Time-dependent frailty model to gap times between recurrent events with application to epilepsy data

In recurrent event a specific event occur repeatedly over time for a person. The frailty models take into account this correlation and provide efficient inferences. The frailties are assumed to be constant over time that it may be insufficient. Therefore time-varying frailty models are more realistic models. The aim of this study was to fit a time-dependent frailty model in the gap time between recurrent events.
In this study, a time-dependent frailty model was introduced in the gap time between recurrent events, that was a generalization of the Wintrebert (2004) model in cluster data (center-effect). The parameters were estimated by Gaussian quadrature method. The model was applied to epilepsy data.
The time-dependent frailty model fitted better in compare to shared frailty model. The observation time for IED on EEG in 56 patients (%73 male, %34 veteran status) with epilepsy was studied. Age and veteran status were the two risk factors in the gap time between IEDs. Variance of frailty was significant too.
The result of time-dependent frailty model was reliable when there were unknown time-dependent factors in medical data and make changes on times of occurring recurrent events. The Gaussian quadrature was an applied method to fit a time-dependent frailty model. The programming for this method was comfortable; hence this method can cause time-dependent fraility models to be more practical in medical studies.