Ebrahimi, Nader B.
Ph.D. (Doctor of Philosophy)
Department of Mathematical Sciences
Recurrent sequences (Mathematics)--Health aspects
Recurrent events data occur frequently in business, engineering, biological and medical fields. In this dissertation we focus on the medical applications (e.g. seizures, heart attacks, cancerous tumors, etc.). However, our proposed methods can be applied to other areas as well. Generally speaking, it is important to use appropriate models for the expected number of events, and sometimes this can be facilitated by modeling the cumulative intensity function or its derivative, the intensity rate. We can interpret the intensity rate as the chance of an individual experiencing the event of interest in the next moment. Modeling the intensity rate function has several advantages. We can incorporate covariates in the specification of the form of the intensity rate in order to determine predictors of the event occurrence. Also, modeling this function allows us to use all available data for an individual, rather than modeling only the first event, as in traditional survival analysis. One particular recurrent events scenario involves individuals experiencing events according to a common intensity rate, and then a treatment may be applied. Assuming the treatment to be effective, the individuals would be expected to follow a different intensity rate after receiving the treatment. Further, the treatment might be effective for a limited amount of time, so that a third rate would govern arrivals of the recurrent events after the effects of the treatment wore out. The points in time where the rate changes are called change-points. Recently, much work has been done on modeling recurrent events, and separately, on modeling hazard rates (one event per subject) with unknown change-points. However, to date, there are few methods to accomodate unknown change-points in the case of recurrent events. In this dissertation, we propose new methods to analyze such situations. Specifically, we will analyze two kinds of data, actual event and panel count. The first involves observing the exact time of each recurrent event, while the second consists of counts of events from successive intervals. Thus, panel count data is essentially interval censoring extended to recurrent events. We develop methods to fit a piecewise constant model for the intensity rate, which includes an unknown change-point. We also allow models for the intensity rate to be at first decreasing and then change to increasing (and vice versa), and estimate the location of this change.
Frobish, Daniel J., "Estimation of change-points in recurrent events models" (2006). Graduate Research Theses & Dissertations. 2911.
viii, 108 pages
Northern Illinois University
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