ABSTRACT
In many applications in the health and social sciences the response of interest is duration to a certain event, such as age at first maternity, survival time after diagnosis, or times spent in different jobs or places of residence. In clinical applications the interest is typically in representing and comparing the distribution of times to an event among different patient groups (e.g., treatment vs. control groups), whereas in social science applications the interest may focus on the impacts of demographic or socioeconomic attributes on human behaviors. Typically durations or event times are not observed for all subjects, either because not all subjects are followed up, or because for some events the event may never occur (e.g., age at first marriage). So some times are missing or censored, and the missingness mechanism is generally assumed to be at random. The most common form is right-censoring, when the event has not occurred by the end of the observation period; the unknown failure time exceeds the subject’s survival time c when observation ceased. A failure time is left censored at c if its unobserved actual value is less than c (e.g., a population census may record limiting illness status by current age, but not the age when it commenced). A failure time is interval censored if it is known only that it lies in the interval (c1, c2).
