Frailty Models in Survival Analysis (2010) Pdf Free Download

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The analysis of lifetime data (or more exactly, time-to-event, event-history, or duration data) plays an important role in medicine, epidemiology, biology, demography, economics, engineering, actuarial science, and other fields. It has expanded rapidly in the last three decades, with works having been published in various disciplines in addition to statistics. But what distinguishes survival analysis from other fields of statistics? Why does survival data need a special statistical theory? The main problem is censoring, which means that, for some individuals in the study population, the researcher only has the information that the event of interest did not occur before a particular time point. To put it plainly, a censored observation contains only partial information about the random variable of interest. This kind of incomplete observation needs special methods. As a consequence of censoring, survival times are usually a mixture of discrete (censoring indicator) and continuous (event/censoring time) data that lend themselves to a different type of analysis from that used in the traditional discrete or continuous case. The mixture is the result of censoring and has an important effect on data analysis. The Kaplan–Meier estimator (Kaplan and Meier 1958) of the survival function is a major step in the development of suitable models for such kind of data. Furthermore, most evaluations are made conditionally on what is known at the time of the analysis, and this changes over time. Usually, as the population under study is changing, we only consider the individual risk to die for those who are still alive, but this means that many standard statistical approaches cannot be applied.

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