Abstract:
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General Point Process with intensity function dependent on history of the process is often observed in various scientific fields. Chronic diseases are typical examples of such processes. Problem of this process is that the unconditional (of history) distribution of event counts, and the unconditional moments, e.g. unconditional expected number of events generated by the process cannot be theoretically derived. For general counting process Stratified Cox model estimates cumulative hazard for individual waiting times and stratified Andersen-Gill model estimates intensity at any given time-point; but there exists no method for estimating a parameter that is cumulative over time, e.g., the marginal mean (i.e., mean of events recurred over time, unconditional on history). A non-parametric estimator of mean is proposed which is easy to understand and may be used by clinical and other scientists to assess intensity of events in respective context. In absence of the estimate for variance, confidence interval for the estimate of mean cannot be derived but the estimates of successive higher-order event occurrence probabilities may be used for statistical inference related to recurrent events
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