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Fahrmeir, Ludwig (1997): Discrete failure time models. Collaborative Research Center 386, Discussion Paper 91
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Abstract

Most methods for analyzing failure time or event history data are based on time as a continuously measured variate. A basic assumption for large parts of theory is that failure times are untied, see Andersen et al. (1993). In practice, there is always some smallest time unit, so that ties can occur. A moderate number of ties, while banned in theory, can be treated by appropriate modifications. If many ties occur, e.g. due to grouping in larger time units or intervals, or if time is truly discrete, then discrete survival or failure time models are more consistent with the data. Such situations arise in medical work when patients are followed up at fixed intervals like months, in certain biostatistical problems, for example human fertility studies and time to pregnancy (Scheike and Jensen, 1997), or in labor market studies where duration of unemployment is measured in weeks, at best, or in months. We review parametric models and outline recent nonparametric approaches. More details, in particular for parametric models, are given e.g. in Fahrmeir and Tutz (1994), ch. 9, and further references cited there.