Discrete failure time models

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.