-144] model. Asymptotic properties of estimators of θ, β, and F are presented. Efficiencies of estimators of θ and F are ascertained relative to estimators which ignore the informative monitoring aspect. These comparisons reveal the gain in efficiency when the informative structure of the model is exploited. Concrete demonstrations were performed for F exponential and a two-parameter Weibull