The Statistical Analysis of Recurrent Events (Statistics for by Richard J. Cook

By Richard J. Cook

This e-book offers versions and statistical equipment for the research of recurrent occasion information. The authors offer extensive, distinct assurance of the key techniques to research, whereas emphasizing the modeling assumptions that they're according to. extra normal intensity-based types also are thought of, in addition to easier types that concentrate on price or suggest features. Parametric, nonparametric and semiparametric methodologies are all lined, with systems for estimation, trying out and version checking.

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Extra resources for The Statistical Analysis of Recurrent Events (Statistics for Biology and Health)

Sample text

4 Selection of Individuals and Observation Schemes 17 calendar time, especially with processes that apply to humans or animals. In technological areas, measures of usage or exposure are often used, for example distance accumulated for motor vehicles or (discrete) usage cycles for printers or copiers. 2, cumulative staff days of testing were deemed most appropriate. The time scale also involves a choice of origin, and this requires some care when multiple individuals are under study. Intensity-based analyses can adapt to the choice of a time origin through specification of the intensity, but it is nevertheless desirable to use an origin that is consistent across individuals and facilitates interpretation and analysis.

The above procedure is not robust to departures from the Poisson model. A robust approach is to note that µT and µC , or log µT and log µC , are approximately normally distributed even when the total counts (Ni (122)) are N (µT , VT /23) and µC not Poisson random variables. In particular, µT N (µC , VC /25), where VT and VC represent var{Ni (122)} for treatment and control animals. 96 VT VC + 2 23µT 25µ2C 1/2 for log ψ, where VT and VC are sample variance estimates given above. The 95% confidence intervals obtained for log ψ and for ψ from the two approaches are as follows.

Formal methods of testing the Poisson assumption are given in Chapter 3 and we give a more detailed analysis there; here we just compare the results from the Poisson model with those of a simple robust analysis. g. Cox and Lewis, 1966) but given the large total tumor counts in the two groups, a simple large sample approach is satisfactory. Because µT is approximately normally distributed as N (µT , µT /23), it follows that log µT is approximately N (log µT , (23µT )−1 ); the latter approximation is typically better when µT is small.

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